![\dfrac{1}{6} \text{ of } 5](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%7D%7B6%7D%20%5Ctext%7B%20of%20%7D%205%20)
"of" is written as "x" in number statement:
![= \dfrac{1}{6} \times 5](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B1%7D%7B6%7D%20%5Ctimes%205)
Write 5 as fraction:
![= \dfrac{1}{6} \times \dfrac{5}{1}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B1%7D%7B6%7D%20%5Ctimes%20%20%5Cdfrac%7B5%7D%7B1%7D%20)
Multiply:
For this case we have the following variables:
P = area covered by a roll of wallpaper
w = the total area of the walls
n = number of rolls to buy
We write the equation for n.
You must take into account that you can determine this amount by dividing the total area between the area covered by each roll of paper.
We have then:
Answer:
a formula that will help them determine how much wall paper they'll need to purchase is:
![n = w / P](https://tex.z-dn.net/?f=%20n%20%3D%20w%20%2F%20P)
Answer:
The answer is in the image below
Answer:
The scale factor used to go from P to Q is 1/4
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ----> the scale factor
x -----> area of polygon Q
y -----> area of polygon P
![z^{2}=\frac{x}{y}](https://tex.z-dn.net/?f=z%5E%7B2%7D%3D%5Cfrac%7Bx%7D%7By%7D)
we have
![y=72\ units^2](https://tex.z-dn.net/?f=y%3D72%5C%20units%5E2)
Find the area of polygon Q
Divide the the area of polygon Q in two triangles and three squares
The area of the polygon Q is equal to the area of two triangles plus the area of three squares
see the attached figure N 2
Find the area of triangle 1
![A=(1/2)(1)(2)=1\ units^2](https://tex.z-dn.net/?f=A%3D%281%2F2%29%281%29%282%29%3D1%5C%20units%5E2)
Find the area of three squares (A2,A3 and A4)
![A=3(1)^2=3\ units^2](https://tex.z-dn.net/?f=A%3D3%281%29%5E2%3D3%5C%20units%5E2)
Find the area of triangle 5
![A=(1/2)(1)(1)=0.5\ units^2](https://tex.z-dn.net/?f=A%3D%281%2F2%29%281%29%281%29%3D0.5%5C%20units%5E2)
The area of polygon Q is
![x=1+3+0.5=4.5\ units^2](https://tex.z-dn.net/?f=x%3D1%2B3%2B0.5%3D4.5%5C%20units%5E2)
Find the scale factor
![z^{2}=\frac{x}{y}](https://tex.z-dn.net/?f=z%5E%7B2%7D%3D%5Cfrac%7Bx%7D%7By%7D)
we have![y=72\ units^2](https://tex.z-dn.net/?f=y%3D72%5C%20units%5E2)
![x=4.5\ units^2](https://tex.z-dn.net/?f=x%3D4.5%5C%20units%5E2)
substitute and solve for z
![z^{2}=\frac{4.5}{72}](https://tex.z-dn.net/?f=z%5E%7B2%7D%3D%5Cfrac%7B4.5%7D%7B72%7D)
![z^{2}=\frac{1}{16}](https://tex.z-dn.net/?f=z%5E%7B2%7D%3D%5Cfrac%7B1%7D%7B16%7D)
square root both sides
![z=\frac{1}{4}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B1%7D%7B4%7D)
therefore
The scale factor used to go from P to Q is 1/4
Answer:
Follows are the solution to the given points:
Step-by-step explanation:
Given:
![A) \ \ 2x+(3.4)^2+(7.7) \\\\B) \ \ 3x+(2.6)+(8.8)^2\\\\C)\ \ 7.6+(28.3)+(4)^2 \\\\D)\ \ 7x-(7.8)+(9:3)](https://tex.z-dn.net/?f=A%29%20%5C%20%5C%202x%2B%283.4%29%5E2%2B%287.7%29%20%5C%5C%5C%5CB%29%20%5C%20%5C%203x%2B%282.6%29%2B%288.8%29%5E2%5C%5C%5C%5CC%29%5C%20%5C%207.6%2B%2828.3%29%2B%284%29%5E2%20%5C%5C%5C%5CD%29%5C%20%5C%207x-%287.8%29%2B%289%3A3%29)
For point A:
![\to 2x+(3.4)^2+(7.7)\\\\\to 2x+(11.56)+(7.7)\\\\\to 2x+19.26\\\\](https://tex.z-dn.net/?f=%5Cto%20%202x%2B%283.4%29%5E2%2B%287.7%29%5C%5C%5C%5C%5Cto%20%202x%2B%2811.56%29%2B%287.7%29%5C%5C%5C%5C%5Cto%20%202x%2B19.26%5C%5C%5C%5C)
For point B:
![\to 3x+(2.6)+(8.8)^2\\\\\to 3x+(2.6)+77.44\\\\\to 3x+80.04](https://tex.z-dn.net/?f=%5Cto%203x%2B%282.6%29%2B%288.8%29%5E2%5C%5C%5C%5C%5Cto%203x%2B%282.6%29%2B77.44%5C%5C%5C%5C%5Cto%203x%2B80.04)
For point C:
![\to \ 7.6+(28.3)+(4)^2 \\\\\to \ 7.6+(28.3)+16 \\\\\to \ 7.6+44.3 \\\\\to 51.9](https://tex.z-dn.net/?f=%5Cto%20%5C%207.6%2B%2828.3%29%2B%284%29%5E2%20%5C%5C%5C%5C%5Cto%20%5C%207.6%2B%2828.3%29%2B16%20%5C%5C%5C%5C%5Cto%20%5C%207.6%2B44.3%20%5C%5C%5C%5C%5Cto%2051.9)
For point D:
![\to 7x-(7.8)+(9:3)\\\\\to 7x-(7.8)+ \frac{9}{3}\\\\\to 7x- \frac{23.4+9}{3}\\\\\to 7x- \frac{32.4}{3}\\\\\to 7x- 10.8](https://tex.z-dn.net/?f=%5Cto%207x-%287.8%29%2B%289%3A3%29%5C%5C%5C%5C%5Cto%207x-%287.8%29%2B%20%5Cfrac%7B9%7D%7B3%7D%5C%5C%5C%5C%5Cto%207x-%20%5Cfrac%7B23.4%2B9%7D%7B3%7D%5C%5C%5C%5C%5Cto%207x-%20%5Cfrac%7B32.4%7D%7B3%7D%5C%5C%5C%5C%5Cto%207x-%2010.8)