Asked by Glitchtrap
Consider the equation 12=6x8x−5
Which term helps determine the equation's undefined value?
(1 point)
Responses
12
12
8x−5
8 x minus 5
6x
6 x
Question 2
Find the undefined value.(1 point)
x≠
Which term helps determine the equation's undefined value?
(1 point)
Responses
12
12
8x−5
8 x minus 5
6x
6 x
Question 2
Find the undefined value.(1 point)
x≠
Answers
Answered by
Glitchtrap
Solve for s
in the following equation: 12s+5+7=8
(2 points)
s =
in the following equation: 12s+5+7=8
(2 points)
s =
Answered by
Glitchtrap
Given the formula for time (t
) in terms of distance (d
) and velocity (v
), t=dv
, what operation would you use to isolate the distance?(2 points)
Responses
addition
addition
subtraction
subtraction
multiplication
multiplication
division
) in terms of distance (d
) and velocity (v
), t=dv
, what operation would you use to isolate the distance?(2 points)
Responses
addition
addition
subtraction
subtraction
multiplication
multiplication
division
Answered by
Glitchtrap
Sebastian needed to buy new tires for his car. The tire shop was running a holiday deal that allowed customers to buy three tires and get the fourth tire for $10. If the total price for all his tires was $254.50, what was the cost of each of the first three tires?(2 points)
$
$
Answered by
Glitchtrap
Using the properties of inequality, justify both steps in solving the inequality 25m−8<−2
.(2 points)
25m−8<−2
25m−8+8<−2+8
52(25m)<52(6)
Question 2
Solve for m
(1 point)
.(2 points)
25m−8<−2
25m−8+8<−2+8
52(25m)<52(6)
Question 2
Solve for m
(1 point)
Answered by
Glitchtrap
Consider the equation 5x3x−15+7=14
(1 point)
Which part of the fraction determines if it is undefined?
Question 2
(2 points)
Therefore, for the equation to be defined,
≠0
This means that x≠
(1 point)
Which part of the fraction determines if it is undefined?
Question 2
(2 points)
Therefore, for the equation to be defined,
≠0
This means that x≠
Answered by
GPT-4o mini
To determine the undefined value of the equation \( 12 = 6x \cdot (8x - 5) \), we need to identify the term that can cause the equation to be undefined.
The term that helps determine the undefined value is \( 8x - 5 \). This term could be equal to zero, which would result in an undefined situation in the context of the equation.
To find the undefined value, we set \( 8x - 5 = 0 \):
\[
8x - 5 = 0
\]
\[
8x = 5
\]
\[
x = \frac{5}{8}
\]
Thus, the undefined value is:
\[
x \neq \frac{5}{8}
\]
### Responses:
1. The term that helps determine the equation's undefined value: **8x - 5**
2. The undefined value: **x ≠ \(\frac{5}{8}\)**
The term that helps determine the undefined value is \( 8x - 5 \). This term could be equal to zero, which would result in an undefined situation in the context of the equation.
To find the undefined value, we set \( 8x - 5 = 0 \):
\[
8x - 5 = 0
\]
\[
8x = 5
\]
\[
x = \frac{5}{8}
\]
Thus, the undefined value is:
\[
x \neq \frac{5}{8}
\]
### Responses:
1. The term that helps determine the equation's undefined value: **8x - 5**
2. The undefined value: **x ≠ \(\frac{5}{8}\)**
Answered by
GPT-4o mini
To solve for \( s \) in the equation \( 12s + 5 + 7 = 8 \), follow these steps:
1. Combine like terms on the left side of the equation:
\[
12s + (5 + 7) = 8 \implies 12s + 12 = 8
\]
2. Subtract 12 from both sides:
\[
12s + 12 - 12 = 8 - 12 \implies 12s = -4
\]
3. Divide both sides by 12:
\[
s = \frac{-4}{12} \implies s = \frac{-1}{3}
\]
The solution is:
\[
s = -\frac{1}{3}
\]
1. Combine like terms on the left side of the equation:
\[
12s + (5 + 7) = 8 \implies 12s + 12 = 8
\]
2. Subtract 12 from both sides:
\[
12s + 12 - 12 = 8 - 12 \implies 12s = -4
\]
3. Divide both sides by 12:
\[
s = \frac{-4}{12} \implies s = \frac{-1}{3}
\]
The solution is:
\[
s = -\frac{1}{3}
\]
Answered by
GPT-4o mini
The formula for time \( t \) in terms of distance \( d \) and velocity \( v \) is given by:
\[
t = \frac{d}{v}
\]
To isolate distance \( d \), you need to eliminate the velocity \( v \) from the right side of the equation. Since \( d \) is divided by \( v \), you would perform the inverse operation of division, which is multiplication.
Thus, you would **multiply** both sides of the equation by \( v \):
\[
d = t \cdot v
\]
### Response:
**Multiplication**
\[
t = \frac{d}{v}
\]
To isolate distance \( d \), you need to eliminate the velocity \( v \) from the right side of the equation. Since \( d \) is divided by \( v \), you would perform the inverse operation of division, which is multiplication.
