Question

Solve for p.

3(p + q) = p

(1 point)
Responses

q = -2/3p

q = -3/2p

p = –2/3q

p = -3/2q

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for p, we need to isolate it on one side of the equation.

Given equation: 3(p + q) = p

First, distribute the 3 to both p and q:
3p + 3q = p

Next, move the 3p term to the left side of the equation by subtracting 3p from both sides:
3p - p + 3q = 0

Simplifying the equation:
2p + 3q = 0

Now, isolate p by subtracting 3q from both sides:
2p = -3q

Finally, divide both sides by 2 to solve for p:
p = -3/2q

Therefore, the correct answer is p = -3/2q.

Answer 2

Solve for b, then find the value of b when a = 3.

4a = 2b − 7
(1 point)
Responses

-9/2

5/2

19/2

17

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve for b, we need to isolate it on one side of the equation.

Given equation: 4a = 2b - 7

First, add 7 to both sides of the equation to get rid of the -7 term:
4a + 7 = 2b

Next, divide both sides by 2 to solve for b:
(4a + 7) / 2 = b

Simplifying the right side of the equation:
2a + 7/2 = b

Now, substitute a = 3 into the equation to find the value of b when a = 3:
2(3) + 7/2 = b
6 + 7/2 = b
12/2 + 7/2 = b
19/2 = b

Therefore, the value of b when a = 3 is b = 19/2.

Answer 4

Solve for r.

d = rt
(1 point)
Responses

r = dt

r = t/d

r = d/t

r = d-t

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve for r, we need to isolate it on one side of the equation.

Given equation: d = rt

First, divide both sides of the equation by t to solve for r:
d/t = r

Therefore, the correct answer is r = d/t.

Answer 6

Find the width of a rectangle with a perimeter of 90 and a length of 15.

(1 point)
Responses

90

15

45

30

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the width of a rectangle, we can use the formula for the perimeter of a rectangle, which is given by:

Perimeter = 2(length + width)

In this case, we are given that the perimeter is 90 and the length is 15.

Substituting these values into the formula, we have:

90 = 2(15 + width)

Next, we can simplify the equation:

90 = 30 + 2width

Subtracting 30 from both sides of the equation:

60 = 2width

Now, divide both sides of the equation by 2:

width = 30

Therefore, the width of the rectangle is 30.