Tacy has some roses. she has 5 more pink roses than red roses. she has twice as many yellow roses as pink roses. she has 8 red roses. how many roses does stacy have altogether? student's solution: work backwards stacy has 8 red roses. she has 5 more pink roses than red roses (8 + 5 = 13). she has twice as many yellow roses as pink roses (13 × 2 = 26). so stacy has 8 +13 + 26 or 47 roses. use a similar strategy to solve this problem. donna has some notebooks. she has 4 more blue notebooks than green notebooks. she has 3 times as many black notebooks as blue notebooks. she has 6 green notebooks. how many notebooks does donna have altogether?

You would have to start by adding the green notebooks and the blue notebooks
6+4=10
Then you can multiply the blue and black notebooks
3*4=12
Then you can solve
6+10+12=28
So Donna has 28 notebooks altogether

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