Question

8. Which correctly shows the area formula for a trapezoid, A = 12h(b1+b2)
, rearranged for the quantity of interest h?(2 points)
Responses

h=12A(b1+b2)
h is equal to 1 half cap A open paren b sub 1 plus b sub 2 close paren

b1=2Ah−b2
b sub 1 is equal to 2 cap A over h minus b sub 2

h=2Ab1+b2
h is equal to the fraction with numerator 2 cap A and denominator b sub 1 plus b sub 2

h=(b1+b2)2A
h is equal to the fraction with numerator open paren b sub 1 plus b sub 2 close paren and denominator 2 cap A
Question 2
9. Given the formula for time in terms of distance and velocity, t=dv
, what operation would you use to isolate the distance?(2 points)
Responses

multiplication
multiplication

division
division

subtraction
subtraction

addition
addition
Question 3
10. Rearrange the slope formula y=mx+b
for the quantity of interest m.(2 points)
m =

Answer 1

Let's address each question one at a time.

**Question 8: Rearranging the area formula for a trapezoid**
The area formula for a trapezoid is given by \( A = \frac{1}{2}h(b_1 + b_2) \). To isolate \( h \), we can perform the following steps:

1. Multiply both sides by 2 to eliminate the fraction:
\( 2A = h(b_1 + b_2) \)

2. Then, divide both sides by \( (b_1 + b_2) \) to solve for \( h \):
\( h = \frac{2A}{b_1 + b_2} \)

Thus, the correct rearranged formula for \( h \) is:
**h = \(\frac{2A}{b_1 + b_2}\)**

The appropriate response is:
**h is equal to the fraction with numerator 2 cap A and denominator b sub 1 plus b sub 2.**

---

**Question 2: Isolating Distance (d) in the Formula for Time**
Given the formula \( t = \frac{d}{v} \), to isolate distance \( d \), you need to perform the following operation:

1. Multiply both sides by \( v \):
\( d = tv \)

Thus, the operation used to isolate distance \( d \) is:
**multiplication.**

---

**Question 3: Rearranging the Slope Formula**
The slope formula is given as \( y = mx + b \). To isolate \( m \), you perform the following steps:

1. Subtract \( b \) from both sides:
\( y - b = mx \)

2. Then, divide by \( x \) to solve for \( m \):
\( m = \frac{y - b}{x} \)

Thus, the rearranged formula for \( m \) is:
**m = \(\frac{y - b}{x}\)**

Let me know if you need further assistance!