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6. E

7. D

8. 5,-8,34

Step-by-step explanation:

A. Parallel to the y-axis and passes through the point (3,5)

For it to be parallel to the y-axis, what this means is that it has an x-intercept and no y intercept.

So what this means is that x = 3 is our line so E is correct

B. Perpendicular to the y-axis means it is parallel to the x-axis

It means is has no x intercept and thus its x value at any point in time is zero

So the equation is y = -5

or simply y + 5 = 0 which means D is correct

C. It is parallel to the line 5x -8y + 12 = 0

Thus: 8y = 5x + 12

dividing both sides by 8

y = 5x/8 + 12/8

y = 5x/8 + 3/2

y = 5x/8 + 1.5

Comparing this with the general equation of a straight line ;

y = mx + c

where m is that slope, this means that 5/8 is the slope of the line

Mathematically if two lines are parallel, they have equal slopes.

So we can say the slope of the other line too is 5/8

Now to find the equation of the other line, we can use the point-slope method

y-y1 = m(x-x1)

where (x1,y1) in this case is (-2,3)

So we have;

y-3 = m(x-(-2))

y-3 = 5/8 (x + 2)

8(y-3) = 5(x + 2)

8y -24 = 5x + 10

5x + 10 + 24 -8y = 0

5x -8y + 34 = 0

So A, B, C = 5, -8, 34

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°