Simplify. (3x3 - 7x2 + 12) - (3x3 + 6x2 + 10x) a) -x2 + 10x + 12 b) -13x2 - 10x + 12 c) -6x3 + x2 - 10x - 12 d) -9x6 - 42x4 - 10x + 12

The answer is B. 

Do you need the explanation?

 (3x^3 - 7x^2 + 12) - (3x^3 + 6x^2 + 10x)
First, remove parentheses

3x^3 - 7x^2 + 12 - 3x^3 -6x^2 -10x
eliminate the opposites 

then collect the like terms 
13x^2 +12 - 10x

and finally, use the commutative property to reorder the terms, and you'll get 
-13x^2-10x+12

Part A:

Part B. All angles are same, so the triangles are similar.  

Part C. RP = 8

Step-by-step explanation:

We are given a right angled triangle with .

PS is perpendicular to the hypotenuse RQ of and S lies on RQ.

Part A:

To identify the pair of similar triangles.

.

Part B:

To identify the type of similarity.

Kindly refer to the image attached in the answer area.

Let us consider the triangles .

Also, is common to both the triangles under consideration.

Now, we can see that two angles of two triangles are equal.

So, third angle of the two triangles will also be same.

i.e. All three angles of two triangles are equal to each other.

So, by A-A-A (Angle - Angle - Angle) similarity, we can say that .

Part C:

RS = 4

RQ = 16, Find RP.

There is one property of similar triangles that:

The ratio of corresponding sides of two similar triangles is equal.

i.e.