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Angle B is 5 times its complement, Angle A. Find the measure if the 2 angles
Let B = measure of angle B
then
90-B = measure of angle A (complement of B)
.
From:"Angle B is 5 times its complement, Angle A" we get our equation:
B = 5(90-B)
B = 450-5B
6B = 450
B = 75 degrees
.
Measure of A:
90-B = 90-75 = 15 degrees

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How do you figure out the percentage off a price, for example I wanna know how much would something cost if it was $65.99 and it is 45% off?
"Sale price" = "Original price" - "discount"
"Sale price" = 65.99 - (.45 * 65.99)
"Sale price" = 65.99(1 - .45)
"Sale price" = 65.99(.55)
"Sale price" = $36.29

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ln(x)+ln(x-8)=5
ln((x)(x-8)) = 5
(x)(x-8) = e^5
x^2-8 = e^5
x^2-8x = e^5
x^2-8x-e^5 = 0
Solving using the "quadratic formula" yields:
x = {16.82, -8.82}
Since you can't take the ln of a negative number, the -8.82 is an extraneous solution. Throw it out leaving:
x = 16.82
.
Details of quadratic follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=657.652636410308 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 16.8223694808166, -8.8223694808166. Here's your graph:

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y=-2(x-3)^2+8
a)State the coordinates of the vertex
You have to remember the "vertex form" of a quadratic:
y = a(x-h)^2 + k
where (h,k) is the vertex
since your equation was:
y=-2(x-3)^2+8
we immediately can see that the vertex is at:
(h,k) = (3,8)
b)State whether is has a max or min value and what that is?
We can tell by the "coefficient" associated with the x^2 term:
y=-2(x-3)^2+8
expanding the above:
y=-2(x^2-6x+9)+8
y=-2x^2+12x-18+8
y=-2x^2+12x-10
Since it will be "negative" -- we conclude that it will be a parabola that opens downwards. Thus the vertex will be the MAX.
Note: do part c first, then come back to this
c)State the equation of the axis of symmetry
axis of symmetry is at:
x = -b/(2a)
x = -12/(2(-2))
x = -12/(-4)
x = 3 (axis of symmetry)
d)State the y-intercept.
set x to zero:
y=-2x^2+12x-10
y=-2(0)^2+12(0)-10
y=0+0-10
y = -10
y-intercept is at (0, -10)

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The value of a coin is 6/5 the value of another coin. Together the two coins have a value of 44 dollars. What is the value of each coin?
Let x = value of one coin
then
(6/5)x = value of other coin
.
x + (6/5)x = 44
multiplying both sides by 5:
5x + 6x = 220
11x = 220
x = $20
.
Second coin:
(6/5)x = (6/5)20 = (6)4 = $24

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Lisa and Kay were asked by their mother to clean their room. Lisa can clean her room in 8 hours, and Kay in 12 hours. How long will it take if they both clean their room together?
Let x = time (hours) for both working together
then
x(1/8 + 1/12) = 1
multiplying both sides by 24:
x(3 + 2) = 24
x(5) = 24
x = 24/5
x = 4.8 hours
or
x = 4 hours and 48 minutes

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If 7 is added to a number the result is 30 times the reciprocal of the number. What is the number?
Let x = the number
then
1/x = the reciprocal
.
From:"7 is added to a number the result is 30 times the reciprocal of the number" we get our equation:
7 + x = 30 * 1/x
7 + x = 30/x
multiplying both sides by x:
7x + x^2 = 30
x^2+7x = 30
x^2+7x-30 = 0
(x+10)(x-3) = 0
x = {-10,3}
The "number" can be either solution -- but, I would pick 3.

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If the length of each side of a square is decreased by 4in., the perimeter of the new square is 10 in. more than half the perimeter of the original square. What are the dimension of the original square?
Let x = length of one side of original square
then
x-4 = length of side decreased by 4
.
perimeter of original square = 4x
perimeter of new square = 4(x-4) = 4x-16
.
From:
"perimeter of the new square is 10 in. more than half the perimeter of the original square" we get our equation:
4x-16 = (1/2)(4x) + 10
4x-16 = 2x + 10
2x-16 = 10
2x = 26
x = 13
.
What are the dimension of the original square?
13 inches by 13 inches

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F=9/5C+32
subtracting 32 from both sides:
F-32 = 9/5C
multiply both sides by 5:
5(F-32) = 9C
divide both sides by 9:
(5/9)(F-32) = C

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Find the function that is finally graphed after the following transformations are applied to the graph of y=square root of x in the order listed.
Starting function:

