Find the GCF of the expression 24a^7 +18a^5+12a^3

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality

If x varies directly as y, and x = 7.5 when y = 10, find x when y = 4

The directions on a sewing pattern say to cut an extra 15% of fabric to account for error. chloe needs 0.75 yard of fabric to make a skirt, and she cuts 0.1125 yard. did chloe cut the correct amount of fabric? why or why not? a. chloe cut enough fabric because she cut the amount of fabric for the skirt. b. chloe cut enough fabric because she cut enough fabric for the skirt and the amount of extra fabric. c. chloe did not cut enough fabric because she only cut the amount of fabric for the skirt. d. chloe did not cut enough fabric because she only cut the amount of extra fabric.