The graph of the equation x^2+6x+y^2-16y=-9 is a circle. Choose True or False for each statement

A. The center of the circle is (3,-8). (true or false?)

B. The circle is tangent to the x-axis. (true or false?)

C. The circle has a radius of 64. (true or false?)

see the explanation

Step-by-step explanation:

we have

Convert the equation of the circle in center radius form

Group terms that contain the same variable

Complete the square twice. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

The center of the circle is (-3,8)

The radius of the circle is 8 units

Verify each statement

A. The center of the circle is (3,-8).

False

The center of the circle is (-3,8)

B. The circle is tangent to the x-axis

True

The circle is tangent to x=5 and x=-11 and is tangent to y=0 and y=16

Remember that y=0 is the x-axis

C. The circle has a radius of 64

False

The radius of the circle is 8 units

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).

answer: b

step-by-step explanation: