#1**+6 **

1) From the diagram, we know the following: Angle B = Angle M = 42, Angle C = Angle N = 90, and Side BC = 4 is half of Side NM = 8.

Since all triangles have an interior measure of 180 degrees, if two triangles have the same measures for two angles, then the third angles must have the same measure, meaning they are similar. We also know that Triangle LMN is 2: 1 ration in side length compared to Triangle ABC. Therefore the area of Triangle LMN is 4 times larger than the area of ABC. (This is not needed in the problem though)

The answer is A, similar by AA.

PartialMathematician
Nov 28, 2018

#2**+2 **

First one

ΔABC is similar to ΔLMN by AA congruency

Second one

This is the absolute value funtion shifted 1 unit to the left and 2 units down

The function is f(x) = l x + 1 l - 2 ⇒ "P"

CPhill
Nov 28, 2018

#3**+6 **

3) Multiply the following polynomial: \((x-7)(3x^2+8)\). We do the same thing we do with a normal polynomial, we use FOIL (multiply each term). If we multiply \(x\) with \((3x^2+8)\), we get \(3x^3 + 8x\). Similarly, if we multiply \(-7\) with \((3x^2+8)\), we get \(-21x^2-56\). If we add our results, we get \(3x^3 + 8x - 21x^2 - 56 = \boxed{3x^3 - 21x^2 + 8x -56}\).

Hope this helps,

- PM

PartialMathematician
Nov 28, 2018