Rewrite each expression by completing the square q^2+12q+32

The given expression can be written as = (q+8)(q+4).

Step-by-step explanation:

Given,

To make it a complete square.

Formula

(a+b)² =

Now,

=

= (q+6)²-36+32

= (q+6)²-4

= (q+6)²-2²

= (q+6+2)(q+6-2)

= (q+8)(q+4)

h/o/e/s mad

step-by-step explanation:

si si si

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).