Question

1. if the sum of the square of the number and 4 time the number is 21 what is the number?

Answer 1

Answer:

Step-by-step explanation:

1. Let the number be x

x^2 + 4x = 21

x^2 + 4x - 21 = 0

Solve the quadratic equation using factorization method

x^2 - 3x + 7x - 21 = 0

x(x - 3) + 7(x - 3) = 0

(x - 3)(x+7) = 0

x - 3 = 0 x + 7 = 0

x = 3 x = -7

The number is either 3 or -7

2. Same solution as number 1

3. Let

Width = x

Length = 2x - 3

Area of the rectangle = 9 square ft

Area of a rectangle = length × width

9 = (2x - 3) (x)

9 = 2x^2 - 3x

2x^2 - 3x - 9 = 0

Solve using quadratic formula

a = 2

b = -3

c = -9

x = -b +or- √b^2 - 4ac / 2a

= -(-3) +or- √(-3)^2 - 4(2)(-9) / 2(2)

= 3 +or- √ 9 - (-72) / 4

= 3 +or- √9 + 72 / 4

= 3 +or- √81 / 4

= 3 +or- 9 / 4

x = (3 + 9)/4 or (3 - 9) / 4

= 12 / 4 or -6 / 4

x = 3 or -3/2

Width can not be a negative value

So,

Width = x = 3 ft

Length = 2x - 3

= 2(3) - 3

= 6 - 3

= 3ft

2.if the sum of the square of the number and 4 time that number is 21 the what is the number?

3. the length of the rectangle is 3 less than twice the width. if the area is 9 square ft, the length and width of the rectangle.

4.given the figure below. find the area of the shaded part of the rectangle if the area of the big but angle is 6 times the area of the unshaded rectangle ​

Unshaded area

Length = 2x

Width = x

Shaded area

Length = (2x+3)

Width = (x+3)

Area of the shaded area = 6 × the unshaded area

(2x) (x) = 6(2x + 3)(x+3)

2x^2 = 6(2x^2 + 6x + 3x + 9)

2x^2 = 12x^2 + 36x + 9x + 54

2x^2 = 12x^2 + 45x + 54

12x^2 + 45x + 54 - 2x^2 = 0

10x^2 + 45x + 54 = 0