Joe has a rectangular shaped garden in his back yard. The width of the garden measures 2x - 4units and the length is 8x + 6 units. Draw a diagram of the garden and then answer the following questions. a. Express both the area and perimeter of the garden as algebraic expressions.

b. If x = 3 feet, what are the area and perimeter in feet?

c. A local landscaper charges $3.50 a square foot to fertilize the garden. Joe can fertilize the garden himself for

$1.75 a square foot. How much will Joe save by fertilizing himself?

d. To keep the deer out, Joe plans on installing a deer fence. How much will this cost him, if deer fencing is

$5.75 a linear foot and then $2.25 a linear foot to install?

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