Astereo system is being installed in a room with a rectangular floor measuring 13 feet by 10 feet and a 9-foot ceiling. the stereo amplifier is on the floor in one corner of the room. a speaker is at the ceiling in the opposite corner of the room. you must run a wire from the amplifier to the speaker, and the wire must run along the floor or walls (not through the air). what is the shortest length of wire you can use for the connection?
(hint: turn the problem into an equivalent simpler problem by imagining cutting the room along its vertical corners and unfolding it so that it is flat. you will be able to apply the pythagorean theorem.)
the shortest length of wire that can be used is ft.

Find the balance at the end of 4 years if 1000 is deposited at the rate of

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

Solve for x in the equation x2 - 12x + 36 = 90. x= 6+3x/10 x=6+2/7 x= 12+3/22 x = 12+3/10