<u>Part 1)</u> Use the fact that there are 12 inches in a foot
a) How many inches tall is a 7 foot basketball player?
we know that
1 foot=12 inches
so by proportion
![\frac{12}{1} \frac{inches}{foot} =\frac{x}{7} \frac{inches}{feet} \\ \\x=12*7\\ \\x=84\ inches](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B1%7D%20%5Cfrac%7Binches%7D%7Bfoot%7D%20%3D%5Cfrac%7Bx%7D%7B7%7D%20%5Cfrac%7Binches%7D%7Bfeet%7D%20%5C%5C%20%5C%5Cx%3D12%2A7%5C%5C%20%5C%5Cx%3D84%5C%20inches)
therefore
<u>the answer Part 1a) is</u>
![84\ inches](https://tex.z-dn.net/?f=84%5C%20inches)
Part b) If a yard is a 3 feet long, how many inches are in a yard?
we know that
1 yard=3 feet
1 foot=12 inches
so
Convert 3 feet to inches
by proportion
therefore
<u>the answer Part 1b) is</u>
![36\ inches](https://tex.z-dn.net/?f=36%5C%20inches)
<u>Part 2) </u>At the farmer's market two pounds of peaches cost $4.20 How much will five pounds cost?
by proportion
therefore
<u>the answer Part 2) is</u>
![\$10.5](https://tex.z-dn.net/?f=%5C%2410.5)
<u>Part 3) </u>Janice mother gave her a ten dollars bill to buy five pounds each of bananas and apples at the grocery store. When she got there she found that bananas were 80 c per pound and apples were $1.40 per pound.
Did Janice's mother give her enough money? If so, should she receive any change? If not, how much more money does she need?
we know that
<u>Find the cost of the bananas</u>
![5\ pounds*0.80\frac{\$}{pounds}=\$4](https://tex.z-dn.net/?f=5%5C%20pounds%2A0.80%5Cfrac%7B%5C%24%7D%7Bpounds%7D%3D%5C%244)
<u>Find the cost of the apples</u>
![5\ pounds*1.40\frac{\$}{pounds}=\$7](https://tex.z-dn.net/?f=5%5C%20pounds%2A1.40%5Cfrac%7B%5C%24%7D%7Bpounds%7D%3D%5C%247)
Sum the cost of the bananas and the cost of the apples
![\$4+\$7=\$11](https://tex.z-dn.net/?f=%5C%244%2B%5C%247%3D%5C%2411)
------> Janice's mother didn't give her enough money
She needs more money
She needs-------> ![\$11-\$10=\$1](https://tex.z-dn.net/?f=%5C%2411-%5C%2410%3D%5C%241)
therefore
<u>the answer part 3) is</u>
She needs
more
Yes, the student's theory is correct, because the survey shows that the seventh graders spend more time playing games on the weekend than the eighth graders.
<u>Answer</u>
The first student was right.
The length of the long side is at least 13 inches.
<u>Explanation</u>
The perimeter of any figure is the distance all round.
Perimeter of a rectangle = 2(l+w). Where l is length and w is the width.
2(l + w) ≥ 30
2{(x-3) + 2} ≥ 30
2(x-3+2) = 30
2(x - 1) ≥ 30
x - 1 ≥ 15
x ≥ 16
When x = 16,
l = 16-3
= 13 inches
The length of the long side is 13 inches. The first student was right.
A) For the equation
![y=- \frac{1}{2}x+3](https://tex.z-dn.net/?f=y%3D-%20%5Cfrac%7B1%7D%7B2%7Dx%2B3)
, the slope is
![- \frac{1}{2}](https://tex.z-dn.net/?f=-%20%5Cfrac%7B1%7D%7B2%7D%20)
.
Slope-intercept form is y = mx + b, where m is slope and b is the y-intercept. This means that if
![m=- \frac{1}{2}](https://tex.z-dn.net/?f=m%3D-%20%5Cfrac%7B1%7D%7B2%7D%20)
, the slope is
![- \frac{1}{2}](https://tex.z-dn.net/?f=-%20%5Cfrac%7B1%7D%7B2%7D%20)
.
B) Since this equation is in the same form, you just find what m is equal to.
Since
![m=2](https://tex.z-dn.net/?f=m%3D2)
, that's the slope.
For the solution, set
![y=- \frac{1}{2}x+3](https://tex.z-dn.net/?f=y%3D-%20%5Cfrac%7B1%7D%7B2%7Dx%2B3)
equal to
![y=2x-4](https://tex.z-dn.net/?f=y%3D2x-4)
, so it would be put together like this:
![y=[tex]- \frac{1}{2}x+3=2x-4\\ -\frac{1}{2}=2x-7\\ 1\frac{1}{2}x=-7\\ x=-4.66667](https://tex.z-dn.net/?f=y%3D%5Btex%5D-%20%5Cfrac%7B1%7D%7B2%7Dx%2B3%3D2x-4%5C%5C%20-%5Cfrac%7B1%7D%7B2%7D%3D2x-7%5C%5C%201%5Cfrac%7B1%7D%7B2%7Dx%3D-7%5C%5C%20x%3D-4.66667)
So your answer is
-4.667.