*urgent algebra 2* anyone know these answers? choices provided. will award brainliest.

These are six questions and six answers

Question 1. Translate y = 2/x 3 units to the left and 4 units up.

      
          2
y =  + 4 < the fourth option
      (x + 3)

Explanation:

1) Given function:

y = f(x) = 2 / x

2) Translatiing 3 units to the left is making f(x + 3), so that implies:

y = 2 / (x + 3)

3) Translating 4 units up is making f(x + 3) + 4, so that implies:
      
          2
y =  + 4
      (x + 3)

Which is the fourth option.

Question 2.  simplify

t^2 + 2t - 24

  t^2 - 36

fourth option

t - 4
, with t ≠ - 6 and t ≠ 6.
t + 6

Explanation:

1) Factor the numerator:

t^2 + 2t - 24 = (t + 6) (t - 4)

2) Factor the denominator:

t^2 - 36 = (t + 6) (t - 6)

3) Rewrite the fraction:

 (t + 6) (t - 4)

(t + 6) (t - 6)

4) Cancel the factor t + 6 which is in both numerator and denominator, which you can do only y t + 6 ≠ 0 => t ≠ -6.

 t - 4

 t - 6

That is the simplified expression, with the restrictions that t ≠ - 6  and t ≠ 6, because the denominator cannot be 0.

Question 3. Find the product of:

x^2 + 7x + 10     x^2 - 3x - 18
*
      x + 3                x^2 + x - 2

the fhird option:

(x + 5) (x - 6)

        x - 1

with x ≠ -3, x ≠ - 2, and x ≠ 1.

Explanation:

1) Factor x^2 + 7x + 10

x^2 + 7x + 10 = (x + 5) (x + 2)

2) Factor x^2 - 3x - 18

x^2 - 3x - 18 = (x - 6)(x + 3)

3) Factor x^2 + x - 2

x^2 + x - 2 = (x + 2) (x - 1)

4) Rewrite the given expression using the factors:

  (x + 5) (x + 2) (x - 6) (x + 3)

     (x + 3) (x + 2) (x - 1)

5) Cancel the factors that appear on both the numerator and denominator:

 (x + 5) (x - 6)

        x - 1

The restrictions are those values of x that make any factor that is or was in the denominator: x ≠ -3, x ≠ - 2, and x ≠ 1.

Question 4. Simplify the complex fraction:

             n - 4
    
      n^2 - 2n - 15

             n + 1
         
             n + 3

option 4.

       n - 4

(n - 5) ( n + 3)

Explanation

1) Factor n^2 - 2n - 15

n^2 - 2n - 15 = (n - 5)(n + 3)

2) rewrite the expression:

             n - 4
   
      (n - 5) ( n + 3)

              n + 1
           
              n + 3

3) Convert (n + 1) / (n + 3) into its reciprocal (n + 3) / (n + 1), and multiply instead of dividing.

             n - 4              n + 3
      *
      (n - 5) ( n + 3)      ( n + 1)

4) Cancel n + 3

       n - 4

(n - 5) ( n + 3)

That is the simplest form.

Question 5. Find the difference

second choice

 1 - n

 n + 4

Explanation:

1) given:

n^2 + 3n + 2        2n
-  
n^2 + 6n + 8       n + 4

2) factor the two quadratic trinomials

n^2 + 3n + 2 = (n + 2) ( n + 1)

n^2 + 6n + 8 = (n + 4) (n + 2)

3) Rewrite the expression:

   (n + 2) (n + 1)          2n
  - 
   (n + 4 ) (n + 2)       n + 4

4) cancel the factor n + 2

   n + 1          2n
  -  
   n + 4         n + 4

5) subract the fractions. They have the same denominator.

  n + 1 - 2n           1 - n
=    
    n + 4                n + 4

And that is the simples form.

Question 6.  Problem

Irina paints 1 room in 9 hours
Paulo paints 1 room in 8 hours

How long working together?

x / 9 + x / 8 = 1, x ≈ 4.24 hours

Explanation:

1) In the time x, Irina will paint x / 9 parts of the room

2) Paulo will paint (in the same time) x / 8 parts of the same room

3) The total painted is 1 room.

So the equation is:

x / 9 + x / 8 = 1

4) The solution of that equation is:

[8x + 9x ] / (9*8) = 1

=> 8x + 9x = 72

=> 17x = 72

=> x = 72 / 17

=> x ≈ 4.24 hours