What is the value of x?
1 answer:
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<u>Given</u>:
The length of a rectangle is 5 less than its width.
The area of the rectangle is 84 square feet.
We need to determine the quadratic equation in standard form that represents the area of the rectangle.
<u>Dimensions of the rectangle:</u>
Let l denote the length of the rectangle.
Let w denote the width of the rectangle.
Since, it is given that the length is 5 less than its width, it can be written as,
and
<u>Area of the rectangle:</u>
The area of the rectangle can be determined using the formula,
Substituting A = 84, and
, we get
Adding both sides of the equation by w², we have;
Subtracting by 5w on both sides, we get;
Thus, the quadratic equation in standard form for the area of the rectangle is
To find the slope of a line that goes through given points with known coordinates, you divide the subtraction of the y of the second point minus the y of the first point, by the subtraction of the x of the second point minus the x of the first point:
m = (yB-yA) / (xB-xA)
Let A(8,5) and B(6,7).
With yB = 7; yA = 5; xB = 6; xA = 8
m = (7-5) / (6-8)
m = 2/-2
m = -1
So the slope of the line that goes through the given points (8,5) and (6,7) is m = -1.
I've added a pic of the line with both points under the answer.
Hope this Helps! :)
m = (yB-yA) / (xB-xA)
Let A(8,5) and B(6,7).
With yB = 7; yA = 5; xB = 6; xA = 8
m = (7-5) / (6-8)
m = 2/-2
m = -1
So the slope of the line that goes through the given points (8,5) and (6,7) is m = -1.
I've added a pic of the line with both points under the answer.
Hope this Helps! :)