Considering the sign-up fee and monthly membership fee for a gym, the equation c = 30m + 25 can be used to represent the total cost of a gym membership for m months. What is the amount of the sign-up fee?

Question

(1 point)
Responses

$30
$30

$25
$25

$55
$55

$5
$5

Answer 1

The amount of the sign-up fee is $25.

Answer 2

Which equation is equivalent to 2x + 4a = 10?
(1 point)
Responses

x equals start fraction 5 over 4 end fraction a
Image with alt text: x equals start fraction 5 over 4 end fraction a

x equals 4 plus 2 a
Image with alt text: x equals 4 plus 2 a

x equals 10 minus 4 a
Image with alt text: x equals 10 minus 4 a

x equals 5 minus 2 a
Image with alt text: x equals 5 minus 2 a

Answer 3

The equation that is equivalent to 2x + 4a = 10 is x = 5 - 2a.

Answer 4

Which equation is equivalent to 2x + 4a = 10?

Answer 5

The equation x = 5 - 2a is equivalent to 2x + 4a = 10.

Answer 6

Name the property of real numbers illustrated by the equation.

5 plus (squre root of 15 plus 6) equals (5 plus square root of 15) plus 6

Answer 7

The property of real numbers illustrated by the equation is the Associative Property of Addition.

Answer 8

Name the property of real numbers illustrated by the equation.

pi ∙ 3 = 3 ∙ pi

Answer 9

The property of real numbers illustrated by the equation is the Commutative Property of Multiplication.

Answer 10

Which algebraic expression models the given word phrase?

6 times the sum of a and b

Answer 11

The algebraic expression that models the given word phrase "6 times the sum of a and b" is written as 6(a + b).

Answer 12

John has $305, and he is spending $3 each day. Which algebraic expression describes this situation, where d represents the number of days?

Answer 13

The algebraic expression that describes this situation, where d represents the number of days, is: 305 - 3d.

Answer 14

You are spending $144 for new sweaters, T-shirts, and pants. Sweaters (s) cost $28, T-shirts (t) cost $14, and pants (p) cost $23, each. Which equation represents this situation?

Answer 15

The equation that represents this situation is: 28s + 14t + 23p = 144.

Answer 16

Which inequality represents the following sentence?

Seven fewer than a number is at least 14.

Answer 17

The inequality that represents the sentence "Seven fewer than a number is at least 14" is: x - 7 ≥ 14.

Answer 18

Solve the absolute value equation.

|4x – 1| = 1

Answer 19

To solve the absolute value equation |4x - 1| = 1, we need to consider two cases: when 4x - 1 is positive and when it is negative.

Case 1: 4x - 1 is positive
In this case, we can remove the absolute value and set the expression inside it equal to 1: 4x - 1 = 1
Solving this equation, we get:
4x = 2
x = 1/2

Case 2: 4x - 1 is negative
In this case, we set the expression inside the absolute value equal to its negation: 4x - 1 = -1
Solving this equation, we get:
4x = 0
x = 0

So, the solutions to the equation are x = 1/2 and x = 0.

Answer 20

Which represents the solution to the absolute value equation?

2|x + 2| – 1 = 5

Answer 21

To solve the absolute value equation 2|x + 2| - 1 = 5, we can start by isolating the absolute value term and then solving for x.

First, add 1 to both sides of the equation to get rid of the -1:
2|x + 2| = 6

Next, divide both sides of the equation by 2 to isolate the absolute value:
|x + 2| = 3

Now, we can consider two cases: when x + 2 is positive and when it is negative.

Case 1: x + 2 is positive
In this case, we can remove the absolute value and set the expression inside it equal to 3: x + 2 = 3
Solving this equation, we get:
x = 1

Case 2: x + 2 is negative
In this case, we set the expression inside the absolute value equal to its negation: x + 2 = -3
Solving this equation, we get:
x = -5

So, the solutions to the equation are x = 1 and x = -5.

Answer 22

Solve the inequality. Graph the solution.

|2x + 7| ≤ 27

Answer 23

To solve the inequality |2x + 7| ≤ 27, we can consider two cases: when 2x + 7 is positive and when it is negative.

Case 1: 2x + 7 is positive
In this case, we can remove the absolute value and keep the expression inside it as is: 2x + 7 ≤ 27
Solving this inequality, we get:
2x ≤ 20
x ≤ 10

Case 2: 2x + 7 is negative
In this case, we set the expression inside the absolute value equal to its negation: -(2x + 7) ≤ 27
Solving this inequality, we get:
-2x - 7 ≤ 27
-2x ≤ 34
x ≥ -17

So, the solutions to the inequality are x ≤ 10 and x ≥ -17.

To graph the solution, we can plot a number line and shade the region between -17 and 10, including the endpoints, to represent the values of x that satisfy the inequality.

Answer 24

Write an inequality that models a real-world situation. Describe your situation and what the variable x represents.

Answer 25

Inequality: 5x + 10 > 30

Description of the situation:
Alice has a part-time job at a local coffee shop. She earns $5 per hour and starts with $10 in her pocket. She wants to have at least $30 to buy a new book.

Variable x:
The variable x represents the number of hours Alice works.