The length of a rectangle is four meters less than twice its width. If the area of the rectangle is 96 m^2, what is the length and the width? (3 points)
An expression for the length of the rectangle in terms of the width would be: ______
The formula for the area of a rectangle is: ______
Using trial and error, if the area is 96 m^2, then the length and width are: _____
3i+5=3i+7
An expression for the length of the rectangle in terms of the width would be: 2w - 4
The formula for the area of a rectangle is: length × width
Using trial and error, if the area is 96 m^2, then the length and width are: length = 12 m and width = 8 m
Match the equation with its solution(s).(5 points)
3(2i+7)=61+21
3(2i+7) = 61 + 21
Multiply:
6i + 21 = 82
Subtract 21 from both sides:
6i = 61
Divide by 6:
i = 10.17
The solution is i = 10.17
3(2i+7)=6i+21
3(2i+7) = 6i + 21
Distribute:
6i + 21 = 6i + 21
Subtract 6i from both sides:
21 = 21
The equation is true for all values of i. There are infinitely many solutions.
3i+5=2i-7
3i + 5 = 2i - 7
Subtract 2i from both sides:
i + 5 = -7
Subtract 5 from both sides:
i = -12
The solution is i = -12.
3(2i-7)=15
3(2i - 7) = 15
Distribute:
6i - 21 = 15
Add 21 to both sides:
6i = 36
Divide by 6:
i = 6
The solution is i = 6.
3i + 5 = 3i + 7
Subtract 3i from both sides:
5 = 7
This equation is not possible as 5 does not equal 7. Therefore, there is no solution.
3i+2i-7=18
3i + 2i - 7 = 18
Combine like terms:
5i - 7 = 18
Add 7 to both sides:
5i = 25
Divide by 5:
i = 5
The solution is i = 5.
Solve the equation justifying each step with the correct reasoning.
2(x+8)=2x+8
(5 points)
2(x+8) = 2x + 8
Distribute the 2:
2x + 16 = 2x + 8
Subtract 2x from both sides:
16 = 8
This equation is not possible as 16 does not equal 8. Therefore, there is no solution.
Match the description of the one variable equation with the number of solutions it will have.(4 points)
A: x−7=7−x =
B: 3(x+5)=3x+5 =
C: 10−x=25 =
D: 2(x+4)=2x+5+3 =
A: x-7=7-x - This equation will have one solution.
B: 3(x+5)=3x+5 - This equation will have infinitely many solutions.
C: 10-x=25 - This equation will have one solution.
D: 2(x+4)=2x+5+3 - This equation will have no solutions.
A student wants to purchase some new school supplies. He wants to buy a calculator that costs $24 and some notebooks for school. Each notebook costs $2. The student only has $37 to spend.
Let n represent the number of notebooks that he buys.
Which inequality describes this scenario?
(1 point)
The inequality that describes this scenario is:
2n + 24 ≤ 37
A student wants to purchase some new school supplies. He wants to buy a calculator that costs $24 and some notebooks for school. Each notebook costs $2. The student only has $37 to spend.
Let n represent the number of notebooks that he buys.
Which inequality describes this scenario?
(1 point)
Responses
37 > 2n + 24
24n + 2 ≥ 37
37 ≥ 2n + 24
37 < 2n + 24