Ross is analyzing a circle, y2 + x2 = 64, and a linear function g(x). will they intersect?

Yes, they will intercept.

The circle, y² + x² = 64, intersects with g(x) at the points (8,0) and (-4.8,-6.4)

Step-by-step explanation:

x g(x)

−1 −4.5

0 −4

1 −3.5

y2 + x2 = 64

First of, we find the equation for g(x).

It is stated that g(x) is a linear function, hence, it has the equation of straight line.

y = mx + c [where y = g(x), m = slope, c = y-intercept]

Putting the values of x and corresponding y into the equation of a straight line, we can obtain the equation of the straight line.

x y

−1 −4.5

0 −4

1 −3.5

-4.5 = -m + c (from the first line)

-4 = c (from the second line)

-3.5 = m + c (from the third line)

So, from these relation, it is evident that

c = -4, m = 0.5

g(x) = y = 0.5x - 4

The equation of the circle is

y² + x² = 64

If the circle and the line, g(x), are to intersect, they will have the same coordinates At the point of intersection.

Equation of line

y = 0.5x - 4

Substituting this value for y in the equation of the circle

y² + x² = 64

(0.5x - 4)² + x² = 64

0.25x² - 4x + 16 + x² = 64

1.25x² - 4x - 48 = 0

Solvingthe quadratic equation

x = 8 or x = - 4.8

when x = 8, y = 0.5(8) - 4 = 0

when x = 4.8, y = 0.5(-4.8) - 4 = -6.4

therefore, it is evident that the circle, y² + x² = 64, intersects with g(x) At the points (8,0) and (-4.8,-6.4)

Hope this Helps!!+

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.