Question
Find the solution set of 4x−3>9 and x+6>−2 .(1 point)
Responses
{3,−8}
left brace 3 comma negative 8 right brace
{x|x>−8}
left brace x vertical bar x greater than negative 8 right brace
The solution set is null.
The solution set is null.
{x|x>3}
Responses
{3,−8}
left brace 3 comma negative 8 right brace
{x|x>−8}
left brace x vertical bar x greater than negative 8 right brace
The solution set is null.
The solution set is null.
{x|x>3}
Answers
Answer
What is the undefined value for the equation 14=7x9+4x ?(1 point)
Responses
x≠0
x does not equal 0
x≠94
x does not equal Start Fraction 9 over 4 End Fraction
x≠−49
x does not equal Start Fraction negative 4 over 9 End Fraction
x≠−94
Responses
x≠0
x does not equal 0
x≠94
x does not equal Start Fraction 9 over 4 End Fraction
x≠−49
x does not equal Start Fraction negative 4 over 9 End Fraction
x≠−94
Answer
just pick one
Answer
Solve for s in the following equation: 11s+3+4=5 .(1 point)
s=
s=
Answer
Which correctly shows the area formula for a trapezoid, A=12h(b1+b2) , rearranged for the quantity of interest h?(1 point)
Responses
h=2Ab1+b2
h equals Start Fraction 2 upper A over b subscript 1 baseline plus b subscript 2 baseline End Fraction
h=12A(b1+b2)
h equals Start Fraction 1 over 2 End Fraction upper A left parenthesis b subscript 1 baseline plus b subscript 2 baseline right parenthesis
h=b1+b22A
h equals Start Fraction b subscript 1 baseline plus b subscript 2 baseline over 2 upper A End Fraction
b1=2Ah−b2
Responses
h=2Ab1+b2
h equals Start Fraction 2 upper A over b subscript 1 baseline plus b subscript 2 baseline End Fraction
h=12A(b1+b2)
h equals Start Fraction 1 over 2 End Fraction upper A left parenthesis b subscript 1 baseline plus b subscript 2 baseline right parenthesis
h=b1+b22A
h equals Start Fraction b subscript 1 baseline plus b subscript 2 baseline over 2 upper A End Fraction
b1=2Ah−b2
Answer
Given the formula for time in terms of distance and velocity, t=dv , what operation would you use to isolate the distance?(1 point)
Responses
addition
addition
division
division
multiplication
multiplication
subtraction
Responses
addition
addition
division
division
multiplication
multiplication
subtraction
Answered by
GPT-4o mini
To solve the inequalities \(4x - 3 > 9\) and \(x + 6 > -2\), we need to solve each inequality separately.
1. **Solving \(4x - 3 > 9\)**:
\[
4x - 3 > 9
\]
Add 3 to both sides:
\[
4x > 12
\]
Divide by 4:
\[
x > 3
\]
2. **Solving \(x + 6 > -2\)**:
\[
x + 6 > -2
\]
Subtract 6 from both sides:
\[
x > -8
\]
Now we combine the two solution sets. The two inequalities give us the following results:
- From \(4x - 3 > 9\), we have \(x > 3\).
- From \(x + 6 > -2\), we have \(x > -8\).
Since \(x > 3\) is the stricter condition (since 3 is greater than -8), the final solution set is:
\[
\{ x | x > 3 \}
\]
Thus, the correct response is:
\(\{x | x > 3\}\) (left brace x vertical bar x greater than 3 right brace).
1. **Solving \(4x - 3 > 9\)**:
\[
4x - 3 > 9
\]
Add 3 to both sides:
\[
4x > 12
\]
Divide by 4:
\[
x > 3
\]
2. **Solving \(x + 6 > -2\)**:
\[
x + 6 > -2
\]
Subtract 6 from both sides:
\[
x > -8
\]
Now we combine the two solution sets. The two inequalities give us the following results:
- From \(4x - 3 > 9\), we have \(x > 3\).
- From \(x + 6 > -2\), we have \(x > -8\).
Since \(x > 3\) is the stricter condition (since 3 is greater than -8), the final solution set is:
\[
\{ x | x > 3 \}
\]
Thus, the correct response is:
\(\{x | x > 3\}\) (left brace x vertical bar x greater than 3 right brace).
Answered by
GPT-4o mini
To find the undefined value for the equation \( 14 = 7 \times 9 + 4x \), we first need to solve for \( x \).
Start by simplifying the equation:
1. Calculate \( 7 \times 9 \):
\[
7 \times 9 = 63
\]
2. Substitute this value back into the equation:
\[
14 = 63 + 4x
\]
3. Next, isolate \( 4x \) by subtracting 63 from both sides:
\[
14 - 63 = 4x
\]
\[
-49 = 4x
\]
4. Now, divide both sides by 4 to solve for \( x \):
\[
x = \frac{-49}{4}
\]
So, the value of \( x \) that makes the equation equal is \( x = -\frac{49}{4} \).
However, the question is asking for the undefined value, which seems to ask what \( x \) cannot be in terms of relevance to the context of the equation. Since there is nothing in the arithmetic that leads to division by zero or any other issue, \( x \) can take on any value except the specific solution calculated here.
Based on the provided options, it appears none specifically align with "undefined." However, the closest interpretation in that context would be:
- \( x \neq -\frac{49}{4} \) (which was computed).
None of the given options match that perfectly, but they do mention certain values that are not relevant. Therefore, to clarify, based on this evaluation:
The correct answer in general interpretation is that \( x \neq -\frac{49}{4} \) from the derived equation. If that option were available, it would be the answer. However, since none of the provided options matched, there is no valid choice here based on the original equation you supplied.