1. reflect about the x-axis

2.shift up 8 units

3. shift right 5 units

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A ball is thrown vertically upward with an initial speed of 35m/s. Its height h metres, after t seconds is given by the formula h=-4.9t^2+35t.
a)What is the maximum height reached by the ball?
because the coefficient associated with the t^2 term is negative, we KNOW it is a parabola that opens downwards. Thus, the VERTEX will be the MAX.
Time t when it reaches max:
t = -b/2a
t = -35/(2*(-4.9))
t = -35/(-9.8)
t = -35/(-9.8)
t = 3.57 seconds
.
Max height, plug t above into equation to find h:
h=-4.9t^2+35t
h=-4.9(3.57)^2+35(3.57)
h= 62.5 metres
.
b)How long is the ball in the air?
set h to zero and find t:
h=-4.9t^2+35t
0=-4.9t^2+35t
0=4.9t^2-35t
0=t(4.9t-35)
t = {0, 35/4.9)
t = {0, 7.14)
throw out the 0 (that's when it started) leaving:
t = 7.14 seconds
.
c)How many seconds is the ball highter than 30m?
set h to 30 and solve for t:
h=-4.9t^2+35t
30=-4.9t^2+35t
0=-4.9t^2+35t-30
0=4.9t^2-35t+30
apply "quadratic equation" to get:
x = {6.15, 1.0}
time higher than 30m:
6.15 - 1.0 = 5.15 seconds
.
Details of quadratic follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=637 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6.14682233961713, 0.996034803240008. Here's your graph:

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How do I set up the equation for "A bank teller cashed a check for $1010 using $20 bills and $50 bills. The teller handed 26 more $20 bills than $50 bills to the customer. Determine how many of each denomination were handed to the customer."?
Let x = number of $50 bills
then
x+26 = number of $20 bills
.
Equation:
50x + 20(x+26) = 1010
50x + 20x+520 = 1010
70x+520 = 1010
70x = 490
x = 70 (number of $50 bills)
.
$20 bills:
x+26 = 70+26 = 96

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Following an investigation into fiance fraud, a daycare center's enrollment decreased by 29% to 53 students. What was the daycare centers enrollment before the investigation?
Let x = enrollment before investigation
then
x - .29x = 53
x(1 - .29) = 53
x(.71) = 53
x = 53/(.71)
x = 75 students

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Log base 2 (8x) - log base 2 (x squared minus 1) = log base 2 3







x = {-1/3, 3}
we can throw out the negative solution (extraneous) leaving:
x = 3

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(-5/4 , 1) (-1/4 , 3/4)
are two pairs of (x,y) points on a line:
(x1, y1) and (x2, y2)
.
Slope between two point is:
(y2-y1)/(x2-x1)
plug in the given values:
(3/4 - 1)/(-1/4 - (-5/4))
(3/4 - 4/4)/(-1/4 + 5/4)
(-1/4)/(4/4)
(-1)/(4)
-1/4 (slope) of line
.
Plug the newly found slope (-1/4) and one of the two given points (-5/4, 1) into the "point-slope" form of a line:
y - y1 = m(x - x1)
y - 1 = (-1/4)(x - (-5/4))
y - 1 = (-1/4)(x + 5/4)
y - 1 = (-1/4)x - 5/16
y = (-1/4)x - 5/16 + 1
y = (-1/4)x - 5/16 + 16/16
y = (-1/4)x + 11/16 (this is what they're looking for in "slope-intercept" form)

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x^2+4x+4=25
x^2+4x-21 = 0
factor the left side:
(x+7)(x-3) = 0
x = {-7, 3}

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x^2+21x+20
(x+20)(x+1)

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what is the unit price of lotion selling at $2.39 for a 7 oz bottle?
this is read:
$2.39 per 7 ounces
or
2.39/7
dividing 2.39 by 7 gives you:
0.34
That's
$0.34 per one ounce
So, the UNIT price is:
"34 cents"

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Two trains are 600 miles apart, and their speeds differ by 20miles per hour. Find the speed of each train if they are traveling towards each other and will meet in three hours? I know the answers are 90 and 110, I just can't figure out the equation or how to get the answer.
Let x = speed of slower train
then
x+20 = speed of faster train
.
3(x + x+20) = 600
x + x+20 = 200
2x+20 = 200
2x = 180
x = 90 mph (slower train)
.
Faster train:
x+20 = 90+20 = 110 mph

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When the problem gives you:
(2,-4)
which gives you the x and y value (x,y).
So, simply plug the values into the equation and check:
12x+3y=6
12(2)+3(-4)=6
24+(-12)=6
24-12=6
12=6 (FALSE)
since, the above is false, we conclude that
(2,-4) is NOT a solution for 12x+3y=6

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whats 3% of $2850?
.03 * 2850 = $85.50

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Angle A and angle B are a linear pair. Measure angle A is 5 more than four times the measure of angle B. Find the measure of each angle.
.
If two angles are a "linear pair" the sum of the two angles MUST be 180.
.
Let x = measure of angle B
then
x+5 = measure of angle A
.
x + x+5 = 180
2x+5 = 180
2x = 175
x = 87.5 degrees (angle B)
.
Angle A:
x+5 = 87.5+5 = 92.5 degrees

