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3 years ago

What is the value of any number raised to the power of zero?

Mathematics

2 answers:

Mars2501 [29]3 years ago

8 0

Answer:

Any non-zero number raised to the power of zero is equal to one. Zero raised to the power of zero is equal to zero.

Step-by-step explanation:

This is one way to think about it

Remember the exponent law where $a^{m} * a^{n} = a^{m+n}$ . Therefore, I can create the equation $5^{0}$ and expand it to $5^{1} * 5^{-1}$ . When calculating this, I get 5*(1/5), which is 1.

This is true for any non-zero number.

mestny [16]3 years ago

5 0

Hey There,

Your answer is:

Any number raised to the power of zero is 1

Best Of Luck,

- Kai -

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When it comes to budgeting, which of the following is considered a fixed expense?

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3 years ago

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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

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3 years ago

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Answer:

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2 years ago

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D'Naisa mixed her favorite shade of orange paint. She had 111 gallon of orange paint and added 222 quarts of yellow paint and 33

natka813 [3]

Answer:

7.5 Quarts

Step-by-step explanation:

D'Naisa mixed the following:

1 gallon of orange paint
2 quarts of yellow paint
3 pints of red paint.

We are to determine in total, the number of quarts of paint that she mixed. this is done by converting each of the volume to quart.

1 gallon of orange paint

1 gallon = 4 Quarts
Orange Paint=4 Quarts

3 pints of red paint.

1 pint =0.5 quart
3 Pints =3 X 0.5 Quart
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See question in attached photo.

statuscvo [17]

9514 1404 393

Answer:

(a, b) = (-2, -1)

Step-by-step explanation:

The transpose of the given matrix is ...

$A^T=\left[\begin{array}{ccc}1&2&a\\2&1&2\\2&-2&b\end{array}\right]$

Then the [3,1] term of the product is ...

$(A\cdot A^T)_{31}=\left[\begin{array}{ccc}a&2&b\end{array}\right]\cdot\left[\begin{array}{ccc}1&2&2\end{array}\right]=a+2b+4$

and the [3,2] term is ...

$(A\cdot A^T)_{32}=\left[\begin{array}{ccc}a&2&b\end{array}\right]\cdot\left[\begin{array}{ccc}2&1&-2\end{array}\right]=2a-2b+2$

Both of these terms in the product matrix are 0. We can solve the system of equations by adding these two terms:

(a +2b +4) +(2a -2b +2) = (0) +(0)

3a +6 = 0

a = -2

Substituting for 'a' in term [3,1] gives ...

-2 +2b +4 = 0

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The ordered pair (a, b) is (-2, -1).

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