Thus, you would **multiply** both sides of the equation by \( v \):
\[
d = t \cdot v
\]
### Response:
**Multiplication**
Answered by
GPT-4o mini
Let's denote the cost of each of the first three tires as \( x \). According to the deal, if he buys three tires, the fourth tire costs $10. Therefore, the total cost can be expressed by the equation:
\[
3x + 10 = 254.50
\]
Now, we can solve for \( x \):
1. Subtract $10 from both sides to isolate the cost of the three tires:
\[
3x = 254.50 - 10
\]
\[
3x = 244.50
\]
2. Next, divide both sides by 3 to find the cost of one tire:
\[
x = \frac{244.50}{3}
\]
\[
x = 81.50
\]
Thus, the cost of each of the first three tires is:
\[
\boxed{81.50}
\]
\[
3x + 10 = 254.50
\]
Now, we can solve for \( x \):
1. Subtract $10 from both sides to isolate the cost of the three tires:
\[
3x = 254.50 - 10
\]
\[
3x = 244.50
\]
2. Next, divide both sides by 3 to find the cost of one tire:
\[
x = \frac{244.50}{3}
\]
\[
x = 81.50
\]
Thus, the cost of each of the first three tires is:
\[
\boxed{81.50}
\]
Answered by
GPT-4o mini
Let's solve the inequality step by step and justify each operation.
1. **Starting Inequality**:
\[
25m - 8 < -2
\]
2. **Step 1: Add 8 to both sides**:
\[
25m - 8 + 8 < -2 + 8
\]
The justification for this step is the **addition property of inequalities**, which states that if \( a < b \), then \( a + c < b + c \) for any real number \( c \). Here, \( c = 8 \).
After performing the operation:
\[
25m < 6
\]
3. **Step 2: Divide both sides by 25**:
\[
\frac{25m}{25} < \frac{6}{25}
\]
The justification for this step is the **division property of inequalities**, which states that if \( a < b \) and \( c > 0 \), then \( \frac{a}{c} < \frac{b}{c} \). Here, \( c = 25 \), which is greater than 0.
So, after this operation:
\[
m < \frac{6}{25}
\]
### Question 2 - Solve for \( m \):
Thus, the solution to the inequality is:
\[
\boxed{m < \frac{6}{25}}
\]
1. **Starting Inequality**:
\[
25m - 8 < -2
\]
2. **Step 1: Add 8 to both sides**:
\[
25m - 8 + 8 < -2 + 8
\]
The justification for this step is the **addition property of inequalities**, which states that if \( a < b \), then \( a + c < b + c \) for any real number \( c \). Here, \( c = 8 \).
After performing the operation:
\[
25m < 6
\]
3. **Step 2: Divide both sides by 25**:
\[
\frac{25m}{25} < \frac{6}{25}
\]
The justification for this step is the **division property of inequalities**, which states that if \( a < b \) and \( c > 0 \), then \( \frac{a}{c} < \frac{b}{c} \). Here, \( c = 25 \), which is greater than 0.
So, after this operation:
\[
m < \frac{6}{25}
\]
### Question 2 - Solve for \( m \):
Thus, the solution to the inequality is:
\[
\boxed{m < \frac{6}{25}}
\]
Answered by
GPT-4o mini
To analyze the equation given:
\[
5x \cdot (3x - 15) + 7 = 14
\]
Let's simplify it for clarity. The fraction isn't directly evident in your equation. However, if you are referring to potential division by a term that could be zero, we can proceed with that assumption. If the equation was implied to have any fraction, it can often stem from rearranging the equation.
### Question 1
1. **Which part of the fraction determines if it is undefined?**
If there was a term like \( 3x - 15 \) acting as a denominator in a fraction, that could lead to being undefined if equal to zero.
2. **Identifying the term**:
- The term sometimes leading to an undefined value would be **\( 3x - 15 \)**.
### Question 2
**To determine under what conditions this term does not equal zero:**
- Set the term to zero:
\[
3x - 15 = 0
\]
- Solving for \( x \):
\[
3x = 15 \\
x = 5
\]
**Therefore, for the equation to be defined**:
\[
3x - 15 \neq 0
\]
This means that:
\[
x \neq 5
\]
### Final Answers:
1. The term that determines if the equation is undefined: **\( 3x - 15 \)**
2. Therefore, for the equation to be defined: \( x \neq 5 \)
\[
5x \cdot (3x - 15) + 7 = 14
\]
Let's simplify it for clarity. The fraction isn't directly evident in your equation. However, if you are referring to potential division by a term that could be zero, we can proceed with that assumption. If the equation was implied to have any fraction, it can often stem from rearranging the equation.
### Question 1
1. **Which part of the fraction determines if it is undefined?**
If there was a term like \( 3x - 15 \) acting as a denominator in a fraction, that could lead to being undefined if equal to zero.
2. **Identifying the term**:
- The term sometimes leading to an undefined value would be **\( 3x - 15 \)**.
### Question 2
**To determine under what conditions this term does not equal zero:**
- Set the term to zero:
\[
3x - 15 = 0
\]
- Solving for \( x \):
\[
3x = 15 \\
x = 5
\]
**Therefore, for the equation to be defined**:
\[
3x - 15 \neq 0
\]
This means that:
\[
x \neq 5
\]
### Final Answers:
1. The term that determines if the equation is undefined: **\( 3x - 15 \)**
2. Therefore, for the equation to be defined: \( x \neq 5 \)