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3 years ago

Bianca has a piece of rope that is 22 feet long.She cuts the rope into 3 pieces of equal length.

Mathematics

1 answer:

FromTheMoon [43]3 years ago

7 0

Each piece is 7 and 1/3 feet long (7 feet 4 inches)

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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

4 0

3 years ago

Solve for t.

STALIN [3.7K]

Step-by-step explanation:

$12gt^2=19\qquad\text{divide both sides by}\ 12g\\\\t^2=\dfrac{19}{12g}\to t=\sqrt{\dfrac{19}{12g}}$

8 0

2 years ago

18+6=__+__=__ /\ 2 4

Arturiano [62]

Answer:

18 pluse 6 equals 14

Step-by-step explanation:

just add

3 0

1 year ago

Read 2 more answers

One leg of a right triangle is 4 less than the other leg. The square of the hypotenuse of the right triangle is 80. How long are

Hitman42 [59]

I hope this helps you

6 0

3 years ago

I need help pleasee thank

Ganezh [65]

Answer:

A=51

a=22.2

c=28.6

Step-by-step explanation:

∠A=180-90-39

=51

a/sin51=18/sin39

a=22.2

c/sin90=18/sin39

c=28.6

4 0

2 years ago

Read 2 more answers