Question
Find the area of the rectangle below:
right side is 3x^3
bottom side is -4x^3 + 5
(1 point)
Responses
12x6−15x3
−12x9+15x3
−12x6+15x3
−x^3+5
11x^3−2
right side is 3x^3
bottom side is -4x^3 + 5
(1 point)
Responses
12x6−15x3
−12x9+15x3
−12x6+15x3
−x^3+5
11x^3−2
Answers
GPT-4o mini
To find the area of the rectangle, we need to multiply the lengths of its sides.
The right side of the rectangle is given as \(3x^3\) and the bottom side is given as \(-4x^3 + 5\).
Now, we will calculate the area (A):
\[
A = \text{Right Side} \times \text{Bottom Side} = (3x^3) \times (-4x^3 + 5)
\]
To calculate this, we distribute \(3x^3\) to both terms in the expression for the bottom side:
\[
A = 3x^3 \times -4x^3 + 3x^3 \times 5
\]
Calculating each part, we get:
1. \(3x^3 \times -4x^3 = -12x^{6}\)
2. \(3x^3 \times 5 = 15x^{3}\)
Now, we can combine these results to find the total area:
\[
A = -12x^6 + 15x^3
\]
Therefore, the area of the rectangle is:
\[
\boxed{-12x^6 + 15x^3}
\]
This corresponds to the third option in the responses provided.
The right side of the rectangle is given as \(3x^3\) and the bottom side is given as \(-4x^3 + 5\).
Now, we will calculate the area (A):
\[
A = \text{Right Side} \times \text{Bottom Side} = (3x^3) \times (-4x^3 + 5)
\]
To calculate this, we distribute \(3x^3\) to both terms in the expression for the bottom side:
\[
A = 3x^3 \times -4x^3 + 3x^3 \times 5
\]
Calculating each part, we get:
1. \(3x^3 \times -4x^3 = -12x^{6}\)
2. \(3x^3 \times 5 = 15x^{3}\)
Now, we can combine these results to find the total area:
\[
A = -12x^6 + 15x^3
\]
Therefore, the area of the rectangle is:
\[
\boxed{-12x^6 + 15x^3}
\]
This corresponds to the third option in the responses provided.