Arestaurant is offering a dinner special that includes one starter and one entree. the choices are listed below. starter: breadsticks, soup, salad entree: beef, fish, chicken, shrimp, pork how many possible dinner special combinations are there? 5 8 10 15

The answer is 15 possible combinations

To solve this kind of problems you need to multiply the number of possible candidates in each category.

Here we have to categories: Starters and Entrees, with 3 and 5 possibilities respectively; so the number of combinations is 3*5=15

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

Ibelieve that c. recording would work best.