If there is still confusion about how to proceed, please share any further context or options, and I’d be glad to assist!
Start by simplifying the equation:
1. Calculate \( 7 \times 9 \):
\[
7 \times 9 = 63
\]
2. Substitute this value back into the equation:
\[
14 = 63 + 4x
\]
3. Next, isolate \( 4x \) by subtracting 63 from both sides:
\[
14 - 63 = 4x
\]
\[
-49 = 4x
\]
4. Now, divide both sides by 4 to solve for \( x \):
\[
x = \frac{-49}{4}
\]
So, the value of \( x \) that makes the equation equal is \( x = -\frac{49}{4} \).
However, the question is asking for the undefined value, which seems to ask what \( x \) cannot be in terms of relevance to the context of the equation. Since there is nothing in the arithmetic that leads to division by zero or any other issue, \( x \) can take on any value except the specific solution calculated here.
Based on the provided options, it appears none specifically align with "undefined." However, the closest interpretation in that context would be:
- \( x \neq -\frac{49}{4} \) (which was computed).
None of the given options match that perfectly, but they do mention certain values that are not relevant. Therefore, to clarify, based on this evaluation:
The correct answer in general interpretation is that \( x \neq -\frac{49}{4} \) from the derived equation. If that option were available, it would be the answer. However, since none of the provided options matched, there is no valid choice here based on the original equation you supplied.
If there is still confusion about how to proceed, please share any further context or options, and I’d be glad to assist!
Answered by
GPT-4o mini
Based on the provided options and the context of evaluating the undefined values of the equation, I would choose:
**x ≠ −\(\frac{49}{4}\)**
If I must pick one from your specific response options, I suggest choosing:
**x ≠ −94**
This is not directly related and doesn't represent a calculation result for the problem. However, it aligns more with the invalid values sometimes mentioned in hypothetical contexts.
If possible, double-check the problem for specifics or multiples for any instructional errors, as my earlier computations do not yield a valid option from your list. Thank you!
**x ≠ −\(\frac{49}{4}\)**
If I must pick one from your specific response options, I suggest choosing:
**x ≠ −94**
This is not directly related and doesn't represent a calculation result for the problem. However, it aligns more with the invalid values sometimes mentioned in hypothetical contexts.
If possible, double-check the problem for specifics or multiples for any instructional errors, as my earlier computations do not yield a valid option from your list. Thank you!
Answered by
GPT-4o mini
To solve for \( s \) in the equation \( 11s + 3 + 4 = 5 \), follow these steps:
1. Combine the constants on the left side:
\[
11s + 7 = 5
\]
2. Subtract 7 from both sides to isolate the term with \( s \):
\[
11s = 5 - 7
\]
\[
11s = -2
\]
3. Divide both sides by 11 to solve for \( s \):
\[
s = \frac{-2}{11}
\]
So the solution is:
\[
s = -\frac{2}{11}
\]
1. Combine the constants on the left side:
\[
11s + 7 = 5
\]
2. Subtract 7 from both sides to isolate the term with \( s \):
\[
11s = 5 - 7
\]
\[
11s = -2
\]
3. Divide both sides by 11 to solve for \( s \):
\[
s = \frac{-2}{11}
\]
So the solution is:
\[
s = -\frac{2}{11}
\]
Answered by
GPT-4o mini
To rearrange the area formula for a trapezoid, given by
\[
A = \frac{1}{2} h (b_1 + b_2)
\]
for the height \( h \), we need to solve for \( h \).
1. Start with the original formula:
\[
A = \frac{1}{2} h (b_1 + b_2)
\]
2. To isolate \( h \), first multiply both sides by 2:
\[
2A = h (b_1 + b_2)
\]
3. Now, divide both sides by \( (b_1 + b_2) \) to solve for \( h \):
\[
h = \frac{2A}{b_1 + b_2}
\]
From the given responses, the correct rearranged formula for \( h \) is:
**h = \(\frac{2A}{b_1 + b_2}\)**
So, the correct option is:
**h = \(\frac{2A}{b_1 + b_2}\)**
(h equals Start Fraction 2 upper A over b subscript 1 baseline plus b subscript 2 baseline End Fraction).
\[
A = \frac{1}{2} h (b_1 + b_2)
\]
for the height \( h \), we need to solve for \( h \).
1. Start with the original formula:
\[
A = \frac{1}{2} h (b_1 + b_2)
\]
2. To isolate \( h \), first multiply both sides by 2:
\[
2A = h (b_1 + b_2)
\]
3. Now, divide both sides by \( (b_1 + b_2) \) to solve for \( h \):
\[
h = \frac{2A}{b_1 + b_2}
\]
From the given responses, the correct rearranged formula for \( h \) is:
**h = \(\frac{2A}{b_1 + b_2}\)**
So, the correct option is:
**h = \(\frac{2A}{b_1 + b_2}\)**
(h equals Start Fraction 2 upper A over b subscript 1 baseline plus b subscript 2 baseline End Fraction).
Answered by
GPT-4o mini
The formula for time in terms of distance and velocity is given as:
\[
t = \frac{d}{v}
\]
To isolate the distance \( d \), you would need to manipulate the equation as follows:
1. Multiply both sides by \( v \) to eliminate the fraction:
\[
t \cdot v = d
\]
So, the operation you would use to isolate the distance \( d \) from the formula is **multiplication**.
Therefore, the correct response is:
**multiplication**.
\[
t = \frac{d}{v}
\]
To isolate the distance \( d \), you would need to manipulate the equation as follows:
1. Multiply both sides by \( v \) to eliminate the fraction:
\[
t \cdot v = d
\]
So, the operation you would use to isolate the distance \( d \) from the formula is **multiplication**.
Therefore, the correct response is:
**multiplication**.
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