10 POINT TO WHOEVER HELPS ME!! URGENT 1. Write a paragraph proof for the following conjecture.
2
Given: < 1 and <3 are vertical angles

prove: <1 congruent to <3

<1 ≅ <3 (congruence property)

Step-by-step explanation:

Given that: <1 and <3 are vertical angles.

Prove: <1 congruent to <3

Vertical angles are angles that are vertically opposite, and are formed under the same conditions. Thus, they are always congruent.

<1 + <2 = (sum of angles on a straight line)

Also,

<2 + <3 = (sum of angles on a straight line)

So that,

<1 + <2 ≅ <2 + <3 =

Thus, we can say that;

<1 + <2 ≅ <2 + <3

Since <2 is a common angle on both sides, then;

<1 ≅ <3 (congruence property)

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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