Question

Which equation has the same solution as x−12=40

?
Responses

x2=14

x4=13

12−x=40

x+12=−40

Answer 1

[AI-generated answer — Bot GPT 3.5]

x+12=−40

Answer 2

why

Answer 3

[AI-generated answer — Bot GPT 3.5]

The equation x+12=−40 has the same solution as x−12=40 because if we rearrange the equation x+12=−40, we can subtract 12 from both sides to get x=-52. Similarly, if we rearrange x−12=40, we can add 12 to both sides to get x=52. Therefore, both equations have the solution x=52.

Answer 4

Given the formula A=2πr+h, solve for r.

r=A(2πr)−h

r=A−2π/h

r=A+h/2π

r=A−h/2π

Answer 5

[AI-generated answer — Bot GPT 3.5]

r=(A−h)/(2π)

Answer 6

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?

Responses

24 m

18 m

8 m

32 m

Answer 7

[AI-generated answer — Bot GPT 3.5]

Let's denote the width of the rectangle as "w". According to the given information, the length of the rectangle is four meters less than twice its width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding up the lengths of all four sides. In this case, the perimeter is given as 100 meters, so we can set up the equation:

2w + 2(2w - 4) = 100

Simplifying this equation, we get:

2w + 4w - 8 = 100
6w - 8 = 100
6w = 108
w = 18

Therefore, the width of the rectangle is 18 meters.

Answer 8

Max completed a 10 mile run in 1 hour 20 minutes. Which dimensional analysis would you use to find her average speed in miles per hour?

Responses

10 miles/1 1/3 hours×20 minutes/1 hour

10 miles/1.2 hours×24 hours/1 day

10 miles/120minutes×60 minutes/1 hour

10 miles/80minutes×60 minutes/1 hour

Answer 9

[AI-generated answer — Bot GPT 3.5]

The correct dimensional analysis to find Max's average speed in miles per hour would be:

10 miles / 1.2 hours × 60 minutes / 1 hour

This is because we want to convert the time of 1 hour 20 minutes to hours, so we multiply by 60 minutes / 1 hour.

Answer 10

Use the following setup and given equation to find the solution:

1st integer = x
2nd integer = x + 2
3rd integer = x + 4
The sum of the integers is : x + x + 2 + x + 4 = 222
. What is the 2nd integer?

Responses

222

64

74

111

Answer 11

[AI-generated answer — Bot GPT 3.5]

The correct response is 74.

To find the second integer, we need to solve the equation x + (x + 2) + (x + 4) = 222.

Combining like terms, we have 3x + 6 = 222.

Subtracting 6 from both sides, we get 3x = 216.

Dividing both sides by 3, we have x = 72.

Therefore, the second integer (x + 2) is 72 + 2, which equals 74.

Answer 12

Harold is collecting Nike Jordans. He currently has 23 pairs and plans to add 3 new pairs to his collection each month. At this rate, how many months will it take for Harold to have 50 pairs of Jordans?

Answer 13

[AI-generated answer — Bot GPT 3.5]

Let's denote the number of months as "m".

Each month, Harold adds 3 pairs to his collection, so after m months, he will have added 3m pairs.

We can set up an equation to represent the total number of pairs after m months:

23 + 3m = 50

To solve for m, we subtract 23 from both sides:

3m = 50 - 23
3m = 27

Next, we divide both sides by 3 to isolate m:

m = 27/3
m = 9

Therefore, it will take Harold 9 months to have 50 pairs of Jordans.

Answer 14

Identify each as True, False or Open. Answers may be used more than once or not at all.

Equation 1: 3(x − 4) + 2= 3x −10


Equation 2: 7x − 8x + 3 = 4(x + 5)

Equation 3: 5x−3=3(x −6) +2x

Answer 15

[AI-generated answer — Bot GPT 3.5]

Equation 1: True

Equation 2: False

Equation 3: Open

Answer 16

why

Answer 17

[AI-generated answer — Bot GPT 3.5]

Equation 1: True

This equation is true because if we simplify the left side of the equation, we get 3x - 12 + 2 = 3x - 10, which is equal to the right side of the equation.

Equation 2: False
This equation is false because if we simplify the left side of the equation, we get -x + 3 = 4x + 20, which is not equal to the right side of the equation.

Equation 3: Open
This equation is open because it depends on the value of x. To determine if it is true or false, we would need to simplify both sides of the equation and solve for x.