Using the distributive property to find the product (y — 4)(y2 + 4y + 16) results in a polynomial of the form y3 + 4y2 + ay – 4y2 – ay – 64. what is the value of a in the polynomial?

product y ³  - 64 and a = 16.

Step-by-step explanation:

Given : (y — 4)(y² + 4y + 16) .

To find : Using the distributive property to find the product a polynomial of the form y³ + 4y² + ay – 4y² – ay – 64. What is the value of a in the polynomial?

Solution : We have given

(y — 4)(y² + 4y + 16) .

Distribute y over (y² + 4y + 16) and - 4 over (y² + 4y + 16).

y (y² + 4y + 16) - 4 (y² + 4y + 16).

y ³+ 4y² + 16 y - 4y² - 16y - 64.

This is in form of y³ + 4y² + ay – 4y² – ay – 64.

Here, a = 16.

Product : combine like terms

y ³+ 4y²  - 4y²  + 16y - 16y - 64.

y ³  - 64.

Therefore , product y ³  - 64 and a = 16.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).