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Money_Word_Problems/586026: Seven people decide to share the cost of a yacht. By bringing in an additional partner, they can reduce the cost to each person by $2000. What is the total cost of the yacht?
1 solutions

Answer 373573 by jim_thompson5910(28476) on 2012-03-12 19:13:22 (Show Source):

You can put this solution on YOUR website!
Hint: if C is the cost of the yacht and x is the cost per person (for 7 people), then

C/7 = x

represents the idea that the cost divided amongst 7 people is x

Now divide that same cost by 8 people to get the cost per person to drop by $2000 which gives us

C/8 = x-2000

From here, you can plug in x = C/7 to get

C/8 = C/7 - 2000

Now solve for C. I'll let you do that.

test/586019: The formula for the perimeter of a square is P = 4s, where P is the perimeter and s is the length of a side. Graph the equation.
1 solutions

Answer 373570 by jim_thompson5910(28476) on 2012-03-12 18:51:41 (Show Source):

You can put this solution on YOUR website!
If we let x take place of s and y take place of P, then we get y = 4x and we get the following graph:

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Jim
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Polygons/586012: Find the value of n for regular n-gon described. Each interior angle of the regular n-gon has a measure of 156 degrees.
1 solutions

Answer 373566 by jim_thompson5910(28476) on 2012-03-12 18:42:48 (Show Source):

You can put this solution on YOUR website!
I = (180(n-2))/n

156 = (180(n-2))/n

156n = 180(n-2)

156n = 180n-360

156n - 180n = -360

-24n = -360

n = -360/(-24)

n = 15

So the solution is n = 15, which means that there are 15 sides.

So this is a 15-gon, which is known as a pendedecagon.
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Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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Surface-area/586011: what exponent goes on the unit when finding volume
1 solutions

Answer 373563 by jim_thompson5910(28476) on 2012-03-12 18:31:29 (Show Source):

You can put this solution on YOUR website!
The exponent of 3 is used to denote that the volume is in cubic units (ex: cubic feet)

test/586003: I need help with 51/2-1/8
1 solutions

Answer 373561 by jim_thompson5910(28476) on 2012-03-12 18:15:04 (Show Source):

You can put this solution on YOUR website!
51/2-1/8

(51/2)*(4/4)-1/8

(51*4)/(2*4)-1/8

204/8-1/8

(204-1)/8

203/8

So 51/2-1/8 = 203/8
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If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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Functions/585997: f(x)=x+4
1 solutions

Answer 373560 by jim_thompson5910(28476) on 2012-03-12 18:05:15 (Show Source):

You can put this solution on YOUR website!
I'm asumming you want to graph this.

Looking at y=x%2B4

we can see that the equation is in slope-intercept form y=mx%2Bb

where the slope is m=1

and the y-intercept is b=4

Since

this tells us that the y-intercept is

.Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point

Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is

, this means:

rise%2Frun=1%2F1

which shows us that the rise is 1 and the run is 1. This means that to go from point to point, we can go up 1 and over 1

So starting at

, go up 1 unit

and to the right 1 unit to get to the next point

Now draw a line through these points to graph y=x%2B4

So this is the graph of y=x%2B4

through the points

and

Systems-of-equations/585970: What is the equation of the line, in point-slope form, that passes through the points (-7, -10) and (-6, -8)?
1 solutions

Answer 373556 by jim_thompson5910(28476) on 2012-03-12 17:42:44 (Show Source):

You can put this solution on YOUR website!
First let's find the slope of the line through the points

and

Note:

is the first point

. So this means that x%5B1%5D=-7

and

.
Also,

is the second point

. So this means that x%5B2%5D=-6

and

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

Start with the slope formula.

m=%28-8--10%29%2F%28-6--7%29

Plug in

, and

Subtract

from

to get

Subtract

from

to get

Reduce

So the slope of the line that goes through the points

and

Now let's use the point slope formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29

Start with the point slope formula

y--10=2%28x--7%29

Plug in

, and

Rewrite

Rewrite

So the solution is y%2B10=2%28x%2B7%29

Equations/585968: i am having a poblem with solving this problem 3t-t=-8
1 solutions

Answer 373555 by jim_thompson5910(28476) on 2012-03-12 17:39:58 (Show Source):

You can put this solution on YOUR website!
3t-t=-8

Start with the given equation.

