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3 years ago

Solve for x 3(x−15)=x+11

Mathematics

2 answers:

Brums [2.3K]3 years ago

7 0

The answer would be x=28

marishachu [46]3 years ago

4 0

3x-45=x+11
+45 +45
3x=x+56
-x -x
2x=56
--------
2
The answer is x=14

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Latasha earned 18 points on her quiz. If 24 points is equivalent to a score of 100% what two proportions could she use to calcul

Ugo [173]

Given:
18 points on her quiz
24 points is equivalent to 100%

18 is to 24 or 18/24
x is to 100% or x/100%

18/24 = x/100%

18 * 100% = 24x
1800% = 24x
1800%/24 = x
75% = x

18/24 = 75%/100%
18 * 100% = 24 * 75%
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3 years ago

Which of the following have the property that a(x)=a−1(x)? I. y=x II. y=1/x III.y=x^2 IV. y=x^3 A. I and II, only B. IV, only C.

valentina_108 [34]

Answer:

Correct answer:

A. I and II

Step-by-step explanation:

First of all, let us have a look at the steps of finding inverse of a function.

1. Replace y with x and x with y.

2. Solve for y.

3. Replace y with $f^{-1}(x)$

Given that:

$I.\ y=x \\II.\ y=\dfrac{1}x \\III.\ y=x^2 \\IV.\ y=x^3$

Now, let us find inverse of each option one by one.

I. y = x, a(x) = x

Replacing y with and x with y:

x = y

x = $a^{-1}(x)$ = $a(x)$ Hence, I is true.

II. $y =\dfrac{1}{x}$

Replacing y with and x with y:

$x =\dfrac{1}{y}$

$x=\dfrac{1}{a^{-1}(x)}$

$\Rightarrow a^{-1}(x) = \dfrac{1}{x}$

$a^{-1}(x)$ = $a(x)$ Hence, II is true.

III. $y =x^{2}$

Replacing y with and x with y:

$x =y^{2}\\\Rightarrow y = \sqrt x\\\Rightarrow a^{-1}(x) = \sqrt{x} \ne a(x)$

Hence, III is not true.

IV. $y =x^{3}$

Replacing y with and x with y:

$x =y^{3}\\\Rightarrow y = \sqrt[3] x\\\Rightarrow a^{-1}(x) = \sqrt[3]{x} \ne a(x)$

Hence, IV is not true.

Correct answer:

A. I and II

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