Answer:
-1266
Step-by-step explanation:
![(28 \times 5 - 5 \times 190) - 2 \times 228 \\ (140 - 950) - 456 \\ ( - 810) - 456 \\ - 810 - 456](https://tex.z-dn.net/?f=%2828%20%5Ctimes%205%20-%205%20%5Ctimes%20190%29%20-%202%20%5Ctimes%20228%20%5C%5C%20%28140%20-%20950%29%20-%20456%20%5C%5C%20%28%20-%20810%29%20-%20456%20%5C%5C%20%20-%20810%20-%20456)
![= - 1266](https://tex.z-dn.net/?f=%20%3D%20%20-%201266)
Answer:
40/27
Step-by-step explanation:
-1/4(4/9-3x)-2/9=7/9
-1/9+3/4x=7/9+2/9
3/4x=9/9-(-1/9)
3/4x=9/9+1/9
3/4x=10/9
x=(10/9)/(3/4)
x=(10/9)(4/3)
x=40/27
The area of the model is 100.25in^2
So, letter D
Answer:
Part A) ![h(4) -m(16)=-4](https://tex.z-dn.net/?f=h%284%29%20-m%2816%29%3D-4)
Part B) The distance between the y-intercepts is equal to 4 units
Part C) The value of h(x) will always be greater than the value of m(x) for any value of x
Step-by-step explanation:
Part A) What is the value of h(4) -m(16)
we have
![h(x)=\frac{1}{2}(x-2)^2](https://tex.z-dn.net/?f=h%28x%29%3D%5Cfrac%7B1%7D%7B2%7D%28x-2%29%5E2)
For x=4
![h(4)=\frac{1}{2}(4-2)^2=2](https://tex.z-dn.net/?f=h%284%29%3D%5Cfrac%7B1%7D%7B2%7D%284-2%29%5E2%3D2)
Find the equation of the line m(x)
Find the slope
take the points
(8,2) and (12,4)
The formula to calculate the slope between two points is equal to
![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
substitute
![m=\frac{4-2}{12-8}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B4-2%7D%7B12-8%7D)
![m=\frac{2}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B2%7D%7B4%7D)
![m=\frac{1}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B2%7D)
Find the equation of the line in slope intercept form
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
we have
![m=\frac{1}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B2%7D)
![point\ (8,2)](https://tex.z-dn.net/?f=point%5C%20%288%2C2%29)
substitute
![2=\frac{1}{2}(8)+b](https://tex.z-dn.net/?f=2%3D%5Cfrac%7B1%7D%7B2%7D%288%29%2Bb)
solve for b
![b=-2](https://tex.z-dn.net/?f=b%3D-2)
![y=\frac{1}{2}x-2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx-2)
therefore
![m(x)=\frac{1}{2}x-2](https://tex.z-dn.net/?f=m%28x%29%3D%5Cfrac%7B1%7D%7B2%7Dx-2)
Find m(16)
![m(16)=\frac{1}{2}(16)-2=6](https://tex.z-dn.net/?f=m%2816%29%3D%5Cfrac%7B1%7D%7B2%7D%2816%29-2%3D6)
so
![h(4) -m(16)=2-6=-4](https://tex.z-dn.net/?f=h%284%29%20-m%2816%29%3D2-6%3D-4)
Part B) we know that
The y-intercept is the value of y when the value of x is equal to zero
Find the y-intercept of h(x)
For x=0
![h(0)=\frac{1}{2}(0-2)^2=2](https://tex.z-dn.net/?f=h%280%29%3D%5Cfrac%7B1%7D%7B2%7D%280-2%29%5E2%3D2)
Find the y-intercept of m(x)
For x=0
![m(0)=\frac{1}{2}(0)-2=-2](https://tex.z-dn.net/?f=m%280%29%3D%5Cfrac%7B1%7D%7B2%7D%280%29-2%3D-2)
therefore
The distance between the y-intercepts is equal to 2-(-2)=4 units
Part C)
Graph both equations
![h(x)=\frac{1}{2}(x-2)^2](https://tex.z-dn.net/?f=h%28x%29%3D%5Cfrac%7B1%7D%7B2%7D%28x-2%29%5E2)
![m(x)=\frac{1}{2}x-2](https://tex.z-dn.net/?f=m%28x%29%3D%5Cfrac%7B1%7D%7B2%7Dx-2)
using a graphing tool
see the attached figure
The value of h(x) will always be greater than the value of m(x) for any value of x