a. What is the area and circumference of circle P? Explain how you calculated this answer. b. If the arc measure of arc COD is 100 degrees and the arc measure of arc BSA is 60 degrees, what is the angle measure of angle CRB ? Explain how you calculated this answer.

a) 9*π or approx 28.26

b) ∡CRB=100°

Step-by-step explanation:

As known for secants crossing each other inside the circle is coorect the following:

BR*RD=AR*RC

=> 3*RD=4*4.5

RD=6

The diameter of the circle with center P is BD=BR+RD=3+6=9

So the radius of the circle is D/2=9/2=4.5

As known the circumference of any circle can be calculated as

C=2*π*r  , where r is the circle's  radius

So C=2*4.5*π=9*π= approx   3.14*9=28.26

b) ∡CRB=∡ARD= (arcBC+arcAD),  where arcBC and arcAD smaller arcs

BD is the circle's  diameter, so arc BD=180°

So arcBC=180°-arcCOD=180°-100°=80°

Similarly arcBD=180°

arcAD=180°-arcBSA=180°-60°=120°

∡CRB= (80°+120°)/2=100°

A.

See Explanation

B.

Vertical shift:

Horizontal shift:

C.

The horizontal shift is:

The vertical shift is:

Step-by-step explanation:

See attachment for graph

A. The possible transformation from f(x) to g(x)

From the attachment, g(x) can be translated or shifted to f(x) in two possible ways.

1. Horizontal Shift which shifts g(x) by k units to the right

And

2. Vertical Shift which shifts g(x) downwards by k units

B. Solve for k

First, we calculate the equations of both lines.

However, we need to calculate the slope (m) of both to do so:

For f(x)

So:

The equation is then:

Where:

So:

For g(x)

So:

The equation is then:

Where:

So:

So, we have:

For the horizontal shift:

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If then

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So, we have:

Subtract 2x from both sides

Add 10 to both sides

Divide through by 2

For the horizontal shift:

Subtract 2x from both sides

Subtract 6 from both sides

Multiply both sides by -1