$\begin{cases} x=-5\implies &x+5=0\\ x=3\implies &x-3=0 \end{cases}\qquad \implies \underline{a(x+5)(x-3)~~ = ~~\stackrel{0}{y}} \\\\\\ \stackrel{\textit{we also know that}}{P(0)=-30}\implies \begin{cases} x=0\\ y=-30 \end{cases}\implies a(0+5)(0-3)~~ = ~~-30 \\\\\\ a(5)(-3)=-30\implies -15a=-30\implies a=\cfrac{-30}{-15}\implies \boxed{a=2} \\\\[-0.35em] ~\dotfill\\\\ 2(x+5)(x-3)=y\implies 2(\stackrel{F~O~I~L}{x^2+2x-15})=y\implies \underline{2x^2+4x-30=y}$

Check the picture below.

8 0

3 years ago

The side lengths of a right triangle are 24 , 45 , and 51 . Determined which is the length of the hypotenuse

HACTEHA [7]

The side length 51 is the hypotenuse.
24*24+45*45=2601
The square root of 2601 is 51.
Please note that the hypotenuse is most likely the longest side.

5 0

4 years ago

Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her teacher

Black_prince [1.1K]

Answer: 16 containers?

Step-by-step explanation:

3 0

3 years ago

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