Tom is given the equation 10x+15=20
to solve. He says the solution is 12
. Which reason justifies his solution?(1 point) a b c d
Responses
Tom says that to solve the equation you first divide by 10 and then subtract 15.
Tom says that to solve the equation you first divide by 10 and then subtract 15.
Tom says that to solve the equation you first subtract 15 and then multiply by 10.
Tom says that to solve the equation you first subtract 15 and then multiply by 10.
Tom says that to solve the equation you first add 15 and then divide by 10.
Tom says that to solve the equation you first add 15 and then divide by 10.
Tom says that to solve the equation you first subtract 15 and then divide by 10.
Tom's solution is not justified because the correct process is to first subtract 15 and then divide by 10.
The correct reason that justifies Tom's solution is:
Tom says that to solve the equation, you first subtract 15 and then divide by 10.
Tom's solution is incorrect.
To solve the equation 10x + 15 = 20, we need to isolate the variable x.
The correct steps to solve the equation are:
1. Subtract 15 from both sides: 10x + 15 - 15 = 20 - 15, which simplifies to 10x = 5.
2. Divide both sides by 10: (10x)/10 = 5/10, which simplifies to x = 0.5.
Therefore, the correct solution to the equation is x = 0.5.
Tom's reason, "Tom says that to solve the equation you first subtract 15 and then divide by 10," is not valid. It is important to ensure the correct order of operations when solving equations.
a
b
c
d
None of the given options justifies Tom's solution. Tom's solution is incorrect as he stated that the solution is 12, which does not satisfy the equation 10x + 15 = 20.
a b c or d
None of the options a, b, c, or d justifies Tom's solution. Tom's solution is incorrect as he stated that the solution is 12, which does not satisfy the equation 10x + 15 = 20. The correct solution to the equation is x = 0.5.
Dr. Burrows is measuring the weight of a substance for a science experiment. He added a mystery substance (m) to his experiment. Dr. Burrows used the equation 13.93 + m = 18.0 to find out how much he added. How much of the mystery substance (m) did he add to his experiment?(1 point)
Responses
5.17
5.17
5.07
5.07
4.07
4.07
4.17
4.17
To find out how much of the mystery substance (m) Dr. Burrows added to his experiment, we need to isolate the variable m.
Given equation: 13.93 + m = 18.0
To isolate m, we subtract 13.93 from both sides of the equation:
(13.93 + m) - 13.93 = 18.0 - 13.93
Simplifying:
m = 18.0 - 13.93
m = 4.07
Therefore, Dr. Burrows added 4.07 units of the mystery substance (m) to his experiment.
Correct option: 4.07
Five times what number plus 10 equals 20?(1 point)
Responses
-6
-6
4
4
6
6
2
To solve the equation "Five times what number plus 10 equals 20," we need to rewrite the equation mathematically.
Let the number be represented by x.
The equation can be written as "5x + 10 = 20."
To solve for x, we can follow these steps:
1. Subtract 10 from both sides of the equation: 5x + 10 - 10 = 20 - 10, which simplifies to 5x = 10.
2. Divide both sides by 5: (5x)/5 = 10/5, which simplifies to x = 2.
Therefore, the number that satisfies the equation is 2.
The correct option is 2.
Solve for z.
z/5+3=2
(1 point)
Responses
5
5
−15
negative 1 fifth
-5
-5
15
To solve the equation (z/5) + 3 = 2, we need to isolate the variable z.
1. Subtract 3 from both sides of the equation: (z/5) + 3 - 3 = 2 - 3, which simplifies to z/5 = -1.
2. Multiply both sides by 5 to get rid of the fraction: (z/5) * 5 = -1 * 5, which simplifies to z = -5.
Therefore, the solution to the equation is z = -5.
The correct option is -5.
Find the solution to
4−2x=10
(1 point)
Responses
3
3
2
2
-7
-7
-3
-3
To solve the equation 4 - 2x = 10, we need to isolate the variable x.
1. Subtract 4 from both sides of the equation: (4 - 2x) - 4 = 10 - 4, which simplifies to -2x = 6.
2. Divide both sides by -2: (-2x)/-2 = 6/-2, which simplifies to x = -3.
Therefore, the solution to the equation is x = -3.
The correct option is -3.
Mariah wants to buy as many collectible dolls as possible, for $4.50 each. If she has $75.00 to spend, how many dolls can she buy? Which equation represents this situation?(1 point)
Responses
75d=4.5
75 d is equal to 4 point 5
d+4.5=75
d plus 4 point 5 is equal to 75
4.5d=75
4 point 5 d is equal to 75
d4.5=75
The correct equation that represents this situation is 4.5d = 75.
Let d represent the number of dolls Mariah can buy.
The equation states that the cost per doll (4.5) multiplied by the number of dolls (d) is equal to the total amount of money she has to spend (75).
By rearranging the equation and solving for d:
4.5d = 75
Divide both sides by 4.5:
d = 75/4.5
d ≈ 16.67
Since Mariah cannot buy a fraction of a doll, she can buy a whole number of dolls.
Therefore, Mariah can buy 16 dolls.
The correct option is 4.5d = 75.
If Jaylan takes the number of stamps he has and multiplies it by 5 and then subtracts 10, he gets 275. How many stamps does he have?(1 point)
Responses
57
57
53
53
23
2 thirds
13
1 third
To solve the equation "If Jaylan takes the number of stamps he has and multiplies it by 5 and then subtracts 10, he gets 275," we need to rewrite the equation mathematically.
Let the number of stamps Jaylan has be represented by x.
The equation can be written as "5x - 10 = 275."
To solve for x, we can follow these steps:
1. Add 10 to both sides of the equation: 5x - 10 + 10 = 275 + 10, which simplifies to 5x = 285.
2. Divide both sides by 5: (5x)/5 = 285/5, which simplifies to x = 57.
Therefore, Jaylan has 57 stamps.
The correct option is 57.
Which situation is best represented by the following equation?
40w+12.50=492.50
(1 point)
Responses
Nikayah paid $492.50 for ballet classes. She paid a $40 registration fee and $12.50 for each week she was enrolled in the classes. Solve for w to find the number of weeks Nikayah was enrolled in ballet classes.
Nikayah paid $492.50 for ballet classes. She paid a $40 registration fee and $12.50 for each week she was enrolled in the classes. Solve for w to find the number of weeks Nikayah was enrolled in ballet classes.
Nikayah paid $12.50 for ballet classes. She paid a $492.50 registration fee and $40 for each week she was enrolled in the classes. Solve for w to find the number of weeks Nikayah was enrolled in ballet classes.
Nikayah paid $12.50 for ballet classes. She paid a $492.50 registration fee and $40 for each week she was enrolled in the classes. Solve for w to find the number of weeks Nikayah was enrolled in ballet classes.
Nikayah paid $492.50 for ballet classes. She paid a $12.50 registration fee and $40 for each week she was enrolled in the classes. Solve for w to find the number of weeks Nikayah was enrolled in ballet classes.
Nikayah paid $492.50 for ballet classes. She paid a $12.50 registration fee and $40 for each week she was enrolled in the classes. Solve for w to find the number of weeks Nikayah was enrolled in ballet classes.
Nikayah paid $40 for ballet classes. She paid a $12.50 registration fee and $492.50 for each week she was enrolled in the classes. Solve for w to find the number of weeks Nikayah was enrolled in ballet classes
The situation best represented by the equation "40w + 12.50 = 492.50" is:
Nikayah paid $492.50 for ballet classes. She paid a $40 registration fee and $12.50 for each week she was enrolled in the classes. Solve for w to find the number of weeks Nikayah was enrolled in ballet classes.
The correct option is "Nikayah paid $492.50 for ballet classes. She paid a $40 registration fee and $12.50 for each week she was enrolled in the classes. Solve for w to find the number of weeks Nikayah was enrolled in ballet classes."
Bella bought b boxes of cookies to bring to a party. She decides to keep two boxes. Each box contains 18 cookies. She brings 90 cookies to the party. Which equation can be used to find the number of boxes, b, Bella bought? How many boxes did she buy?(1 point)
Responses
18b−2=90; b=5
18b−2=90; b=5
2b−18=90; b=54
2b−18=90; b=54
18b−36=90; b=7
18b−36=90; b=7
18b−36=90; b=6
To find the number of boxes, b, that Bella bought, we need to set up an equation based on the given information.
Bella initially bought b boxes of cookies, and she decided to keep two boxes. Each box contains 18 cookies. So, the number of cookies she brings to the party is (b - 2) * 18.
The equation that represents this situation is: (b - 2) * 18 = 90.
To solve for b, we can follow these steps:
1. Divide both sides of the equation by 18: ((b - 2) * 18) / 18 = 90 / 18, which simplifies to b - 2 = 5.
2. Add 2 to both sides of the equation: (b - 2) + 2 = 5 + 2, which simplifies to b = 7.
Therefore, Bella bought 7 boxes of cookies.
The correct option is 18b - 2 = 90; b = 5.
Delia spent $250 to rent a boat 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. How much does each additional hour of boat rental cost?(1 point)
Responses
$20
$20
$17
$17
$67
$67
$25
To find out how much each additional hour of boat rental costs, we need to determine the difference between the total cost of renting the boat for 6 hours and the base rate for the first 2 hours.
Delia spent $250 to rent the boat for 6 hours and the base rate for the first 2 hours is $150.
The additional cost for renting the boat for 4 extra hours is $250 - $150 = $100.
To find out how much each additional hour costs, we divide the additional cost by the number of additional hours, which is $100 / 4 = $25.
Therefore, each additional hour of boat rental costs $25.
The correct option is $25.
Solve the equation for y.
−1/5y+3=−7
(1 point)
Responses
50
50
-35
-35
15
15
55
To solve the equation (-1/5)y + 3 = -7, we can follow these steps:
1. Subtract 3 from both sides of the equation: (-1/5)y + 3 - 3 = -7 - 3, which simplifies to (-1/5)y = -10.
2. Multiply both sides by -5 to isolate y: (-1/5)y * -5 = -10 * -5, which simplifies to y = 50.
Therefore, the solution to the equation is y = 50.
The correct option is 50.
Darcy and JoJo are decorating cupcakes for a party. Darcy decorates 8 cupcakes which is 2 more than 13
the number of cupcakes that JoJo decorates. How many cupcakes does JoJo decorate?(1 point)
Responses
18
18
2
2
30
30
3
To find out how many cupcakes JoJo decorates, we need to find the number that Darcy decorates and then subtract 2.
Given that Darcy decorates 8 cupcakes, which is 2 more than the number of cupcakes JoJo decorates, we can set up the equation:
8 = 13 - 2
Simplifying the equation:
8 = 11
This equation is not possible, as 8 is not equal to 11.
Therefore, there is no valid response among the options provided for the number of cupcakes JoJo decorates.
What is the answer?
Based on the given information and equation, there is no valid response to determine the number of cupcakes JoJo decorates. The equation 8 = 13 - 2 yields an incorrect result, so we cannot determine the number of cupcakes JoJo decorates.
Tom is given the equation 10x +15=20 to solve. He says the solution is 1/2 . Which reason justifies his solution?(1 point) Responses Tom says that to solve the equation you first divide by 10 and then subtract 15. Tom says that to solve the equation you first divide by 10 and then subtract 15. Tom says that to solve the equation you first subtract 15 and then multiply by 10. Tom says that to solve the equation you first subtract 15 and then multiply by 10. Tom says that to solve the equation you first add 15 and then divide by 10. Tom says that to solve the equation you first add 15 and then divide by 10. Tom says that to solve the equation you first subtract 15 and then divide by 10.
Tom's solution is justified by the reason: "Tom says that to solve the equation you first subtract 15 and then divide by 10."
To solve the equation 10x + 15 = 20, we need to isolate the variable x.
Following Tom's reasoning, the steps to solve the equation are:
1. Subtract 15 from both sides of the equation: 10x + 15 - 15 = 20 - 15, which simplifies to 10x = 5.
2. Divide both sides by 10: (10x)/10 = 5/10, which simplifies to x = 1/2.
Therefore, the solution to the equation is x = 1/2.
The correct option is "Tom says that to solve the equation you first subtract 15 and then divide by 10."
When multiplying two rational numbers, how is the sign of the product determined?(1 point) Responses The product is positive if the signs of the factors are the same. The product is positive if the signs of the factors are the same. The product is negative if the signs of the factors are the same. The product is negative if the signs of the factors are the same. The sign of the product is always the same as the larger factor. The sign of the product is always the same as the larger factor. The sign of the product is always the same as the smaller factor.
The product is positive if the signs of the factors are the same.
Solve for x. −3x 4=−8 (1 point) Responses 43 4 thirds -4 -4 4 4 −43 negative 4 thirds
To solve the equation -3x + 4 = -8, we can follow these steps:
1. Subtract 4 from both sides of the equation: -3x + 4 - 4 = -8 - 4, which simplifies to -3x = -12.
2. Divide both sides by -3: (-3x)/-3 = -12/-3, which simplifies to x = 4.
Therefore, the solution to the equation is x = 4.
The correct option is 4.
Solve for w. −0.1w +23.2=−0.8 (1 point) Responses -224 -224 -240 -240 240 240 224 224
To solve the equation -0.1w + 23.2 = -0.8, we can follow these steps:
1. Subtract 23.2 from both sides of the equation: -0.1w + 23.2 - 23