You can put this solution on YOUR website!
your equation is:

y = -log(3.5,(-x))

graph of this equation looks like this:



you can use the conversion formula to change the base of the logarithm so you can solve it using your calculator.

the conversion formula is:

log(a,(x)) = log(b,x) / log(b,a)

what this formula says is:

log of x to the base of a equals the log of x to the base of b divided by the log of a to the base of b.

in your problem, this conversion formula becomes:

-log(3.5,(-x)) = - (log(10,(-x)) / log(10,3.5)

you can now use your calculator to solve for selected points of that log.

you get:

y = - (log(10,(-x)) / log(10,3.5)

substitute the following values for x:

y = - (log(10,-(-4)) / log(10,3.5) = -1.106589511

y = - (log(10,-(-3)) / log(10,3.5) = -.87695144

y = - (log(10,-(-2)) / log(10,3.5) = -.553294756

y = - (log(10,-(-1)) / log(10,3.5) = -0

y = - (log(10,-(-.1)) / log(10,3.5) = 1.838005394

y = - (log(10,-(-.0000001)) / log(10,3.5) = 12.86603776

the graph appears to be asymptotic at x = 0

the closer you get to 0, the bigger y gets.

the value of y is undefined at x = 0

all you need to do is plot the points on a piece of graph paper and draw the resulting curve.

You can put this solution on YOUR website!
let x = number of singers in each row.
let y = number of rows.

at BC we have x*y = 330

at Coquitlam we have (x-4)*(y+1) = 319

we need to solve both these equations simultaneously to get our answer.

use the first equation to solve for one of the variable in terms of the other.

you get y = 330/x

substitute for y in the second equation to get:

(x-4) * (330/x + 1) = 319

simplify by performing indicated operations to get:

330 + x - (4*330)/x - 4 = 319

multiply both sides of the equation by x to get:

330*x + x^2 - (4*330) - 4*x = 319*x

subtract 319*x from both sides of the equation to get:

330*x + x^2 - (4*330) - 4*x - 319*x = 0

simplify by performing indicated operations to get:

330*x + x^2 - 1320 - 4*x - 319*x = 0

simplify by combine like terms to get:

x^2 + 7*x - 1320 = 0

factor to get:

(x+40) * (x-33) = 0

solve for x to get:

x = -40 and x = 33

since x can't be negative, x must equal 33.

x = 33 means there were 33 singers in each row at BC.

this means y = 10 which means there were 10 rows at BC.

at Coquitlam they had 4 less singers in each row and 1 more row.

This makes 29 singers and 11 rows at Coquitlam.

29 * 11 = 319 singers total at Coquitlam.

Everything checks out so your answer is:

there were 10 rows of singers at BC.

You can put this solution on YOUR website!
here's your diagram.

http://theo.x10hosting.com/problems/249561.html

you draw a line parallel to the ground from the window to the opposite building.

that would be line AB

you draw a line from the windoiw to the base of the building next door.

that would be line AC.

you draw a line from the window to the top of the building next door.

that would be line AE.

your angle of depression is angle BAC.

your angle of elevation is angle EAB.

line AD is 30 feet.

so is line BC because it's on the opposite end of the rectangle that you drew which is rectangle ABCD.

you need to find the length of line AB.

use tan(31) = BC/AB go get line AB.

use tan(40) = EB/AB to get line EB.

height of building is line EC which is the sum of lines EB and BC.

any further questions, send me an email.

i'll be checking in the morning.

You can put this solution on YOUR website!
I would have to say selection (C) which is equal to 8.

Here's why:

you have 2 equations in 3 unknowns which means the best you can do is find a relationship between 2 of the variables.

Let:

x = number of men
y = number of women
z = number of children

your equations are:

                      x +  y + z   = 100
                     3x + 2y + z/2 = 100

you can eliminate one of the variable by multiplying the second equation by 2 to get:

                      x +  y + z = 100
         minus:      6x + 4y + z = 200
         equals:    -5x - 3y     = -100

you can solve for y in the resulting equation as follows:

your equation to solve is:
-5x - 3y = -100
add 5x to both sides to get:
-3y = -100 + 5x
multiply both sides by -1 to get:
3y = 100 - 5x
divide both sides by 3 to get:
y = (100-5x)/3

you equation you need to work with is:

y = (100-5x)/3

look at all your solutions and solve for the given value of x.

when x = 16, y = 6.67
when x = 12, y = 13.33
when x = 8, y = 20
when x = 4, y = 26.67
when x = 0, y = 33.33

in all of these, the only integer value is 20, so the only possible solution would be x = 8 and y = 20

that means that there could be 8 men and 20 women which means that there must be 72 children because x + y + z = 100

if so, then the distribution is among 8 men, 20 women, and 72 children.

each man gets 3 bushels so the men get 24 bushels
each woman gets 2 bushels so the women get 40 bushels
each child gets 1/2 bushel so the children get 36 bushels.

24 + 40 + 36 = 100 bushels so that checks out ok.

your answer is selection (C) which is 8 men as a possible solution.

there could be other solutions as well since you did not solve for the number of women.

you only solved for the number of women in relataion to the number of men.

example:

if x = 2, then (100-5x)/3 = 90/3 = 30 women.

you could have 2 men, 30 women, and 68 children
3*2 = 6
2 * 30 = 60
68 * .5 = 34

60 + 34 + 6 = 100

number of men equals 2 is a possibility as well.

