The rectangle below has an area of 14x^4+6x^214x 4 +6x 2 square meters. the width of the rectangle (in meters) is equal to the greatest common monomial factor of 14x^414x 4 and 6x^26x 2 . what is the length and width of the rectangle?

Width = 2x² ,  Length = 7x² + 3

Step-by-step explanation:

The area of the rectangle = 14x⁴ + 6x²

The width of the rectangle (in meters) is equal to the greatest common monomial factor of 14x⁴ and 6x²

Factors of 14: 1 * 2 * 7

Factors of 6:  1 * 2 *     *3

∴ The greatest common monomial factor of 14 and 6 = 2

Factors of x⁴: x , x² , x³ , x⁴

Factors of x²: x , x²

∴ The greatest common factor of x⁴ and x² = x²

∴ Width = 2x²

∵ Area = length times  the width

∴ Length = Area/Width

Length =

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.