The function p(x) = 3x2 + 4x + 5,is dilated by the function i(x) = p(2x). write the new function i(x).

I(x) = 12x² + 8x + 5

Step-by-step explanation:

* Lets talk about the solution

- P(x) is a quadratic function represented graphically by a parabola

- The general form of the quadratic function is f(x) = ax² + bx + c,

  where a is the coefficient of x² and b is the coefficient of x and c is

  the y-intercept

- To find I(x) from P(x) change each x in P by 2x

∵ P(x) is dilated to I(x) by change x by 2x

∵ I(x) = P(2x)

∵ P(x) = 3x² + 4x + 5

∴ I(x) = 3(2x)² + 4(2x) + 5 ⇒ simplify

∵ (2x)² = (2)² × (x)² = 4 × x² = 4x²

∵ 4(2x) = 8x

∴ I(x) = 3(4x²) + 8x + 5

∵ 3(4x²) = 12x²

∴ I(x) = 12x² + 8x + 5

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6

x is greater than 5

step-by-step explanation:

2x+7 is greater than 17

    -7                           -7

2x is greater than 10

divide by 2 each side

x is greater than 5