You can put this solution on YOUR website!
if it has sides of length 30 and 40 then the area is fixed at 30*40 = 1200.

area = L*W = 30*40 = 1200

You can put this solution on YOUR website!
ratio of length to width is 3/5
p = 78
2*L + 2*W = 78

L/W = 3/5
cross multiply to get 3W = 5L
divide both sides by 3 to get:
W = 5L/3

substitute for W in perimeter equation to get:
2*L + 2*(5*L/3) = 78
simplify by removing parentheses to get:
2*L + 10*L/3 = 78
multiply both sides of equation by 3 to get:
3*2*L + 10*L = 78*3
simplify to get:
6*L + 10*L = 234
combine like terms to get:
16*L = 234
divide both sides by 16 to get:
L = 234/16 = 14.625
W = 5*L/3 = 5*14.625/3 = 24.375

you have:
L = 14.625
W = 24.375

L/W = 3/5 = .6

L/W = 14.625/24.375 = 3/5 after you divide both numerator and denominator by 4.875

ratio is good.

perimeter is equal to:

2*L + 2*W which becomes:

2*14.625 + 2*24.375 = 29.25 + 48.75 = 78

perimeter is good.

your answer is:

length = 14.625 yards
width = 24.375 yards

You can put this solution on YOUR website!
here's your triangle.

                                        A
                                        x
                                       x  x
                                      x    x
                                     x      x
                                    x        x
                                   x          x
                                  x            x
                                 x              x
                                x                x
                               x                  x
                            B xxxxxxxxxxxxxxxxxxxxxx C

it is labeled triangle ABC.
There is an angle at point A, point B, point C.
There are labeled angle A, angle B, angle C
They are also labeled angle BAC, angle ABC, angle BCA
The vertex of the angle is the point where the two sides of the angle meet.
These would be the sides that include the angle.
There are 3 sides to the triangle. They are sides AB, BC, and AC. The sides are labeled by their endpoints. The sides are also called line segments.
Two of the sides of this triangle are AB and BC.
The included angle between these sides would be at the intersection of the 2 sides which would be at the common point of the two sides which would be at point B. Angle B, otherwise labeled as ABC or CBA, is included between the sides of AB and BC.

You can put this solution on YOUR website!
x = number of beggars
y = money you have.

your formulas are:

y - 7x = 24 (equation 1)
y - 9x = -32 (equation 2)

subtract equation 1 from equation 2 to get:

2x = 56

solve for x to get:

x = 28

substitute in first equation to get:

y - 7*28 = 24

solve for y to get:

y = 7*28 + 24 = 220

you have $220 dollars and there are 28 beggars at your door.

220 - 7*28 = 24 (true)
220 = 9*28 = -32 (true)

You can put this solution on YOUR website!
x = amount of fertilizer 1
y = amount of fertilizer 2
z = amount of fertilizer 3

it helps to make a table for this.

your table would look like this:

amount of fertilizer in kilograms
fertilizer     total     potassium     nitrogen     phosphorus

1                x          .2x          .3x           .5x
2                y          .1y          .2y           .7y
3                z          ---          .3z           .7z 
4              200           24           50           126

the amounts of potassium, nitrogen, and phosphorous for fertilizer 4 are given to you by weight because you are told the proportions and you know what the total weight is.

potassium = .12 * 200 = 24
nitrogen = .25 * 200 = 50
phosphorus = .63 * 200 = 126

you wind up with 3 equations that need to be solved simultaneously.

note that these equations are from the vertical columns for potassium, nitrogen, and phosphorus in your original table above.

those equations are:

           .2x + .1y + .0z = 24  (equation 1)
           .3x + .2y + .3z = 50  (equation 2)
           .5x + .7y + .7z = 126 (equation 3)

once you solve these simultaneously, you will have the amounts of x,y,z that you need which are the amounts of fertilizer 1, fertilizer 2, fertilizer 3 that you need.

we will eliminate the decimals first so they won't bother us.

multiply all equations by 10 to get:

           2x + 1y + 0z = 240  (equation 1)
           3x + 2y + 3z = 500  (equation 2)
           5x + 7y + 7z = 1260 (equation 3)

first we will take equation 1 and 2 and eliminate the y variable.

we will do that by multiplying equation 1 by 2 and then subtract equation 2 from equation 1 to get equation 4.

           4x + 2y + 0z =  480  (equation 1 multiplied by 2)
 minus:    3x + 2y + 3z =  500  (equation 2)
 equals:   1x      - 3z =  -20  (equation 4)

next we will take equation 2 and 3 and eliminate the y variable.

we will do that by multiplying equation 2 by 7 and multiplying equation 3 by 2 and then subtracting equation 3 from equation 2.

