Annie is creating a stencil for her artwork using a coordinate plane. The beginning of the left edge of the stencil falls at (1, −1). She wants to align an important detail on the left edge of her stencil at (3, 0). She knows this is 1:3 of the way to where she wants the end of the stencil. Where is the end of the stencil located? (1.5, −0.75)
(2.5, −0.25)
(6, 2)
(9, 3)

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

Horatian satire is more witty and tolerant.named after the roman satirist horacegently criticizes human nature and human follyjuvenalian satire is more angry and personal, attempting to produce anger in the reader.named after roman satirist juvenalattacks human vice-indignant