y > x + 3 → y = x + 3
for x = 0 → y = 0 + 3 = 3 → (0, 3)
for x = -3 → y = -3 + 3 = 0 → (-3, 0)
dot line and shading above the line
y ≤ 3x - 3 → y = 3x - 3
for x = 0 → y = 3(0) - 3 = 0 - 3 = -3 → (0, -3)
for x = 1 → y = 3(1) - 3 = 3 - 3 = 0 → (1, 0)
solid line and shading below the line
Answer in attachment.
Answer:
Agree
Step-by-step explanation:
Answer:
![-(a+1\frac{3}{4}b)](https://tex.z-dn.net/?f=-%28a%2B1%5Cfrac%7B3%7D%7B4%7Db%29)
Step-by-step explanation:
Perimeter of a polygon = Sum of the measures of all sides of the polygon
For the given trapezoid,
Perimeter = ![1\frac{1}{2}a+1\frac{1}{2}b+1\frac{1}{2}a+2\frac{3}{4}b](https://tex.z-dn.net/?f=1%5Cfrac%7B1%7D%7B2%7Da%2B1%5Cfrac%7B1%7D%7B2%7Db%2B1%5Cfrac%7B1%7D%7B2%7Da%2B2%5Cfrac%7B3%7D%7B4%7Db)
By combining similar terms,
Perimeter = ![(1\frac{1}{2}+1\frac{1}{2})a+(1\frac{1}{2}+2\frac{3}{4})b](https://tex.z-dn.net/?f=%281%5Cfrac%7B1%7D%7B2%7D%2B1%5Cfrac%7B1%7D%7B2%7D%29a%2B%281%5Cfrac%7B1%7D%7B2%7D%2B2%5Cfrac%7B3%7D%7B4%7D%29b)
= ![(1+\frac{1}{2}+1+\frac{1}{2})a+(1+\frac{1}{2}+2+\frac{3}{4})b](https://tex.z-dn.net/?f=%281%2B%5Cfrac%7B1%7D%7B2%7D%2B1%2B%5Cfrac%7B1%7D%7B2%7D%29a%2B%281%2B%5Cfrac%7B1%7D%7B2%7D%2B2%2B%5Cfrac%7B3%7D%7B4%7D%29b)
= (2 + 1)a + ![(3+\frac{1}{2}+\frac{3}{4})b](https://tex.z-dn.net/?f=%283%2B%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B3%7D%7B4%7D%29b)
= 3a + ![(3+\frac{2}{4}+ \frac{3}{4})b](https://tex.z-dn.net/?f=%283%2B%5Cfrac%7B2%7D%7B4%7D%2B%20%5Cfrac%7B3%7D%7B4%7D%29b)
= 3a + ![(3+\frac{5}{4})b](https://tex.z-dn.net/?f=%283%2B%5Cfrac%7B5%7D%7B4%7D%29b)
= 3a + ![(3+1+\frac{1}{4})b](https://tex.z-dn.net/?f=%283%2B1%2B%5Cfrac%7B1%7D%7B4%7D%29b)
= 3a + ![4\frac{1}{4}b](https://tex.z-dn.net/?f=4%5Cfrac%7B1%7D%7B4%7Db)
For rectangle,
Perimeter = 2(Length + Width)
= 2(2a + 3b)
Difference between the perimeter of trapezoid and rectangle,
= (3a +
) - 2(2a + 3b)
= (3a - 4a) + (
- 6b)
= -a + ![(4+\frac{1}{4}-6)b](https://tex.z-dn.net/?f=%284%2B%5Cfrac%7B1%7D%7B4%7D-6%29b)
= -a + ![(\frac{1}{4}-2)b](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B4%7D-2%29b)
= -a + ![(\frac{1}{4}-\frac{8}{4})b](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B4%7D-%5Cfrac%7B8%7D%7B4%7D%29b)
= -a - ![\frac{7}{4}b](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B4%7Db)
= ![-(a+1\frac{3}{4}b)](https://tex.z-dn.net/?f=-%28a%2B1%5Cfrac%7B3%7D%7B4%7Db%29)
Well the best way is to plug into the slope equation
![m = \frac{rise}{run} = \frac{y2 - y1}{x2 - x1}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7Brise%7D%7Brun%7D%20%20%3D%20%20%5Cfrac%7By2%20-%20y1%7D%7Bx2%20-%20x1%7D%20)
Where (x1, y1) and (x2,y2) are ordered pairs on the xy plane.