           21x + 14y + 21z = 3500  (equation 2 multiplied by 7)
 minus:    10x + 14y + 14z = 2520  (equation 3 multiplied by 2)
 equals:   11x       +  7z = 980   (equation 5)

next we will take equation 4 and equation 5 and eliminate the x variable.

we will do that by multiplying equation 4 by 11 and then subtracting equation 5 from equation 4

                  11x - 33z =  -220   (equation 4 multiplied by 11)
      minus:      11x +  7z =   980   (equation 5)
      equals:         - 40z = -1200

we solve for z to get:

z = 30

we use this value of z and substitute in equation 5 to get:
11x + 7z = 980 becomes:
11x + 7*(30) = 980 which becomes:
11x + 210 = 980
subtract 210 from both sides to get:
11x = 980-210 = 770
divide both sides by 11 to get:
x = 70

next we use the values of z = 30 and x = 70 and go to equation 3 to get:
5x + 7y + 7z = 1260 becomes:
5*(70) + 7y + 7*30) = 1260 which becomes:
350 + 7y + 210 = 1260 which becomes
7y + 560 = 1260
subtract 560 from both sides to get:
7y = 1260 - 560 = 700
divide both sides by 7 to get:
y = 100

we have values for x,y,z.

they are:

x = 70
y = 100
z = 30

we need to test these values to see if they are good.

our original equations are:

           .2x + .1y + .0z = 24  (equation 1)
           .3x + .2y + .3z = 50  (equation 2)
           .5x + .7y + .7z = 126 (equation 3)

first we check to see if x + y + z = 200.

it does.

that's good because the total of fertilizer 1, 2, 3 should equal 200 and it does.

next we substitute in all 3 equations to get:

           .2x + .1y + .0z = 24  (equation 1)
           .3x + .2y + .3z = 50  (equation 2)
           .5x + .7y + .7z = 126 (equation 3)

becomes:

           .2*70 + .1*100 + .0*30 = 24  (equation 1)
           .3*70 + .2*100 + .3*30 = 50  (equation 2)
           .5*70 + .7*100 + .7*30 = 126 (equation 3)

we simplify to get:

           14 +  10 +  0 =  24  (equation 1)
           21 +  20 +  9 =  50  (equation 2)
           35 +  70 + 21 = 126  (equation 3)
           -------------------
  total:   70 + 100 + 30 = 200  (sum of equations 1,2,3)

Looks like we have the answer.

he needs:
70 pounds of fertilizer 1
100 pounds of fertilizer 2
30 pounds of fertilizer 3

he will get:

200 pounds of fertilizer 4 that contains:

24 pounds of potassium
50 pounds of nitrogen
126 pounds of phosphorus

You can put this solution on YOUR website!
Apparently there is no easy way to do this.

I found the answer here.

the answer was not complete but it started me on my way to finding out how it was done.

here's what I found.

you need to find a pattern.

if you follow the directions you will see that the pattern is every 8 exponents.

2^0 = 1 / 17 = remainder of 1
2^8 = 256 / 17 = remainder of 1
2^16 = 65536 / 17 = remainder of 1

the first 8 numbers in the sequence are:

2^0 = 1 / 17 = 0 with a remainder of 1
2^1 = 2 / 17 = 0 with a remainder of 2
2^2 = 4 / 17 = 0 with a remainder of 4
2^3 = 8 / 17 = 0 with a remainder of 8
2^4 = 16 / 17 = 0 with a remainder of 16
2^5 = 32 / 17 = 1 with a remainder of 15
2^6 = 64 / 17 = 3 with a remainder of 13
2^7 = 128 / 17 = 7 with a remainder of 9
2^8 = 256 / 17 = 15 with a remainder of 1 and the pattern starts all over again.

what happens if you are given 2^9 / 17 and are asked to find the remainder.

you can actually solve this, and your answer will be 2 because the pattern repeated all over again.

2^9 = 512 / 17 = 30 with a remainder of 2.

if the number was very large, like 2^2006, you can't do this.

If you know the repeating pattern, however, you can figure it out.

since the pattern repeats every 8 exponents, just divide 9 by 8 to get 1.something.

take the integer part and multiply it by 8 to get 8.

subtract 8 from 9 to get 1.

your 2^9 remainder is equivalent to the remainder of 2^1.

That remainder equals 2.

try it again with a larger number.

suppose your number is 2^20 / 17 and they want to know what the remainder is.

take the exponent of 20 and divide it by 8 to get 2.5

take the integer part of the answer and multiply it by 8 to get 2 * 8 = 16

subtract 16 from 20 to get 4.

your remainder will be equivalent to the remainder of 2^4 which would equal 16

again, this is small enough that we can prove it, so:

2^20 = 1048576 / 17 = 61680.94118 and the remainder is .9411765 * 17 = 16

there will be some rounding errors, but 16 is the remainder and the equivalent of 2^4 remainder is also 16 so we're good.

applied to your problem, you would do the following:

2^2006 / 17 = remainder of ?????

take 2006 and divide it by 8 to get 250.75

multiply 8 by 250 to get 2000.

subtract 2000 from 2006 to get 6

your remainder will be equivalent to the remainder of 2^6.

that would equal 13

I calculated up to 2^23 just to ensure myself that the pattern repeated every 8 exponents.

It does, but you have to start from 2^0 in order to see that for the first 8 exponents.

