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.
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
7 answers
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
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.
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
The inequality that describes this scenario is:
2n + 24 ≤ 37
2n + 24 ≤ 37
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
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.
1 answer