2t=-8

Combine like terms on the left side.

t=%28-8%29%2F%282%29

Divide both sides by

to isolate

Reduce.

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Answer:

So the solution is t=-4

test/585982: Beatriz thinks (1, -1) is a solution of y = 2x -1. Grace thinks it is not a solution. Who is correct? Explain your reasoning.
1 solutions

Answer 373554 by jim_thompson5910(28476) on 2012-03-12 17:39:25 (Show Source):

You can put this solution on YOUR website!
If (1,-1) is a solution, then x = 1 and y = -1 should satisfy the equation. Let's see if it does.

y = 2x -1

-1 = 2(1) -1

-1 = 2 - 1

-1 = 1

Since the equation is false, x = 1 and y = -1 do NOT satisfy the equation.

Therefore, (1,-1) is NOT a solution.
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If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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Linear-equations/585943: Explain how you can tell that the graphs of 7x - 3y = 5 and
7x - 3y = 8 are parallel without ﬁnding their slopes.
1 solutions

Answer 373550 by jim_thompson5910(28476) on 2012-03-12 16:35:04 (Show Source):

You can put this solution on YOUR website!
If we let z = 7x-3y, then we can say that z = 5 and z = 8. This is a contradiction and this visually corresponds to parallel lines (since they never intersect).

Distributive-associative-commutative-properties/585942: (7x + 4x) + (11 + 10)
is an examle of which associative distributive or commutative ? i believe it is distribution am i correct?
1 solutions

Answer 373549 by jim_thompson5910(28476) on 2012-03-12 16:34:02 (Show Source):

You can put this solution on YOUR website!
You can think of (7x + 4x) + (11 + 10) as 1(7x + 4x) + 1(11 + 10) which becomes 1*7x+1*4x + 1*11 +1*10 and that simplifies to 7x+4x+11+10

So you are correct, this is the distributive property in action.
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Percentage-and-ratio-word-problems/585930: In 2006, Joan had to pay $1,580 in taxes. In 2007, she had to pay $1,738 in taxes. What was the percent of increase?
1 solutions

Answer 373547 by jim_thompson5910(28476) on 2012-03-12 16:11:55 (Show Source):

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Percent Increase = [(New - Old)/Old] * 100

Percent Increase = [(1738-1580)/1580] * 100

Percent Increase = [158/1580] * 100

Percent Increase = 0.1 * 100

Percent Increase = 10%
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Percentage-and-ratio-word-problems/585927: In 2004, John sold 390 bikes However, in 2005 he only 273 bikes. What was the percent of decrease?
1 solutions

Answer 373546 by jim_thompson5910(28476) on 2012-03-12 16:10:25 (Show Source):

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Percent Decrease = [(Old - New)/Old] * 100

Percent Decrease = [(390-273)/390] * 100

Percent Decrease = [117/390] * 100

Percent Decrease = 0.3 * 100

Percent Decrease = 30%
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Miscellaneous_Word_Problems/585922: The regression equation is 7.25-0.021x. Find the predicted time in the 40-yard dash for a subject who can do 10 sit-ups.
1 solutions

Answer 373545 by jim_thompson5910(28476) on 2012-03-12 16:00:34 (Show Source):

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I'm assuming that x is the number of sit-ups. If so, then the predicted time in the 40-yard dash is

y = 7.25-0.021x

y = 7.25-0.021(10)

y = 7.25-0.21

y = 7.04

So the predicted time is 7.04 seconds.
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Percentage-and-ratio-word-problems/585919: Last month a book sold for $25.00. This month it sold for $25.50. What was the percent of increase?
1 solutions

Answer 373544 by jim_thompson5910(28476) on 2012-03-12 15:57:00 (Show Source):

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Percent Increase = [(New - Old)/Old] * 100

Percent Increase = [(25.5-25)/25] * 100

Percent Increase = [0.5/25] * 100

Percent Increase = 0.02 * 100

Percent Increase = 2%
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Geometry_Word_Problems/585914: A library is 46.5 feet tall. It casts a shadow of 8.2 feet.
What is the sun's angle of elevation?
I don't understand how to find the elevation. My teacher has gone over it and I have asked for help, but I still don't get it.
1 solutions

Answer 373543 by jim_thompson5910(28476) on 2012-03-12 15:51:58 (Show Source):

You can put this solution on YOUR website!
The angle of elevation is

arctan(46.5/8.2) = 79.999 or about 80 degrees

The reason why I'm using the arctangent function is because the tangent of this unknown angle is equal to the ratio or quotient of the opposite side (46.5) divided by the adjacent side (8.2). We must use the arctangent to find the unknown angle (since it "undoes" the tangent function)
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Equations/585912: how do you solve the problem -10x-7=3

1 solutions

Answer 373540 by jim_thompson5910(28476) on 2012-03-12 15:45:21 (Show Source):

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-10x-7=3

Start with the given equation.