2^7 - 2^0 = 8
2^7 equals a remainder of 9
2^(7+8) = 2^15 equals a remainder of 9
2^(15+8) = 2^23 equals a remainder of 9

Once the number of exponents in the repeating pattern was derived, the rest was how to apply that number to the exponents which is the procedure I just gave you.

You can put this solution on YOUR website!
let t = time
let s = speed

s = k/t

k is the constant of variation.

let t = 6 seconds
let s = 45 miles per hour.

use these values to find k.

equation of s = k/t becomes:

6 seconds = k / 45 miles per hour

without changing the units used, the constant of variation here would be:

k = 6*45 = 270

If it takes 5 seconds, then the equation becomes:

5 = 270 / x and you get

x = 270/5 = 54 miles per hour.

with changing the units used, the equation of:

6 = k/45mph becomes:

6 = k/.0125 miles per second.

now the units are consistent with each other.

solve for k to get:

k = .0125*6 = .075

with 5 seconds, the equation now becomes:

5 = .075 / x

solve for x to get:

x = .075/5 = .015 miles per second.

convert to miles per hour to get 54 miles per hour.

you get the same answer whether you converted the units or not.

the constant of proportionality took care of the difference in the units used.

if you divide the constant of proportionality by 3600 which is what we did to convert the miles per hour to miles per second, then the constant of proportionality of 270 becomes .075.

mathematically the two answers are equivalent to each other.

you did not have to convert the units to make them consistent in this case.

however, in a lot of other cases, you will need to, so converting to similar units for all variables in the equation is always a good idea.

You can put this solution on YOUR website!
the string is the hypotenuse of the right triangle.
the point which it is directly overhead forms the adjacent side of the angle of the triangle that you need.

you need to find the angle first and then you can find the height.

cosine (angle) = adjacent divided by hypotenuse.

let the angle be called A.

adjacent side is 60 feet (length on the ground from the point of the holding of the kite to the point just underneath the kite.

hypotenuse side is 100 feet (length of the string holding the kite).

cosine (A) = 60/100 = .6

look up in the cosine tables to find that arccosine(.6) = 53.13010235 deegrees.

arccosine (x) means the angle whose cosine is x.

In this case we solved for arcosine (.6) to get our answer.

now that we know what the angle is, we can solve for the opposite side of the angle to get the height.

we can use either of 2 equations.

sine (53.13010235) = opposite / hypotenuse = x/100

tangent (53.13010235) = opposite / adjacent = x/60

both equations will lead to the same answer.

solving for x, first equation becomes

x = 100 * sine (53.13010235) = 80 feet.

x = 60 * tangent (53.13010235) = 80 feet.

your triangle looks like this:

                       (C)  x
                            x  x
                            x     x    100
                            x        x
                            x           x
                            x              x  
                       (B)  x  x  x  x  x  x  x  (A)
                                     60

The triangle is ABC
The right angle is CBA
The person holding the string is at A.
Point B is directly beneath the kite.
Point C is the kite.
The line AC is the string
The line BA is the distance from the person holding the string to the point directly underneath the kite.
The angle you need to find is angle A, otherwise known as angle CAB.

You can put this solution on YOUR website!
f(x) = sqrt(x+2)

g(x) = (2x+3)

you want:

f(g(2))

first find g(2)

in the equation of g(x) = (2x+3), you replace x with 2 to get:

g(2) = (2*2 + 3) = 4+3 = 7

in the equation of f(x) = sqrt(x+2), you replace x with g(x) to get:

f(g(x) = sqrt(g(x)+2)

since g(x) = 7, you replace g(x) with 7 to get:

f(7) = sqrt(7+2) = sqrt(9) = 3

the equation is the rules by which you relate the independent variable to the dependent variable.

the independent variable is the variable that does not depend on any rules to establish a value for it.

the dependent variable is the variable that depends on the rules of the equation to establish a value for it.

when x is a certain value, y has to be a certain value.

x is also called the argument of the function.

the argument of the function is the variable that the rules of the equation are working on.

y = f(x) = x^2 means the independent variable in the equation is x.

y = f(a) = a^2 means the independent variable in the equation is a.

the rules are the same.

the only difference is the variable that the equation is working with.

that is why when you say f(x) = x^2, f(x) becomes the dependent variable and x is the independent variable.

when you say f(2) using the same equation, then the rules stay the same but the independent variable becomes 2 instead of x.

f(2) = 2^2 = 4.

when you say f(g(x)), then the independent variable in the equation becomes g(x).

g(x), however, was the dependent variable in another equation, so it's value had to be calculated before you could put it into f(g(x)).

that's exactly what we did above.

we solved for g(2) to get 7.

then we solved for f(g(x)) to get f(7) = 3.

you are placing g(x) into the argument of the equation f(x) = sqrt(x+2) which means you are replacing the existing argument of x with the argument of g(x).

