The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the
legs of the triangle? Select three options.
0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x - 24 = 0
10 ft
(x + 2) ft
x2 + 2x - 48 = 0
x2 + (x + 2)2 = 100
xft
Not drawn to scale

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

Given the numbers c = –3 and d = 4, which statement is true? a. |–c| = 3 and |–d| = –4 b. |–c| = 3 and –|d| = –4 c. –|c| = –4 and –|d| = 3 d. |–c| = 3 and –|d| = 4

Eiko is wearing a magic ring that increases the power of her healing spell by 30%. without the ring, her healing spell restores h health points. which of the following expressions could represent how many health points the spell restores when eiko is wearing the magic ring?