-10x=3%2B7

Add

to both sides.

-10x=10

Combine like terms on the right side.

x=%2810%29%2F%28-10%29

Divide both sides by

to isolate

Reduce.

----------------------------------------------------------------------

Answer:

So the solution is x=-1

Polynomials-and-rational-expressions/585909: Essay: Show all work. Find the following product:
(x^2+8)(x^3+7x-3)
1 solutions

Answer 373538 by jim_thompson5910(28476) on 2012-03-12 15:44:28 (Show Source):

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%28x%5E2%2B8%29%28x%5E3%2B7x-3%29

Start with the given expression.

x%5E2%28x%5E3%2B7x-3%29%2B8%28x%5E3%2B7x-3%29

Expand.

Distribute.

x%5E5%2B7%2Ax%5E3-3%2Ax%5E2%2B8%2Ax%5E3%2B56%2Ax-24

Multiply.

x%5E5%2B15%2Ax%5E3-3%2Ax%5E2%2B56%2Ax-24

Now combine like terms.

So %28x%5E2%2B8%29%28x%5E3%2B7x-3%29

expands to x%5E5%2B15x%5E3-3x%5E2%2B56x-24

.

In other words, %28x%5E2%2B8%29%28x%5E3%2B7x-3%29=x%5E5%2B15x%5E3-3x%5E2%2B56x-24

for all values of x.

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Age_Word_Problems/585908: Uncle Munch is three times as old as his nephew, Crunch. Three years ago, Uncle Munch was two times as old as Crunch will be in four years. How old are Uncle Munch and Crunch?
Note:
Just give me the two equations and i'll solve it from there. Thank you!
I started one of my equations as 3x=y but i'm not sure if it is correct and I also need help on the second equation. Thank you again!
1 solutions

Answer 373537 by jim_thompson5910(28476) on 2012-03-12 15:40:44 (Show Source):

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Let x = current age of Uncle Munch and y = current age of the nephew Crunch

Since "Uncle Munch is three times as old as his nephew", you know that 3y+=+x

Note: say for example the nephew is 9 yrs old, so y = 9 and x = 3y ---> x = 3(9) = 27, which means that x = 27 and the uncle is 27 years old.

Now, three years ago, the uncle was x-3 years old. In four years, the nephew will be y+4 years old.

Because "Three years ago, Uncle Munch was two times as old as Crunch will be in four years", this means that the second equation is x-3=2%28y%2B4%29

Rectangles/585906: 4x=20
6(3x-3)=8
1 solutions

Answer 373536 by jim_thompson5910(28476) on 2012-03-12 15:34:25 (Show Source):

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4x=20

4x/4=20/4

x = 5

=======================================================

6(3x-3)=8

18x-18=8

18x=8+18

18x=26

x=26/18

x = 13/9
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Numeric_Fractions/585903: eight less than five times c is four more than eight times c.

1 solutions

Answer 373533 by jim_thompson5910(28476) on 2012-03-12 15:27:19 (Show Source):

You can put this solution on YOUR website!
"eight less than five times c is four more than eight times c" translates to 5c-8=8c%2B4

logarithm/585897: how do i find the answer to this logarithm?
5^x+2=25^x
1 solutions

Answer 373531 by jim_thompson5910(28476) on 2012-03-12 15:09:10 (Show Source):

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5^(x+2)=25^x

5^(x+2)=(5^2)^x

5^(x+2)=5^(2x)

Since the bases are equal, the exponents are equal

x+2=2x

2 = 2x-x

2 = x

x = 2

So the answer is x = 2
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Probability-and-statistics/585891: The name of each contestant is written on a separate card, the cards are placed in a bag, and three names are picked from the bag. Identify which type of sampling is used and why

1 solutions

Answer 373530 by jim_thompson5910(28476) on 2012-03-12 15:07:14 (Show Source):