You can put this solution on YOUR website!
x = 4 is a vertical line.

the slope is undefined because there is never a change in the value of x for a change in the value of y.

the slope of the equation is (y2-y1) / (x2-x1)

x2 and x1 are the same so the denominator of the equation is 0 which leads to an undefined slope because division by 0 causes the result to be infinity which is an undefined number.

the standard form of the equation for a straight line is:

ax + by = c, where:

a = the coefficient of the x term
b = the coefficient of the y term
c = the constant.

you can convert the standard form of the equation to the slope intercept form by doing the following:

ax + by = c
subtract ax from both sides to get:
by = -ax + c
divide both sides by b to get:
y = (-a/b)*x + (c/b)

that's the slope intercept form of the equation of a straight line.
(-a/b) = the slope of the line, called m.
(c/b) = the y-intercept of the line, called b

the slope intercept form of the equation is called y = m*x + b, where:

m is the slope
b is the y-intercept.

In the standard form of the equation or:

ax + by = c,

if b = 0, then the equation becomes:

ax = c, because the y terms drops out (anything multiplied by 0 equals 0).

Because the y term drops out of the equation, the value of y is not constrained to be anything special in relationship to x.

It is not limited by the rules of the equation.

this means that y can be anything, but x has to be what the equation says it has to be.

when you graph the equation, you are plotting the value of x in relation to the value of y.

x = 4 means that the value of x has to be equal to 4.

y not in the equation means that y is free to be any value it wants.

this is what creates the vertical line.

when you plot the equation of a vertical line, you can see that the value of x has to be 4.

you can also see that, along that line, the value of y can be any value.

that is why your solution showed you (4,a), (4,b), (4,c), etc.

there was no equation to force the selection of y given a specific value of x.

for example, if the equation was y = 4x, then when x = 1, y has to be 4*1 and could be nothing else.

In the example x = 4, there is no such restriction for the value of y, meaning the value of y could be anything, but the value of x had to be 4.

when you plot the line you will see that it is a vertical line on the graph.

the requirements of the equation are that x = 4.

there are no requirements on the value of y, so pick any value of y when x = 4 and create your vertical line.

if your equation was y = 5, then you would have a horizontal line.

this might be easier for you to see.

In that case, x can be any value and y always has to be 5, regardless of the value of x.

x = 4 is the same concept. y can be any value and x always has to be 4, regardless of the value of y.

the only difference is, that in the case of y = 5, the slope is equal to 0, while in the case of x = 4, the slope is undefined (division by 0 caused undefined).

look at the standard form of the equation again:

ax + by = c.

when b = 0, y drops out of the equation, and when a = 0, x dropes out of the equation.

you get:

ax = c when y drops out.

you get:

by = c when x drops out.

since the slope is (-a/b), when b = 0, the slope is undefined because you are dividing by 0, and when a = 0, the slope is 0 because you are dividing into 0.

best answer I can give. i don't know how to explain it any other way.

the answer is:

since you are plotting a graph of y in relationship to x, since y is not in the equation, y can be any value as long as x = 4 because the only constraint in the equation is that x = 4. y, not being in the equation, has no constraints. you are free to pick any value of y as long as x = 4.

You can put this solution on YOUR website!
m looks like it is months.

usually you are given the annual interest rate and you have to divide that by the number of months to get the monthly interest rate.

this assumed the compounding of the interest rate is monthly.

It could be:

semi-annually (2)
quarterly (4)
monthly (12)

yours is monthly.

if the compounding is monthly, then the number of time periods have to be in months.

if they are specified in years, then you have to multiply them by 12 to get months.


your formula is:

If $1,000 is invested in an account paying 10% compounded monthly, how much will be in the account at the end of 10years? compute the answer to the nearist cent.
Compound interest formula:
A=P(1+(r/m))^(mt)
P=1,000 ***** money invested in the account today.
r=0.1 ***** annual interest rate of 10% per year.
m=12 ***** compounding period is in months and there are 12 months to the year.
t=10 ***** number of years
A=1,000(1+(0.10/12)^((12)(10))
A=$2,707.04

you take the annual interest rate and divide it by 12 to get the monthly interest rate per time period equal to .000833333333

you take the number of years and multiply it by the number of months in a year to get the number of time periods equal to 120

your formula becomes:

A = 1,000 * (1.00833333^120)

Your answer of 2707... is correct.

A more general formula would be:

F = P * (1+(r/c)^(n*c)) where:

F = future value
P = present amount
r = annual interest rate
c = number of compounding periods per year
n = number of years

this works with all compounding periods, not just months.

You can put this solution on YOUR website!
cosecant is equal to 1 / sine.

find the sine and then divide that into 1 and you get your answer.

sine (22.5) = .382683432

1/.382683432 = 2.61312593

you can use this online trigonometry calculator to find the answer directly.

You can change the number of significant digits by scrolling down further and entering the number of digits accuracy you want. Don't press the enter key. It resets the calculator. Just enter the number of digits accuracy you want and then scroll back up and continue without pressing the enter key. If you entered your angle and it's still in the input box, then press csc. Otherwiee re-enter the angle and press csc. That's the only bug with this calculator. Otherwise it works fine.

You can put this solution on YOUR website!
average score on first 6 mathematics tests is 84.

total score on first 6 tests = 6 * 84 = 504

average score on first 7 mathematics tests is 85.

total score on first 7 tests = 7 * 85 = 595

score on your 7th test is 595 - 504 = 91

(504 + 91) / 7 = 85 average on 7 tests.

