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Answer 1

• (7).

The function f(x) = 3x³ - 4x² + x - 1.

f (2) = 3(2)³ - 4(2)² + (2) - 1

= 3(8) - 4(4) + 2 - 1

= 24 - 16 + 1

= 9.

Option E is the correct choice.

• (8).

To find the answer we will set up an equation :
M = 0.25q + 0.1d, where M is the amount of money they have, q is how many quarters they have, and d is how many dimes they have. ( we put a .25 in front of the q and a .1 in front of the d because it is how much a quarter and a dime are worth, respectively.

We plug in known values :
3.6 = .25 q + .1d

We can set up the equation :
q = d + 13, because he has 13 more quarters than dimes.

We can then use the substitution method to get :
3.6 = 0.25(d + 13) + 0.1d
3.6 =0.25d + 3.25 + 0.1d
3.6 = 0.35d + 3.25
0.35d = 0.35
d = 1
So there is 1 dime.

The answer is thus B.

If we wanted to find how many quarters there are we could plug in d = 1 into the equation q = d + 13:
q = 1 + 13
q = 14

Thus we have 1 dime and 14 quarters.
Again, the answer is thus B.

Source:

https://answers.yahoo.com/question/index?qid=20121220175704AAdvHSr

Answer 2

Contd.........

• (9).

The equations are y = - 2x + 3 and y = (5/8)x - (9/4).

A.  Substitute the values of  (x, y) = (1, 1) in y = - 2x + 3 and y = (5/8)x - (9/4).

1 = - 2(1) + 3           and            1 = (5/8)1 - (9/4)

1 = - 2 + 3                                   1 = 5/8 - 9/4

 1 = 1.                                          1 = (5 - 18)/8 = - 13/8

                                                     1 = - 13/8.

Since the first statement is true and second statement is false, the ordered pair (1,1) is not a solution of the given  equations.

B. Substitute the values of  (x, y) = (- 2, 0) in y = - 2x + 3 and y = (5/8)x - (9/4).

0 = - 2(- 2) + 3           and           0 = (5/8)(- 2) - (9/4)

0 = 4 + 3                                      0 = - 5/4 - 9/4

0 = 7.                                           0 = (- 5 - 9)/4

                                                     0 =  - 14/4 = - 7/2.

The above two statements are false, so, the ordered pair (- 2,0) is not a solution of the given  equations.

C. Substitute the values of  (x, y) = (2, - 1) in y = - 2x + 3 and y = (5/8)x - (9/4).

- 1 = - 2(2) + 3           and                - 1 = (5/8)(2) - (9/4)

- 1 = - 4 + 3                                      - 1 = 5/4 - 9/4

- 1 = - 1.                                           - 1 = (5 - 9)/4

                                                         - 1 =  - 4/4

                                                         - 1 = - 1.

The above two statements are true, so, the ordered pair (2, - 1) is a solution of the given equations.

D. Substitute the values of  (x, y) = (- 6, - 6) in y = - 2x + 3 and y = (5/8)x - (9/4).

- 6 = - 2(- 6) + 3           and              - 6 = (5/8)(- 6) - (9/4)

- 6 = 12 + 3                                      - 6 = - 15/4 - 9/4

- 6 = 15.                                           - 6 = (- 15 - 9)/4

                                                         - 6 =  - 24/4

                                                         - 6 = - 6.

Since the first statement is false and second statement is true, the ordered pair (- 6, - 6) is not a solution of the given  equations.

 

Option C is the correct choice.

Answer 3

Contd.......

• (10).

The expression is (4√12)(3√6).

(4√12)(3√6) = (4√(6 * 2))(3√6)

= (4√6√2)(3√6)

= 4 * 6 * 3 * √2

= 24 * 3√2

 = 72√2.

Option D is the correct choice.

Answer 4

Contd......

• (11).

A. {(5, 5), (- 5, 5)}.

A  function  is a special type of relation in which each element of the domain is paired with exactly one element of the range.

The relation is  a function because the each element of the domain is paired with exactly one element of the range.

For each element of the domain, there is only one corresponding element in the range. So, this mapping represents a function.

It does not matter if two elements of the domain are paired with the same element in the range.

The relation is a function.

B. {(1, 3), (1, - 1)}.

A  function  is a special type of relation in which each element of the domain is paired with exactly one element of the range.

The relation is not a function because the 1 in the domain is paired with both 3 and - 1 in the range.

The relation is not a function.

C. {(- 2, - 2), (- 2, 2)}.

A  function  is a special type of relation in which each element of the domain is paired with exactly one element of the range.

The relation is not a function because the -2 in the domain is paired with both - 2 and 2 in the range.

The relation is not a function.

 

D. {(0, 0), (0, 3)}.

A  function  is a special type of relation in which each element of the domain is paired with exactly one element of the range.

The relation is not a function because the 0 in the domain is paired with both 0 and 3 in the range.

The relation is not a function.

 

Option A is the correct choice.

 

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