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marishachu [46]
3 years ago
6

84. Use properties of exponents to rewrite each expression with only positive, rational exponents. Then find the numerical value

of each expression when x = 9, y= 8, and z= 16. In each case, the expression evaluates to a rational number.
C. X-3/2 Y4/3 Z-3/4
Mathematics
1 answer:
Yakvenalex [24]3 years ago
4 0

Answer:

a) 1/27

b) 16

c) 1/8

Step-by-step explanation:

a) x^{-3/2}

One of the properties of the exponents tells us that when we have a negative exponent we can express it in terms of its positive exponent by turning it into the denominator (and changing its sign), so we would have:

x^{-3/2}=\frac{1}{x^{3/2} }

And now, solving for x = 9 we have:

\frac{1}{x^{3/2}}=\frac{1}{9^{3/2} }  =\frac{1}{27}

b) y^{4/3}

This is already a positive rational exponent so we are just going to substitute the value of y = 8 into the expression

y^{4/3}=8^{4/3}=16

c) z^{-3/4}

Using the same property we used in a) we have:

z^{-3/4}=\frac{1}{z^{3/4} }

And now, solving for z = 16 we have:

\frac{1}{z^3/4} } =\frac{1}{16^{3/4} } =\frac{1}{8}

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tresset_1 [31]
I believe 5 different ways. The options being two packs of 9-one pack of 9 and 3 packs of 3- 1 pack of 9, 2 packs of 3 and 3 singles- one pack of 9, one pack of 3, and 6 singles- and then one pack of 9 and 9 singles.
Hope this helped!

8 0
3 years ago
Question: State whether each table of values represents a function​
Mashcka [7]

Answer:

Please check the explanation.

Step-by-step explanation:

  • As we know that the values in the table represent a function​ only if there there is only 1 input for every output.

Given the table 1

x              y

-12           2

-10           10

0              -2

5              -6

8               -11

15              -15

From the table, it is clear that for each input there exists a unique output.

i.e.

According to the given table,

y = 2 at x=-12

y = 10 at x=-1 0

y = -1 at x=0

y = -11 at x=8

y = -15 at x=15

From the table, it is clear that for each input x, it has a unique output y.

Hence, table 1 is a function.

Given the table 2

x              y

9            -18

-20           0

-6              1

-17              16

9                17

11              19

This table does not produce a function, because the input x=9 produces two outputs.

i.e.

at x = 9, the y = -18

at x = 9, the y = 17

Therefore, the table 2 does not represent a function.

3 0
3 years ago
A quadratic equation is shown below: 3x^2 − 15x + 20 = 0 Part A: Describe the solution(s) to the equation by just determining th
Anuta_ua [19.1K]
These are two questions and two answers:

Question 1:

<span>A quadratic equation is shown below: 3x^2 − 15x + 20 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work.

Answer: </span><span>The negative value of the radicand means that the equation does not have real solutions.

Explanation:

1) With radicand the statement means the disciminant of the quadratic function.

2) The discriminant is: b² - 4ac, where a, b, and c are the coefficients of the quadratic equation: ax² + bx + c

3) Then, for 3x² - 15x + 20, a = 3, b = - 15, and c = 20

and the discriminant (radicand) is: (-15)² - 4(3)(20) = 225 - 240 = - 15.

4) The negative value of the radicand means that the equation does not have real solutions.

Question 2:

Part B: Solve 3x^2 + 5x − 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.

Answer:
</span> two solutions x = 1 and x = - 8/3x

Explanation:

1) I choose factoring (you may use the quadratic formula if you prefer)

2) Factoring

Given: 3x² + 5x − 8 = 0

Make 5x = 8x - 3x: 3x² + 8x - 3x - 8 = 0

Group: (3x² - 3x) + (8x - 8) = 0

Common factors for each group: 3x(x -1) + 8(x - 1) = 0

Coomon factor x - 1: (x - 1) (3x + 8) = 0

The two solutions are for each factor equal to zero:

x - 1 = 0 ⇒ x = 1
3x + 8 = 0 ⇒ x = -8/3

Those are the two solutions. x = 1 and x = - 8/3
4 0
3 years ago
What is the measure of the missing angle?
Lostsunrise [7]
The three angles of a triangle should equal 180 so add 52+34 which equals 86.Then subtract 86 from 180 to get the third angles measure which is 94 so the answer is 94.
3 0
3 years ago
Can someone answer this for me?
Sophie [7]

Answer:

D 26

Step-by-step explanation:

154+154=308

308-360=52

52 divided by 2

=26

7 0
3 years ago
Read 2 more answers
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