You can put this solution on YOUR website!
Formula is RT = W

From this formula, you can derive:

T = W/R
and
R = W/T

printing press can print 300,000 cards in 12 hours.

T = 12
W = 300,000
R = W/T = 300,000/12 = 25,000 cards per hour.

older press requires 18 hours to print 300,000 cards.

T = 18
W = 300,000
R = W/T = 16,666.66666667 cards per hour.

working together, their rates will combine.

you get:

T = x
W = 300,000
R = 25,000 + 16,666.66666667 = 41,666.66666667 cards per hour.

When solving for T, formula becomes:

T = W/R

This equation becomes:

T = 300,000/41,666.66666667 = 7.2 hours.

In 7.2 hours, the printing press has completed 25,000 * 7.2 = 180,000 cards.

In 7.2 hours, the old press has completed 16,666.66666667 * 7.2 = 120,000 cards.

total cards produced is 180,000 + 120,000 = 300,000

You can put this solution on YOUR website!
V = k*T/P where:

V = volume
T = temperature
P = pressure
k = constant of variation.

When:

V = 231 cm^3
T = 42 degrees
P = 20kg/cm^2,

The formula becomes:

231 = k*42/20

Solve for k to get:

k = 110

The constant of variation is equal to 110.

When T = 30 and P = 15 and k = 110, the formula becomes:

V = 30*110/15 = 220 cm^3

Here's a reference that explains how the variation formulas work.

You can put this solution on YOUR website!
(1.10)^4 = 1.4641

His salary has gone up 46.41% which is more than 45% so your answer is selection (D).

Here's what happened.

Assume his salary was $30,000 a year.

At the end of the first year it became $30,000 * 1.10 = $33,000

At the end of the second year it became $33,000 * 1.10 = $36,300

At the end of the third year it became $36,300 * 1.10 = $39,930

At the end of the fourth year it became $39,930 * 1.10 = $43,923

$43,923 minus $30,000 is an increase of $13,923

$13,923 / $30,000 is an increase proportion of .4641 * 100% equals an increase percent of 46.41%.

This is the same as $30,000 * (1.10)^4 = $30,000 * 1.4641 = $43,923.

You can put this solution on YOUR website!
future value is 3
present amount is 1
annual interest rate is 6%

6% / 2 = 3% every half a year.

interest rate equals interest rate percent divided by 100% = .03 every half a year.

the formula you need is:

3 = 1 * (1.03)^x

you need to solve for x.

formula becomes:

3 = (1.03)^x

take the log of both sides of the equation to get:

log(3) = log((1.03)^2)

by the rules of logarithms, this equation becomes:

log(3) = x*log(1.03)

divide both sides of this equation by log(1.03) to get:

x = log(3)/log(1.03)

solve for x to get:

x = 37.16700967

this means that it would take 37.16700967 half years to triple your money.

divide this by 2 to get:

18.58350483 years.

We required half years because our interest rate was every half a year (semi-annually).

these would be called semi-annual time periods.

there are 37.16700967 semi-annual time periods which equate to 18.58350483 years.

You can put this solution on YOUR website!
what you would be lookikng for is 1/4 minus 1/6 divided by 2.

1/6 is equivalent to 2/12

1/4 is equivalent to 3/12

3/12 minus 2/12 equals 1/12

1/12 divided by 2 is equal to 1/24

if you add 1/12 to 1/6 then you will find your number.

1/6 is the same as 4/24.

4/24 plus 1/24 is equal to 5/24.

your anser is selection (c).

since you added 1/24 to get halfway, then you add 1/24 again and you will be all the way.

5/24 + 1/24 = 6/24 which is the same as 1/4.

your answer is confirmed to be halfway between 1/6 and 1/4.

You can put this solution on YOUR website!
bert joined the christmas club on september 8th.
65 dollars is deducted from his checking account at the end of every month and deposited into the christmas club account.
the christmas club account earns 6% interest a year.
the account comes to term on december 1.

here's how it works.

the annual interest rate is 6%.
the monthly rate is 6% / 12% = .5% / 100% = .005

the account starts at 0.
at the end of september the account has 65 dollars in it.
at the end of october the account has 65 * 1.005 + 65 = 130.325 dollars in it.
at the end of november the account has 130.325 * 1.005 + 65 = 195.976625 dollars in it.
on december 1st, the account has $195.98 in it.

your questions are:

(a) Find the future value of the account, using an annuity formula. (Round your answer to the nearest cent.)

See the bottom for how to solve this using the annuity formula.

(b) Find the future value of the account, using the compound interest formula. (Round your answer to the nearest cent.)

This was done up top when I provided you with the month by month details.

(c) Find Bert's total contribution to the account.

Bert's total contribution was 3 * 65 = $195.00

(d) Find the total interest. (Round your answer to the nearest cent.)

The total interest was $.98

the assumption is that the interest is an annual interest rate.

to convert that to monthly interest rate you have to divide it by 12.

