Part a: explain why the x-coordinates of the points where the graphs of the equations y = 2^x and y = 4^x−2 intersect are the solutions of the equation 2^x = 4^x−2. (4 points)

part b: make tables to find the solution to 2^x = 4^x−2. take the integer values of x between −4 and 4. (4 points)

part c: how can you solve the equation 2^x = 4^x−2 graphically? (2 points)

A and B. See explanation

C. x=4

Step-by-step explanation:

A: Consider two functions and The point of intersection of the graphs of these two functions is the solution of the system

When you are solving this system, you have to equate the right sides of these equations and get So, the x-coordinate of the point of intersection is the solution of the equation

B.

C. Graphically, graphs intersect at point (4,16), so x=4 is the solution of the equation

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12