Translate to a quadratic equation, then solve using the quadratic formula. The length of a rectangular air filter is 3 inches less than twice the width. Find the length and width of the filter if the area is 527 square inches.

Width of the rectangle = 17 inches

Length of the rectangle = 31 inches

Step-by-step explanation:

Let w be the width of the rectangle.

Given:

Width of the rectangle = w

Length of the rectangle = 2w - 3

Area of the rectangle

Solution:

We know that the area of the rectangle.

Now, we first find the root of the above equation.

Use quadratic formula with .

Put a, b and c value in above equation.

For positive sign

w = 17 inches

So, width of the rectangle is 17 inches.

Length of the rectangle.

Length = 31 inches

So, length of the rectangle is 31 inches.

Therefore, width and length of the rectangle is 17 inches and 31 inches.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3