SOLVING USING AN ANNUITY FORMULA

The formula you want is future value of a payment.

payments and annuities are terms that are sometimes used interchangeably.

future value of a payment formula is the same as future value of an annuity formula.

sometimes they call it future worth rather than future value.

that formula is:

FUTURE VALUE OF A PAYMENT



FV = future value
PMT = payment per time period
i = interest rate per time period
n = number of time periods

in your problem

FV = x
PMT = 65
i = .06 / 12 = .005
n = 3 (you make payments in september, october, and november)

this formula assumed end of time period payments.

your formula becomes



your answer becomes:

x = 195.976625

this round out to x = $195.98

I confirmed using a financial calculator.

the principal is number of payments times the payment = 3 * 65 = 195.

the interest is the future value of the payments minus the payments = 195.98 minus 195 = .98

You can put this solution on YOUR website!
annuity payment is equal to x.
future value is equal to 250000
annual interest = 11%

the assumption is that monthly compound interest is being used.

this means that you have to convert your annual interest rate to monthly interest rate.

it also means you have to convert your number of time periods from years to months.

the formula you need would be:



PMT = Payment per Time Period
FV = Future Value
i = Interest Rate per Time Period
n = Number of Time Periods

In your problem:

PMT = x
FV = 250000
i = .11 / 12 = .0091666666667
n = 39 * 12 = 468

you convert your annual interest rate to monthly interest rate by dividing it by 12.

you convert your number of time periods from years to months by multiplying it by 12.

your formula becomes:



your answer becomes:

x = 32.48088508

I confirmed using a financial calculator.

the answer is valid except that the financial calculator returned an answer of x = 32.1858482

i'm attributing the difference in the answers to rounding.


**************************** NOTE ****************************************

The difference was not due to rounding.

The difference was due to the fact that my financial calculator was set to calculate based on payments at the beginning of the month rather than at the end of the month.

I changed the option and recalculated and got an answer of 32.48088514

This is much closer to the answer of 32.48088508 I got using a scientific calculator based on the formula.

The 32.48088508 number is confirmed fully now.

There's a much smaller difference that is definitely most likely due to rounding.

*************************************end of note****************************

i would go with what your calculator says after you do the operations as indicated above.

your formula was:



first problem is your formula should have been:



second problem is you should have used 468 instead of 39 to get:

You can put this solution on YOUR website!
your equation is:



the conjugate of the denominator would be

multiply the expression by to get:



perform the indicated operations to get:



you got the denominator ok.

you got pieces of the numerator ok but something went wrong somewhere.

the numerator became:



multiplying these terms together you would get:






combining like terms you would get

your answer is .

You can put this solution on YOUR website!
complement of an angle is 90 degrees minus the angle.

let a be the angle.

a = (90-a)/2 - 18

this means that the angle equals half its complement minus 18 degrees.

this means the same as the angle equals 18 degrees less than half its complement.

solve for a.

equation is:

a = (90-a)/2 - 18

simplify by removing parentheses to get:

a = 90/2 - a/2 - 18

simplify further to get:

a = 45 - a/2 - 18

combine like terms to get:

a = 27 - a/2

add a/2 to both sides to get:

a + a/2 = 27

multiply both sides of the equation by 2 to get:

2a + a = 54

combine like terms to get

3a = 54

divide both sides of the equation by 3 to get:

a = 18

your answer should be that the angle is equal to 18 degrees.

if the angle is 18 degrees, then its complement is equal to 90 - 18 = 72 degrees.

half its complement is equal to half of 72 is equal to 36 degrees

18 degrees less than that is equal to 36 - 18 is equal to 18 degrees.

Your answer is that the measure of the angle is 18 degrees.

You can put this solution on YOUR website!
m = .3*q
q = .2*p
n = .5*p

m/n = ?????

replace n with .5*p to get:

m/(.5*p)

since q = .2*p, this means that p = (q/.2)

replace p with (q/.2) to get:

m/(.5*p) = m/(.5*(q/.2)) = m/(2.5*q)

Since m = .3*q, this means that q = (m/.3)

replace q with (m/.3) to get:

m/(2.5*q) = m/(2.5*(m/.3)) = m/(8.33333333*m) = 1/8.33333333 = .12.

Your answer should be .12.

That would be selection (b) since .12 = 3/25.

You can put this solution on YOUR website!
(x-2)^2=2(y+2)?

Your solution is at this link.

http://home.windstream.net/okrebs/page64.html

Your equation needs to be put in the right form.

The right form is:

(y-k) = +/- (1/4p) * (x - h)^2

Where:

(h,k) is the vertex of the parabola.
p is the distance from the focus to the vertex and from the vertex to the directrix.

your equation is:

(x-2)^2=2(y+2)

flip it around so you get:

2 * (y+2) = (x-2)^2

divide both sides by 2 so you get:

(y+2) = (1/2)*(x-2)^2

looks like your vertex is at (h,k) = (2,-2)

You have 1/(4*p) = 1/2

multiply both sides by 4*p and you get:

1 = (1/2) * 4p which becomes:

1 = 2*p which becomes

p = (1/2) after you divide both sides of the equation by 2.

Solve for y to be able to graph this equation.

(y+2) = (1/2)*(x-2)^2 becomes:

y = (1/2)*(x-2)^2 - 2 after you subtract 2 from both sides of the equation.

Graph of this equation looks like:



Your vertex is at the point (x,y) = (2,-2)

Your focus is at at the point (x,y) = (2,-3/2)

Your directrix is at the line (x,y) = (x,-5/2) which translates to the equation of the line as y = -5/2.

