Asked by _behindyou_
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?
An expression for the length of the rectangle in terms of the width would be Response area
If the area of the rectangle is 96 m^2, what is the length and the width?
An expression for the length of the rectangle in terms of the width would be Response area
Answers
Answered by
_behindyou_
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?
The formula for the area of a rectangle is Response area
If the area of the rectangle is 96 m^2, what is the length and the width?
The formula for the area of a rectangle is Response area
Answered by
_behindyou_
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?
2n + 24 is less than or equal to 37
24n + 2 is greater than or equal to 37
37 > 2n + 24
37 < 24n + 2
Let n represent the number of notebooks that he buys.
Which inequality describes this scenario?
2n + 24 is less than or equal to 37
24n + 2 is greater than or equal to 37
37 > 2n + 24
37 < 24n + 2
Answered by
_behindyou_
A student claims the graph below represents the solutions to the inequality −4 < x with this graph:
What was the student's mistake?
The student should have multiplied by a negative and switched the direction of the arrow on the graph to go right instead of left
The student should have multiplied by a negative and switched the direction of the arrow on the graph to go right instead of left
The student did not make a mistake; this is the correct graph of the inequality
The student did not make a mistake; this is the correct graph of the inequality
The student did x is less than -4, when the variable is on the other side; -4 is less than x so x is greater than -4
The student did x is less than -4, when the variable is on the other side; -4 is less than x so x is greater than -4
The student should have filled in the point at -4 to show the solution x could be equal to -4
The student should have filled in the point at -4 to show the solution x could be equal to -4
What was the student's mistake?
The student should have multiplied by a negative and switched the direction of the arrow on the graph to go right instead of left
The student should have multiplied by a negative and switched the direction of the arrow on the graph to go right instead of left
The student did not make a mistake; this is the correct graph of the inequality
The student did not make a mistake; this is the correct graph of the inequality
The student did x is less than -4, when the variable is on the other side; -4 is less than x so x is greater than -4
The student did x is less than -4, when the variable is on the other side; -4 is less than x so x is greater than -4
The student should have filled in the point at -4 to show the solution x could be equal to -4
The student should have filled in the point at -4 to show the solution x could be equal to -4
Answered by
GPT 3.5
Let the width of the rectangle be x meters.
Accordingly, the length of the rectangle is (2x - 4) meters.
The formula for the area of a rectangle is length * width.
Given that the area of the rectangle is 96 m^2, we can set up the following equation:
(x)(2x - 4) = 96
Simplifying the equation, we have:
2x^2 - 4x = 96
Dividing the equation by 2, we get:
x^2 - 2x = 48
Rearranging the equation, we have:
x^2 - 2x - 48 = 0
To solve this quadratic equation, we can factor it:
(x - 8)(x + 6) = 0
Setting each factor equal to zero, we find two possible solutions: x - 8 = 0 and x + 6 = 0.
Therefore, the width of the rectangle can be either 8 meters or -6 meters.
Since the width cannot be negative, we disregard the solution x = -6.
Thus, the width of the rectangle is 8 meters.
Substituting this value into the expression for the length, we find:
Length = 2(8) - 4 = 16 - 4 = 12 meters.
Therefore, the length of the rectangle is 12 meters and the width is 8 meters.
Accordingly, the length of the rectangle is (2x - 4) meters.
The formula for the area of a rectangle is length * width.
Given that the area of the rectangle is 96 m^2, we can set up the following equation:
(x)(2x - 4) = 96
Simplifying the equation, we have:
2x^2 - 4x = 96
Dividing the equation by 2, we get:
x^2 - 2x = 48
Rearranging the equation, we have:
x^2 - 2x - 48 = 0
To solve this quadratic equation, we can factor it:
(x - 8)(x + 6) = 0
Setting each factor equal to zero, we find two possible solutions: x - 8 = 0 and x + 6 = 0.
Therefore, the width of the rectangle can be either 8 meters or -6 meters.
Since the width cannot be negative, we disregard the solution x = -6.
Thus, the width of the rectangle is 8 meters.
Substituting this value into the expression for the length, we find:
Length = 2(8) - 4 = 16 - 4 = 12 meters.
Therefore, the length of the rectangle is 12 meters and the width is 8 meters.
Answered by
GPT 3.5
The formula for the area of a rectangle is A = length * width.
Let's represent the width of the rectangle as x meters.
Accordingly, the length of the rectangle is 2x - 4 meters, as it is four meters less than twice the width.
We know that the area of the rectangle is 96 m^2.
Using the formula for the area, we can write the following equation:
96 = (2x - 4) * x
Expanding the equation:
96 = 2x^2 - 4x
Rearranging the equation:
2x^2 - 4x - 96 = 0
Dividing the entire equation by 2:
x^2 - 2x - 48 = 0
This quadratic equation can be factored as:
(x - 8)(x + 6) = 0
Setting each factor equal to zero:
x - 8 = 0 or x + 6 = 0
Solving each equation:
x = 8 or x = -6
Since the width cannot be negative, we disregard the solution x = -6.
Therefore, the width of the rectangle is 8 meters.
Substituting this value into the expression for the length:
Length = 2(8) - 4 = 16 - 4 = 12 meters.
Therefore, the length of the rectangle is 12 meters and the width is 8 meters.
Let's represent the width of the rectangle as x meters.
Accordingly, the length of the rectangle is 2x - 4 meters, as it is four meters less than twice the width.
We know that the area of the rectangle is 96 m^2.
Using the formula for the area, we can write the following equation:
96 = (2x - 4) * x
Expanding the equation:
96 = 2x^2 - 4x
Rearranging the equation:
2x^2 - 4x - 96 = 0
Dividing the entire equation by 2:
x^2 - 2x - 48 = 0
This quadratic equation can be factored as:
(x - 8)(x + 6) = 0
Setting each factor equal to zero:
x - 8 = 0 or x + 6 = 0
Solving each equation:
x = 8 or x = -6
Since the width cannot be negative, we disregard the solution x = -6.
Therefore, the width of the rectangle is 8 meters.
Substituting this value into the expression for the length:
Length = 2(8) - 4 = 16 - 4 = 12 meters.
Therefore, the length of the rectangle is 12 meters and the width is 8 meters.
Answered by
GPT 3.5
The inequality that describes this scenario is:
2n + 24 ≤ 37
2n + 24 ≤ 37
Answered by
GPT 3.5
The student's mistake was that they did not fill in the point at -4 to show that x could be equal to -4.
The correct graph should have a filled-in dot at -4 to represent that x could take the value of -4.
The correct graph should have a filled-in dot at -4 to represent that x could take the value of -4.