Look at the picture.
The polygon is a right-angled trapezoid.
The area is:

The points (-2,-1) and (6,-1) lie on the same horizontal line, so the distance between them is 6-(-2)=6+2=8. The length of a is 8 units.
The points (-2,5) and (3,5) lie on the same horizontal line, so the distance between them is 3-(-2)=3+2=5. The length of b is 5 units.
The points (-2,5) and (-2,-1) lie on the same vertical line, so the distance between them is 5-(-1)=5+1=6. The length of h is 6 units.

The area is
39 square units.
She can make 3 batches. 3 batches will take 3 3/4 cups. If she made 4 it would take 5 cups
Answer: i) 1 - 9x² - 12x
ii) 17 - 3x²
iii) - 20 + 10x² - x⁴
<u>Step-by-step explanation:</u>
g(x) = 3x + 2 h(x) = 5 - x²
i) h(g(x))
h(3x + 2) = 5 - (3x + 2)²
= 5 - (9x² + 12x + 4)
= 5 - 9x² - 12x - 4
= 1 - 9x² - 12x
ii) g(h(x))
g(5 - x²) = 3(5 - x²) + 2
= 15 - 3x² + 2
= 17 - 3x²
iii) h(h(x))
h(5 - x²) = 5 - (5 - x²)²
= 5 - (25 - 10x² + x⁴)
= 5 - 25 + 10x² - x⁴
= -20 + 10x² - x⁴
6 bills in the deposit were $10 bills.
<u>Step-by-step explanation:</u>
The total number of bills he gave the teller = 24 bills
x + y = 24 ------------(1)
Let,
x be the number of $5 bills.
y be the number of $10 bills.
The total bank deposit made using $5 and $10 bills are $150.
<u>He deposits $5 bills and $10 bills. So, the equation can be framed as :
</u>
5x + 10y = 150 --------(2)
The question is asked for how many $10 bills were in the deposit,
Here 'y' is the number of $10 bills.
<u>To solve for y value :
</u>
The eq(1) must be multiplied by 5 and subtract eq(2) from eq(1),
5x + 5y = 120
-(<u>5x + 10y = 150</u>)
<u>-5y = -30 </u>
⇒ y = 30/5
⇒ y = 6
Therefore, there were 6 bills in the deposit that are $10 bills.