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This is simple random sampling because the names are drawn out at random and each name has an equal probability of being selected.
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Permutations/585884: The digits of the locker combination consist of 3 one digit numbers, 1-9. If the digits are not repeated, what is the probabiliity of the combination being 1, 2, 3?
1 solutions

Answer 373528 by jim_thompson5910(28476) on 2012-03-12 14:43:29 (Show Source):

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There's only one combo of "123" out of $\large _9C_3 = \frac{9!}{3!(9-3)!}= 84$ different combinations. So the probability is 1%2F504

Triangles/585883: i have a triangle with angle l p m o and n the middle value is 7 and im trying to figure out the x value help?? pleas

1 solutions

Answer 373526 by jim_thompson5910(28476) on 2012-03-12 14:37:57 (Show Source):

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It's hard to visualize what you are describing. Can you post a picture of it? Thanks.

Complex_Numbers/585882: solve the equation for x and express the roots in simplest a+ bi form: 3x^2=2x-1

1 solutions

Answer 373525 by jim_thompson5910(28476) on 2012-03-12 14:36:49 (Show Source):

You can put this solution on YOUR website!

3x%5E2=2x-1

Start with the given equation.

3x%5E2-2x%2B1=0

Get every term to the left side.

Notice that the quadratic 3x%5E2-2x%2B1

is in the form of Ax%5E2%2BBx%2BC

where

, and

Let's use the quadratic formula to solve for "x":

x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29

Start with the quadratic formula

x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%283%29%281%29+%29%29%2F%282%283%29%29

Plug in

, and

x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%283%29%281%29+%29%29%2F%282%283%29%29

Negate

to get

x+=+%282+%2B-+sqrt%28+4-4%283%29%281%29+%29%29%2F%282%283%29%29

Square

to get

x+=+%282+%2B-+sqrt%28+4-12+%29%29%2F%282%283%29%29

Multiply

to get

x+=+%282+%2B-+sqrt%28+-8+%29%29%2F%282%283%29%29

Subtract

from

to get

x+=+%282+%2B-+sqrt%28+-8+%29%29%2F%286%29

Multiply

and

to get

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

x+=+%282%2B2i%2Asqrt%282%29%29%2F%286%29

Break up the expression.

x+=+%281%2Bi%2Asqrt%282%29%29%2F%283%29

Reduce

Break up the fraction and rearrange terms.

So the solutions are x+=+1%2F3+%2B+expr%28sqrt%282%29%2F3%29i

Linear-equations/585881: the chapter title is : Quadratic Equations and Functions
Referring to the figure, use the graph to estimate the
roots of the equation: y = x^2 - 4
theres supposed to be a graph for it but i cant put it
1 solutions

Answer 373524 by jim_thompson5910(28476) on 2012-03-12 14:34:07 (Show Source):

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The graph is shown below

The graph crosses the x-axis at (-2,0) and at (2,0). So the roots are -2 and 2.
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Linear-equations/585880: given that the slope of the line is 5/7.
the slope of the line that is parallel to that line would be?
and the slope of the line that is perpendicular to that line would be?

1 solutions

Answer 373523 by jim_thompson5910(28476) on 2012-03-12 14:32:20 (Show Source):

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the slope of the line that is parallel to that line would be ___5/7____

and the slope of the line that is perpendicular to that line would be ___-7/5____

Recall that parallel lines have slopes that are equal to one another.

Also, remember that perpendicular lines have slopes that are negative reciprocals of one another.
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Average/585878: what is the average of 86 and 62?

1 solutions

Answer 373521 by jim_thompson5910(28476) on 2012-03-12 14:27:33 (Show Source):

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Average = (86+62)/2 = 148/2 = 74
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Functions/585875: State the domain of the following function. y=9x+14

1 solutions

Answer 373520 by jim_thompson5910(28476) on 2012-03-12 14:21:10 (Show Source):

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This is a linear function and a polynomial function. Therefore, the domain is the set of all real numbers. This is because you can plug in ANY number in for x and get some number out for y.
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Triangles/585873: Susie drew a triangle with angles that measured 47°, 43°, and 90°. What type of triangle did Susie draw?
A acute
B equiangular
C obtuse
D right
1 solutions

Answer 373519 by jim_thompson5910(28476) on 2012-03-12 14:19:24 (Show Source):

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The 90 degree angle is a right angle. Therefore, this is a right triangle.
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