Which point on the x-axis lies on the line that passes through point c and is parallel to lino ab?

(2,0)

Step-by-step explanation:

For given line AB:

y-intercept = b = -2

slope = m = y₂-y₁/x₂-x₁

= -3/2-(-4) = -3/6 = -1/2

Equation of line AB:

y = (-1/2)x - 2

Finding equation of line that is parallel to line AB and passes through the point C(2,2):

Substituting the slope from line AB into the equation of the line

y = (-1/2)x + b.

Substituting the given point (-2,2) into the x and y values 2 = (-1/2)-2 + b.

Solving for b (the y-intercept) , we get b = 1

Substitute this value for 'b' in the slope intercept form equation y = (-1/2)x + 1.

For x-intercept of the line, we let y = 0

0 = (-1/2)x + 1

x = -1(-2/1)

x = +2

So, the point on the x-axis that lies on the line that passes

through point C and is parallel to line AB is (2,0).

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.