Emmy throws a doggy toy up in the air. The path of the toy is modeled by the function f(x)=−x^2+4x+5, where x is the number of feet the toy is from Emmy and f(x) is the height of the toy. What is the maximum height of the toy?

9feet

Step-by-step explanation:

Given the path of the toy modeled by the function f(x)=−x^2+4x+5, where x is the number of feet the toy is from Emmy and f(x) is the height of the toy.

AT maximum height, the velocity of the toy will be zero. Hence;

df(x)/dx = 0

-2x + 4 = 0

-2x = -4

x = -4/-2

x = 2

Get the maximum height;

Substitute x = 2 into the given function;

f(x)=−x^2+4x+5

f(2)=−2^2+4(2)+5

f(2) = -4+8+5

f(2) = 9feet

Hence the maximum height of the toy is 9feet

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2 equivalent expressions to represent the area of a rectangle and the top is n-3 and the side is 2

area of the rectangle = length * width

given length = n - 3

width = 2

replace it in the area

so area of the rectangle = (n-3) *2

= 2(n-3)

one of the expression is 2(n-3)

to get another expression we distribute 2 inside the parenthesis

2(n-3) is 2n - 6

so another expression is 2n - 6

two equivalent expression are

2(n - 3)   , 2n - 6