To find the equation that has a solution of x = -3, you need to substitute -3 into each equation and see which one results in a true statement.
A: 2(-3) - 7 = -12
-6 - 7 ≠ -12
Therefore, A is not the correct equation.
B: 3(-3) + 8 = 13
-9 + 8 ≠ 13
Therefore, B is not the correct equation.
C: (1/2)(-3) + 8 = 10
-1.5 + 8 = 10
6.5 ≠ 10
Therefore, C is not the correct equation.
D: (1/2)(2(-3) - 6) = -6
(1/2)(-6 - 6) = -6
(1/2)(-12) = -6
-6 = -6
Therefore, D is the correct equation.
E: (1/2)(4(-3) - 8) = -2
(1/2)(-12 - 8) = -2
(1/2)(-20) = -2
-10 ≠ -2
Therefore, E is not the correct equation.
The equation that has a solution of x = -3 is D: 1/2(2x - 6) = -6.
Which equation has solution x = -3?
Responses
A 2x - 7 = -12
B 3x + 8 = 13
C 1/2 x + 8 = 10
D 1/2(2x - 6) = -6
E 1/2(4x - 8) = -2
11 answers
Which situation is best represented by the following equation?
40w + 12.50 = 492.50
Responses
A Nicole paid $40 for self-defense classes. She paid a $12.50 registration fee and $492.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?Nicole paid $40 for self-defense classes. She paid a $12.50 registration fee and $492.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
B Nicole paid $12.50 for self-defense classes. She paid a $492.50 registration fee and $40 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?Nicole paid $12.50 for self-defense classes. She paid a $492.50 registration fee and $40 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
C Nicole paid $492.50 for self-defense classes. She paid a $40 registration fee and $12.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?Nicole paid $492.50 for self-defense classes. She paid a $40 registration fee and $12.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
D Nicole paid $492.50 for self-defense classes. She paid a $12.50 registration fee and $40 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
40w + 12.50 = 492.50
Responses
A Nicole paid $40 for self-defense classes. She paid a $12.50 registration fee and $492.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?Nicole paid $40 for self-defense classes. She paid a $12.50 registration fee and $492.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
B Nicole paid $12.50 for self-defense classes. She paid a $492.50 registration fee and $40 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?Nicole paid $12.50 for self-defense classes. She paid a $492.50 registration fee and $40 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
C Nicole paid $492.50 for self-defense classes. She paid a $40 registration fee and $12.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?Nicole paid $492.50 for self-defense classes. She paid a $40 registration fee and $12.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
D Nicole paid $492.50 for self-defense classes. She paid a $12.50 registration fee and $40 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
The equation is 40w + 12.50 = 492.50.
This equation represents the scenario described in option D: Nicole paid $492.50 for self-defense classes. She paid a $12.50 registration fee and $40 for each week she was enrolled in the classes. The variable w represents the number of weeks Nicole was enrolled in self-defense classes.
This equation represents the scenario described in option D: Nicole paid $492.50 for self-defense classes. She paid a $12.50 registration fee and $40 for each week she was enrolled in the classes. The variable w represents the number of weeks Nicole was enrolled in self-defense classes.
What is the distance between 32 and -67 on a number line?
Responses
A -35
B 35
C 45
D 49.5
E 99
Responses
A -35
B 35
C 45
D 49.5
E 99
To find the distance between two numbers on a number line, you subtract the smaller number from the larger number and take the absolute value of the result.
In this case, you have 32 and -67. Taking the absolute value of the difference of these two numbers gives you the distance.
|32 - (-67)| = |32 + 67| = |99| = 99
Therefore, the distance between 32 and -67 on a number line is 99. The correct answer is E.
In this case, you have 32 and -67. Taking the absolute value of the difference of these two numbers gives you the distance.
|32 - (-67)| = |32 + 67| = |99| = 99
Therefore, the distance between 32 and -67 on a number line is 99. The correct answer is E.
A taxi fare has a fixed charge of $1.75 and an additional charge $0.45 per mile. A fare for m miles is $13.90. Which equation could be used to find m miles?
Responses
A 1.75(13.90 + m) = 1
B 1.75 + 0.45m = 13.90
C 0 45 + 1.75m = 13.90
D (0.45 + 11.20)m = 1.75
Responses
A 1.75(13.90 + m) = 1
B 1.75 + 0.45m = 13.90
C 0 45 + 1.75m = 13.90
D (0.45 + 11.20)m = 1.75
To find the correct equation to determine the number of miles (m), we can set up an equation based on the given information.
The fixed charge is $1.75, and the additional charge per mile is $0.45. The total fare for m miles is $13.90.
We can set up the equation as:
1.75 + 0.45m = 13.90.
Therefore, the correct equation to find the number of miles (m) is B: 1.75 + 0.45m = 13.90.
The fixed charge is $1.75, and the additional charge per mile is $0.45. The total fare for m miles is $13.90.
We can set up the equation as:
1.75 + 0.45m = 13.90.
Therefore, the correct equation to find the number of miles (m) is B: 1.75 + 0.45m = 13.90.
Dwight spent $250 to rent a jet ski for 6 hours. The rental company charges a base rate of $150 for the first two 2 hours, and then an hourly rate for each additional hour, h. The equation 4h + 150 = 250 models Dwight's cost of renting the jet ski. How much does each additional hour of rental cost?
Responses
A $20
B $25
C $30
D $45
Responses
A $20
B $25
C $30
D $45
To find the cost of each additional hour of rental, we need to solve the equation:
4h + 150 = 250
First, we isolate h by subtracting 150 from both sides:
4h = 250 - 150
4h = 100
Then, we divide both sides by 4 to solve for h:
h = 100 / 4
h = 25
Therefore, each additional hour of rental costs $25. The correct answer is B: $25.
4h + 150 = 250
First, we isolate h by subtracting 150 from both sides:
4h = 250 - 150
4h = 100
Then, we divide both sides by 4 to solve for h:
h = 100 / 4
h = 25
Therefore, each additional hour of rental costs $25. The correct answer is B: $25.
Crystal bought b boxes of cookies to bring to a party. Each box contains 18 cookies. She decides to keep two boxes for herself. She brings 90 cookies to the party. Which equation can be used to find the number of b boxes Crystal bought?
To find the number of boxes of cookies Crystal bought, we can set up the following equation based on the given information:
(b - 2) * 18 = 90
Here, (b - 2) represents the number of boxes Crystal brings to the party, as she kept two boxes for herself. We multiply this number by 18, as each box contains 18 cookies. The result should be equal to the total number of cookies she brings to the party, which is 90.
Therefore, the correct equation to find the number of boxes Crystal bought is:
(b - 2) * 18 = 90.
(b - 2) * 18 = 90
Here, (b - 2) represents the number of boxes Crystal brings to the party, as she kept two boxes for herself. We multiply this number by 18, as each box contains 18 cookies. The result should be equal to the total number of cookies she brings to the party, which is 90.
Therefore, the correct equation to find the number of boxes Crystal bought is:
(b - 2) * 18 = 90.
2 answers