Question

The volume of a rectangular prism can be calculated with the formula V=lwh, where V is the volume, l is the length, w is the width, and h is the height. If a rectangular prism has a Volume of 45 ft3 , the length is 5 feet, the width is 3 feet, what is the height?(1 point) Responses
Answered by GPT-4o mini
To find the height of the rectangular prism, you can use the volume formula \( V = lwh \).

Given:
- Volume \( V = 45 \, \text{ft}^3 \)
- Length \( l = 5 \, \text{ft} \)
- Width \( w = 3 \, \text{ft} \)

Substituting the known values into the volume formula:

\[
45 = 5 \cdot 3 \cdot h
\]

Calculate \( 5 \cdot 3 \):

\[
5 \cdot 3 = 15
\]

Now substitute back into the equation:

\[
45 = 15h
\]

To find \( h \), divide both sides by 15:

\[
h = \frac{45}{15} = 3
\]

Thus, the height \( h \) is \( 3 \) feet.
Answer
Solve for b. 10b + 5 = 7b - 16 (1 point) Responses 7 7 26 26 -26 -26 -7 -7
Answered by GPT-4o mini
To solve the equation \(10b + 5 = 7b - 16\), follow these steps:

1. **Subtract \(7b\) from both sides**:

\[
10b - 7b + 5 = -16
\]

This simplifies to:

\[
3b + 5 = -16
\]

2. **Subtract 5 from both sides**:

\[
3b = -16 - 5
\]

This simplifies to:

\[
3b = -21
\]

3. **Divide both sides by 3**:

\[
b = \frac{-21}{3} = -7
\]

Thus, the solution for \(b\) is \(-7\).
Answer
Which of the following equations has no solutions?(1 point) Responses -6x + 4 = -6x + 3 -6x + 4 = -6x + 3 -6x + 4 = 6x + 3 -6x + 4 = 6x + 3 6x + 4 = 6x + 4 6x + 4 = 6x + 4 6x + 3 = -6x + 3
Answered by GPT-4o mini
To determine which of the following equations has no solutions, we can analyze each one by attempting to isolate the variable or by observing whether contradictions arise.

1. **\(-6x + 4 = -6x + 3\)**
- Add \(6x\) to both sides:
\[
4 = 3 \quad (\text{Contradiction})
\]
- **No solution.**

2. **\(-6x + 4 = 6x + 3\)**
- Add \(6x\) to both sides:
\[
4 = 12x + 3
\]
- Subtract 3 from both sides:
\[
1 = 12x \implies x = \frac{1}{12} \quad (\text{Has a solution})
\]

3. **\(6x + 4 = 6x + 3\)**
- Subtract \(6x\) from both sides:
\[
4 = 3 \quad (\text{Contradiction})
\]
- **No solution.**

4. **\(6x + 4 = 6x + 4\)**
- This simplifies to:
\[
0 = 0 \quad (\text{Infinite solutions})
\]

5. **\(6x + 3 = -6x + 3\)**
- Add \(6x\) to both sides:
\[
12x + 3 = 3
\]
- Subtract 3 from both sides:
\[
12x = 0 \implies x = 0 \quad (\text{Has a solution})
\]

Thus, the equations with no solutions are:

- \(-6x + 4 = -6x + 3\)
- \(6x + 4 = 6x + 3\)

So the final answer is that both **\(-6x + 4 = -6x + 3\)** and **\(6x + 4 = 6x + 3\)** have no solutions. However, since you need only one, the first one you listed is sufficient:

**The equation with no solutions is: \(-6x + 4 = -6x + 3\)**.
Answer
ax + 3 = 33(1 point) Responses 30/a a/30 a/36 36/a
Answered by GPT-4o mini
To solve the equation \( ax + 3 = 33 \) for \( x \), we first isolate \( x \) by following these steps:

1. **Subtract 3 from both sides**:
\[
ax = 33 - 3
\]
This simplifies to:
\[
ax = 30
\]

2. **Divide both sides by \( a \)** (assuming \( a \neq 0 \)):
\[
x = \frac{30}{a}
\]

Thus, the solution for \( x \) is \( \frac{30}{a} \).

The correct response from the options you provided is:
**\(\frac{30}{a}\)**.
Answer
-10 - 2m = -8
Answered by GPT-4o mini
To solve the equation \(-10 - 2m = -8\), follow these steps:

1. **Add 10 to both sides**:
\[
-2m = -8 + 10
\]
This simplifies to:
\[
-2m = 2
\]

2. **Divide both sides by -2**:
\[
m = \frac{2}{-2} = -1
\]

Thus, the solution for \(m\) is \(-1\).
Answer
5 = 2k -11
Answered by GPT-4o mini
To solve the equation \(5 = 2k - 11\), follow these steps:

1. **Add 11 to both sides**:
\[
5 + 11 = 2k
\]
This simplifies to:
\[
16 = 2k
\]

2. **Divide both sides by 2**:
\[
k = \frac{16}{2} = 8
\]

Thus, the solution for \(k\) is \(8\).