If this is the true focus and directrix, then the distance between the focus and any point on the graph of the equation of the parabola should be the same as the distance between any point on the graph of the equation of the parabola and a perpendicular line dropped from that point to a point on the line of the directrix.

you can see this is true at the point (2,-2) on the graph because the distance from (2,-2) to (2,-3/2) is the same as the distance from (2,-2) to (2,-5/2).

Another easy point to check is where a horizontal line from the focus intersects with the graph.

Based on your equation of ...

y = (1/2)*(x-2)^2 - 2, when y = -3/2, then x = 2 +/- sqrt(1).

This comes out to be x = 1 and x = 3.

Since the focus is at x = 2, this means that x is 1 unit away from the focus in either direction when y = -3/2.

Since the directrix is at y = -5/2, and the points on the graph are at (1,-3/2) and (3,-3/2), then each point is 1 unit away from the directrix because ((-5/2) - (-3/2)) = 1.

Your solution is:

Vertex is (x,y) = (h,k) = (2,-2)

p = 1/2 = distance from focus to vertex and distance from vertex to directrix when x = 2.

Focus is at (x,y) = (2,(-3/2))

Directrix is at (x,y) = (x,(-5/2))

You can put this solution on YOUR website!
a = 3
18 ÷ 2a

Technically speaking you would be correct if you interpreted it as (18/2) * a because the order of arithmetic says multiplication and division are done together from left to right if parentheses don't change the natural order.

The natural order without parentheses is:

exponents and roots first.
then multiplication and division.
then addition and subtraction.

within each level, you process left to right.

this means if you have a multiplication followed by a division, you do the multiplication first, and if you have a division followed by a multiplication, you do the division first.

Select the following link to see one of the tutorials on the web concerning this.

http://www.math.com/school/subject2/lessons/S2U1L2GL.html

I tend to think, the way it was written with the other division sign, and the way the 2 and the a were stuck together, that they meant 18 / (2*a), but that would not be technically correct if you follow the rules exactly.

It's a matter of interpretation.

You would not be wrong if you assumed (18/2) * a based on a strict interpretation of the rules.

If the book shows you the answer, you can determine from that.

If not, you can answer with an (if it is this way, then the answer is ...) and (if it is that way, then the answer is ...)

My gut says 18 / (2*a) but the strict interpretation of the rules says (18/2) * a.

I can see why you're confused.

You can put this solution on YOUR website!
x/3=x+10/6

is this (x/3) = (x+10)/6

or is this (x/3) = x + (10/6)

If I follow the rules of algebra, without parentheses, it would be the second form.

assuming it is the first form, then your equation is:

(x/3) = (x+10)/6

multiply both sides of this equation by 6 to get:

6 * (x/3) = 6 * (x+10) / 6 which becomes:

2 * x = x + 10

subtract x from both sides of this equation to get x = 10

substitute in original equation to get:

10/3 = 20/6 which is true so the answer of x = 10 is good.

assuming it is the second form, then your equation is:

(x/3) = x + (10/6)

multiply both sides of this equation by 6 to get:

6 * (x/3) = 6 * (x + 10/6) which becomes:

2 * x = 6 * x + 10

subtract 6 * x from both sides of this equation to get:

2 * x - (6 * x) = 10

combine like terms to get:

-4 * x = 10

divide both sides by (-4) to get:

x = -10/4

substitute in original equation to get:

((-10/4)/3)) = (-10/4) + (10/6)

multiply both sides of this equation by 6 to get:

6 * ((-10/4)/3) = 6 * ((-10/4) + (10/6))

simplify to get:

(-20/4) = (-60/4) + (60/6)

simplify further to get:

-5 = -15 + 10

combine like terms to get:

-5 = -5 confirming that the answer of x = -10/4 is good.

You can put this solution on YOUR website!
area of a triangle equals 1/2 * b * h

from your triangle, I don't think we can find the base very easily.

fortunately there is a formula that allows you to find the area of a triangle when you only know the sides.

It's called Heron's formula.

that formula is:

Area of a Triangle = sqrt((s*(s-a)*(s-b)*(s-c)),

where s=(a+b+c)/2 which is the same as p/2 where p equals the perimeter of the triangle.

assuming that c is the base of the triangle, Heron's formula allows us to find the height of the triangle as well.

That formula would be:

h = (2 * (SQRT(s(s-a)(s-b)(s-c))) / 2

I believe this comes from the fact that A = 1/2 * b * h, so if we solve for h, we get h = 2*A/b

In your triangle:

s = (5+6+7)/2 = 18/2 = 9

In your triangle:

A = sqrt(9 * (9-5) * (9-6) * (9-7)) which equals:

sqrt (9 * 4 * 3 * 2) which equals:

sqrt (216) which equals:

14.69693846

Since A = 14.69693846, then h = 2/c * 14.69693846 = 2/7 * 14.69693846 = 4.199125273

If A = 1/2 * b * h, then A = 1/2 * 7 * 4.199125273 = 14.69693846 which is back where we started from.

You can check Heron's formula for yourself by selecting the following link.

http://mste.illinois.edu/dildine/heron/triarea.html