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2^(x+3)= 6^(x-1)
take the log of both sides:
log(2^(x+3)) = log(6^(x-1))
(x+3)*log(2) = (x-1)*log(6)
xlog(2)+3log(2) = xlog(6)-log(6)
xlog(2) = xlog(6)-log(6)-3log(2)
xlog(2) - xlog(6) = -log(6)-3log(2)
multiplying both sides by -1:
xlog(6) - xlog(2) = log(6)+3log(2)
x(log(6) - log(2)) = log(6)+3log(2)
x = (log(6)+3log(2)) / (log(6) - log(2))
x = (1.681241237) / (0.47712125472)
x = 3.52372

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I think you meant:

take log base 32 of both sides:






to 4 significant figures:

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For the parabola of the equation y = 5x² + 20x - 7, what is the equation of the axis of symmetry
.
Axis of symmetry can be found using:
x = -b/(2a) (from part of the quadratic equation)
plugging in the coefficients:
x = -20/(2*5)
x = -20/(10)
x = -2 (answer)

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The bacteria in a certain culture double every 7.1 hours. The culture has 6,500 bacteria at the start. How many bacteria will the culture contain after 4 hours?
.
General exponential growth/decay equation:
A = Pe^(rt)
where
A is amount after time t
P is initial amount
r is growth/decay rate
t is time
.
From: "The bacteria in a certain culture double every 7.1 hours." we can determine r:
P/2 = Pe^(r*7.1)
1/2 = e^(r*7.1)
.5 = e^(r*7.1)
ln(.5) = r*7.1
ln(.5)/7.1 = r
-0.09763 = r
.
Now, we can answer:
How many bacteria will the culture contain after 4 hours?
A = Pe^(rt)
A = 6500e^(-0.09763*4)
A = 6500e^(-0.3905055)
A = 4398.65 (answer)

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Write in slope-intercept form the equation of the line passing through the given point and perpendicular to the given line. (2,6),y=-1/2x+4
.
First, determine slope of:
y=-1/2x+4
because the above is in the "slope-intercept" form (y=mx+b) we can see that the slope is -1/2
.
a line perpendicular must have a slope that is the "negative-reciprocal".
Therefore, slope of the new line is 2 (because -1/2 * 2 = -1)
.
For our NEW line then, we have the slope (2) and one point (2,6)
plug into the "point-slope" form:
y - y1 = m (x - x1)
y - 6 = 2(x - 2)
y - 6 = 2x - 4
y = 2x - 4 + 6
y = 2x + 2 (answer in "slope-intercept" form)

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A toy glider is tossed into the air. Its height, h, in metres, after t seconds is modelled by h = 9t – 3t2. Find the maximum height the toy glider reaches. Show the steps of your solution.
.
The equation:
h = 9t – 3t^2
can be written as:
h = –3t^2 + 9t
is a parabola that opens downwards (based on the negative coefficient associated with the t^2 term). This means that the max will be at the vertex:
Find t value of the vertex:
t = -b/(2a)
t = -9/(2(-3))
t = -9/(-6)
t = 3/2 seconds
.
To find the height, we plug the value above back into the original equation:
h = –3t^2 + 9t
h = –3(3/2)^2 + 9(3/2)
h = –3(9/4) + 9(3/2)
h = –27/4 + 27/2
h = –27/4 + 54/4
h = (–27+54)/4
h = 27/4
h = 6.75 meters

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If a Triangle's height is 4 inches less than two times its base, and has an area of 120 square inches. What is the height of the triangle?
.
Let b = base
then
2b-4 = height
.
area = (1/2)bh
120 = (1/2)b(2b-4)
240 = b(2b-4)
240 = 2b^2-4b
120 = b^2-2b
0 = b^2-2b-120
0 = (b-12)(b+10)
b = 12 inches (base)
.
height:
2b-4 = 2(12)-4 = 24-4 = 20 inches

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do i use the formula A=p(1+r/m)^mt?
yes
.
Money_Word_Problems/701775 (2013-01-13 23:03:55): How long will it take for an investment to double in value if it is invested at 5.75% interest compounded monthly?
A is 2p (double initial value)
p is initial value
r is .0575
m is 12
t is what we're looking for
.
A=p(1+r/m)^(mt)
2p=p(1+.0575/12)^(12t)
2=(1+.0575/12)^(12t)
2=(1.0.0047917)^(12t)
taking log base 1.0.0047917 of both sides of the equation:
log(2)/log(1.0.0047917) = 12t
log(2)/log(1.0.0047917) = 12t
145.0031 = 12 t
12.1 years = t

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Geometry_Word_Problems/701768 (2013-01-13 22:24:33): The four blades of a helicopter meet at right angles and are all the same length. The distance the tips of two adjacent blades is 36 feet. How long is each blade? Round your answer to the nearest tenth.
.
Apply Pythagorean theorem:
Let x = length (feet) of a blade
then
x^2 + x^2 = 36^2
2x^2 = 36^2
2x^2 = 1296
x^2 = 648
x = 25.5 feet