Triangle P N M is shown. The length of P N is 7, the length of N M is 8, and the length of M P is 11. Law of cosines: a2 = b2 + c2 – 2bccos(A)

Which equation correctly applies the law of cosines to solve for an unknown angle measure?

72 = 82 + 112 – 2(8)(11)cos(N)
82 = 72 + 112 – 2(7)(11)cos(M)
72 = 82 + 112 – 2(8)(11)cos(P)
82 = 72 + 112 – 2(7)(11)cos(P)

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)