What happens when a value causes a denominator in a fraction to be equal to zero?(1 point) Responses There are infinite solutions. There are infinite solutions. This fraction is undefined. This fraction is undefined. The value of the equation becomes zero. The value of the equation becomes zero. This value is a solution to the equation.

When a value causes a denominator in a fraction to be equal to zero, the correct response is: **This fraction is undefined.**

What value makes the equation −5=4−3x/4−3x undefined?(1 point)

−4/3
3/4
−3/4
4/3

To determine the value that makes the equation \(-5 = \frac{4 - 3x}{4 - 3x}\) undefined, we need to analyze the denominator \(4 - 3x\).

The expression is undefined when the denominator is equal to zero:

\[
4 - 3x = 0
\]

To solve for \(x\):

\[
3x = 4
\]

\[
x = \frac{4}{3}
\]

Therefore, the value that makes the equation undefined is **\(\frac{4}{3}\)**.

Solve the equation for the variable k: 30/k+1=4 .(1 point)

10
1/6
6
1/10

To solve the equation \(\frac{30}{k} + 1 = 4\) for the variable \(k\), follow these steps:

1. Subtract 1 from both sides:

\[
\frac{30}{k} = 4 - 1
\]

\[
\frac{30}{k} = 3
\]

2. Multiply both sides by \(k\) to eliminate the fraction:

\[
30 = 3k
\]

3. Divide both sides by 3 to solve for \(k\):

\[
k = \frac{30}{3}
\]

\[
k = 10
\]

So the solution for \(k\) is **10**.

What is the value for the variable f in 17/3f−1 =1 ?(1 point)

6
5
4
3

To solve the equation \(\frac{17}{3f} - 1 = 1\) for the variable \(f\), follow these steps:

1. **Add 1 to both sides of the equation:**
\[
\frac{17}{3f} = 1 + 1
\]
\[
\frac{17}{3f} = 2
\]

2. **Multiply both sides by \(3f\) to eliminate the fraction:**
\[
17 = 2 \cdot 3f
\]
\[
17 = 6f
\]

3. **Divide both sides by 6 to solve for \(f\):**
\[
f = \frac{17}{6}
\]

Since \(\frac{17}{6}\) does not match any of the provided options (6, 5, 4, 3), it appears there may have been a misunderstanding of the equation.

To check, let’s go back and confirm:

The original equation is:
\[
\frac{17}{3f} - 1 = 1
\]

This rearrangement and solving produce \(f = \frac{17}{6}\).

If you meant the equation is supposed to be \( \frac{17}{3f} = 2\) without the \(-1\), then:
- Multiply both sides by \(3f\) first as shown, gives \(17=6f\), leading to \(f = \frac{17}{6}\).

Please clarify if there's an alternate equation or if there's a different approach to solving, as standard calculations yield \(f = \frac{17}{6}\), which simplifies to approximately 2.83, not one of the provided answers.

1. 4

2. This fraction is undefined
3. 4/3
4.10
5.6

It looks like you're providing a list of answers for different questions or problems. Here’s what each item corresponds to based on previous discussions:

1. **4** - This could correlate with various potential equations or problems.
2. **This fraction is undefined** - This matches the answer regarding what happens when the denominator of a fraction equals zero.
3. **4/3** - This is the value that made the denominator of an equation equal zero.
4. **10** - This was the value calculated for the variable \(k\) in the equation \(\frac{30}{k} + 1 = 4\).
5. **6** - This might refer to a separate problem or question about finding \(f\), but from the previous discussion, \(f\) was calculated as \(\frac{17}{6}\).

If you need clarification or assistance with specific questions related to these answers, please provide additional context or questions!