Question
Tom needs to solve this equation for x.
3x−5=26
Which would be the best first step Tom could make to solve the equation?
(1 point)
Responses
add 5 to both sides of the equation
add 5 to both sides of the equation
subtract 5 from the left side of the equation
subtract 5 from the left side of the equation
divide both sides of the equation by 26
divide both sides of the equation by 26
divide 2x by 2
The length of a rectangle is four meters less than twice its width. If the perimeter of the rectangle is 100 meters, what is the width?(1 point)
Responses
8m
8m
24m
24m
32m
32m
18m
Given the formula A=2πr+h
, solve for r.(1 point)
Responses
r=A+h2π
r is equal to the fraction with numerator cap A plus h and denominator 2 pi
r=A−h2π
r is equal to the fraction with numerator cap A minus h and denominator 2 pi
r=A−2πh
r is equal to the fraction with numerator cap A minus 2 pi and denominator h
r=A(2πr)−h
Which equation has the same solution as x−12=40
?(1 point)
Responses
12−x=40
12 minus x is equal to 40
x4=13
x over 4 is equal to 13
x2=14
x over 2 is equal to 14
x+12=−40
3x−5=26
Which would be the best first step Tom could make to solve the equation?
(1 point)
Responses
add 5 to both sides of the equation
add 5 to both sides of the equation
subtract 5 from the left side of the equation
subtract 5 from the left side of the equation
divide both sides of the equation by 26
divide both sides of the equation by 26
divide 2x by 2
The length of a rectangle is four meters less than twice its width. If the perimeter of the rectangle is 100 meters, what is the width?(1 point)
Responses
8m
8m
24m
24m
32m
32m
18m
Given the formula A=2πr+h
, solve for r.(1 point)
Responses
r=A+h2π
r is equal to the fraction with numerator cap A plus h and denominator 2 pi
r=A−h2π
r is equal to the fraction with numerator cap A minus h and denominator 2 pi
r=A−2πh
r is equal to the fraction with numerator cap A minus 2 pi and denominator h
r=A(2πr)−h
Which equation has the same solution as x−12=40
?(1 point)
Responses
12−x=40
12 minus x is equal to 40
x4=13
x over 4 is equal to 13
x2=14
x over 2 is equal to 14
x+12=−40
Answers
GPT-4o mini
Let's go through each question one by one:
1. **For the equation:**
**3x − 5 = 26**
The best first step Tom could make to solve the equation is to **add 5 to both sides of the equation.**
- This will simplify the equation to 3x = 31, making it easier to isolate x.
2. **For the rectangle's width given the perimeter:**
The problem states that the length (L) is four meters less than twice the width (W), or:
**L = 2W - 4**
The perimeter (P) of a rectangle is given by the formula:
**P = 2L + 2W**
Setting the perimeter equal to 100 meters gives:
**2L + 2W = 100**
Substituting the expression for L into the perimeter equation:
**2(2W - 4) + 2W = 100**
Solving this yields:
**4W - 8 + 2W = 100**
**6W - 8 = 100**
**6W = 108**
**W = 18**
Therefore, the width of the rectangle is **18m**.
3. **Given the formula:**
**A = 2πr + h**
To solve for r, we first isolate the term containing r:
**A - h = 2πr**
Then, we divide both sides by 2π:
**r = (A - h) / (2π)**
The correct response here is:
**r = A − h / 2π** (correctly stated as r is equal to the fraction with numerator A minus h and denominator 2π).
4. **Which equation has the same solution as x − 12 = 40?**
We can add 12 to both sides of the original equation:
**x - 12 + 12 = 40 + 12**
This simplifies to x = 52.
To find which option has the same solution, we analyze the choices:
- **12 − x = 40** → rearranging gives x = -28 (not the same)
- **x/4 = 13** → gives x = 52 (same solution)
- **x/2 = 14** → gives x = 28 (not the same)
- **x + 12 = −40** → gives x = -52 (not the same)
The correct response is:
**x/4 = 13**, which has the same solution as the original equation.
In summary, the answers are:
1. Add 5 to both sides of the equation.
2. 18m.
3. r = (A - h) / (2π).
4. x/4 = 13.
1. **For the equation:**
**3x − 5 = 26**
The best first step Tom could make to solve the equation is to **add 5 to both sides of the equation.**
- This will simplify the equation to 3x = 31, making it easier to isolate x.
2. **For the rectangle's width given the perimeter:**
The problem states that the length (L) is four meters less than twice the width (W), or:
**L = 2W - 4**
The perimeter (P) of a rectangle is given by the formula:
**P = 2L + 2W**
Setting the perimeter equal to 100 meters gives:
**2L + 2W = 100**
Substituting the expression for L into the perimeter equation:
**2(2W - 4) + 2W = 100**
Solving this yields:
**4W - 8 + 2W = 100**
**6W - 8 = 100**
**6W = 108**
**W = 18**
Therefore, the width of the rectangle is **18m**.
3. **Given the formula:**
**A = 2πr + h**
To solve for r, we first isolate the term containing r:
**A - h = 2πr**
Then, we divide both sides by 2π:
**r = (A - h) / (2π)**
The correct response here is:
**r = A − h / 2π** (correctly stated as r is equal to the fraction with numerator A minus h and denominator 2π).
4. **Which equation has the same solution as x − 12 = 40?**
We can add 12 to both sides of the original equation:
**x - 12 + 12 = 40 + 12**
This simplifies to x = 52.
To find which option has the same solution, we analyze the choices:
- **12 − x = 40** → rearranging gives x = -28 (not the same)
- **x/4 = 13** → gives x = 52 (same solution)
- **x/2 = 14** → gives x = 28 (not the same)
- **x + 12 = −40** → gives x = -52 (not the same)
The correct response is:
**x/4 = 13**, which has the same solution as the original equation.
In summary, the answers are:
1. Add 5 to both sides of the equation.
2. 18m.
3. r = (A - h) / (2π).
4. x/4 = 13.