Atriangle rpq is shown. s is a point on side pq and t is a point on side pr. points s and t are joined using a straight line. the length of ps is equal to 3x, the length of sq is equal to 24, the length of pt is equal to 51 and the length of tr is equal to 34.dora is writing statements as shown to prove that if segment st is parallel to segment rq, then x = 12.statement: 1. segment st is parallel to segment qr.2. angle qrt is congruent to angle stp.3. angle spt is congruent to angle qpr.4. triangle spt is similar to triangle qpr.5. (3x + 24): 3x =reason: 1. given.2. corresponding angles formed by parallel lines and their transversal are congruent.3. reflexive property of angles.4. angle-angle similarity postulate.5. corresponding sides of similar triangles are in proportion. which of the following can she use to complete statement 5? a. 85: 51b. 3x: 85c. 3x: 51d. 34: 24

Anew shopping mall is gaining in popularity. every day since it opened, the number of shoppers is 5% more than the number of shoppers the day before. the total number of shoppers over the first 10 days is 1258 how many shoppers were on the first day?

Cone w has a radius of 8 cm and a height of 5 cm. square pyramid x has the same base area and height as cone w. paul and manuel disagree on how the volumes of cone w and square pyramid x are related. examine their arguments. which statement explains whose argument is correct and why? paul manuel the volume of square pyramid x is equal to the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is three times the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is (area of base)(h) = (200.96)(5) = 1,004.8 cm3. paul's argument is correct; manuel used the incorrect formula to find the volume of square pyramid x. paul's argument is correct; manuel used the incorrect base area to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect formula to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect base area to find the volume of square pyramid x.

Consider this equation. |y + 6| = 2 what can be concluded of the equation? check all that apply. there will be one solution. there will be two solutions. the solution to –(y + 6) = 2 will be also be a solution to the given absolute value equation. the solution(s) will be the number(s) on the number line 2 units away from –6. the value of y must be positive since the variable is inside absolute value signs.