Match the simplified expression with the correct problem.
3/4 (8x + 16)
2x - 5x + 5 - 4
x + x + x +3 + 5 - 2
6x - 7 + 3x + 5
3 + 2(2x + 5)

3/4 (8x + 16) simplified expression is 6x + 12

                2x - 5x + 5 - 4 simplified expression is -3x + 1

                 x + x + x +3 + 5 - 2 simplified expression is 3x + 6

               6x - 7 + 3x + 5 simplified expression is 9x  - 2

                3 + 2(2x + 5) simplified expression is 4x + 13

Step-by-step explanation:

3/4 (8x + 16) in the example the 3 is multiplying and the 4 is dividing,

so you can start with multiplication, multiply the 3 for each value into the parenthesis after that you can place 4 as the divisor of this equation

(3 * 8x + 3 * 16) / 4

after we perform this equation the product is the following

(24x + 48) / 4

after this step you can divide the each value into the parenthesis between 4, this process give us separate equations.

(24x/ 4) + (48/4)

if you proceed with the division of each value we will find the last equation.

(24x/ 4) = 6x

(48/4) = 12

then the simplified expression is 6x + 12.

2x - 5x + 5 - 4, with this case you can resolve the equation with the similar values, for example, you can start with the values that has the x, and after that proceed with the simple values.

2x - 5x = -3x

5 - 4 = 1

after we resolve this, you only need placed the values with its sign in one equation then the simplified expression is  -3x + 1.

x + x + x +3 + 5 - 2, in this example you can start with the sum of x, and after that proceed with sum of the simple values.

x + x + x = 3x

3 + 5 - 2 = 6

after that we place the values in one expression , then the simplified expression is 3x + 6.

6x - 7 + 3x + 5, in this equation we can star with the similar values, the values with x and after that the simple values

6x + 3x = 9x

-7 + 5 = -2 ( as the 7 is bigger than 5 the result get value of the biggest number.

after you only need to place the values in one equation, then the simplified expression is 9x - 2.

3 + 2(2x + 5), with this example you can start with the product of 2 with the values into the parenthesis.

2 * (2x + 5) the 2 is passing to multiply each value into the parenthesis.

2 * 2x + 2 * 5

4x + 10

after that we can place the result of this product in the first equation

3 + 4x + 10

after that you only need to sum the similar values and we get that the simplified expression is 13 + 4x

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.