Which set of numbers could represent the lengths of sides of a right triangle? a) 7, 9, 11 b) 10, 15, 20 c) 12, 18, 22 d) 8, 15, 17

Hello from MrBillDoesMath!

 D

In a right (angle) triangle with sides a,b, c, the Pythagorean that gives us that

a^2 + b^2 = c^2. Let go through the 4 cases presented in the problem>

A)    Does 7^2 + 9^2 = 11 ^2. That is, does  49 + 81 = 121 ? Nope so these sides do not form a right triangle.

B) Does 10^2 + 15^2 = 20^2. That is, does 100 + 225 = 400 ? Nope so these sides do not form a right triangle

C) Does 12^2 + 18^2 = 22^2. That is, does 144 + 324 = 484 ? Nope, so these sides do not form a right triangle.

D) Does 8^2 + 15^2 = 17^2 ? That is, does 64 + 225  = 289. YES, so these sides can form a right triangle.

Regards, MrB.

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x