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4 years ago

6

Given the expression 12 over 12 to the third power. Part A: Explain how the Quotient of Powers was used to simplify the expressi

on. (6 points) Part B: Simplify the expression. (4 points)

1 answer:

natta225 [31]4 years ago

5 0

We have the following fractional expression:

12

-------- is the same as

12^3

12^1

-------

12^3

We want to simplify this expression. To do so, we need the formula for exponents as follows:

x^a / x^b = x^(a-b).

In this particular problem we have

12^1 / 12^3, and know by this formula that the correct result is 12^(1-3), or 12^(-2), which is equivalent to 1 / 144.

You might be interested in

The normal monthly temperatures (°F) for Omaha, Nebraska, are recorded below.

AfilCa [17]

Answer

$y = 28 \sin(\frac{\pi}{6} - \frac{2\pi}{3}) + 49$

Step by Step Explanation

Given

See attachment for table

Required

Determine the sinusoidal function

The sinusoidal function is represented as:

$y = A \sin(Bx + C) + D$

Where

$|A| = Amplitude$

And it is calculated as:

$A = \frac{1}{2}[Highest - Least]$

From the table:

Highest = 77 and Least = 21

So:

$A = \frac{1}{2}[77 - 21]$

$A = \frac{1}{2}[56]$

$A = 28$

B is calculated as:

$Period = \frac{2\pi}{B}$

The period is 12 i.e. 12 months

So:

$\frac{2\pi}{B} = 12$

$B = \frac{2\pi}{12}$

$B = \frac{\pi}{6}$

C is calculated as:

$\frac{C}{B} = -4$

$C = -4 * B$

$C = -4 * \frac{\pi}{6}$

$C = -2 * \frac{\pi}{3}$

$C = -\frac{2\pi}{3}$

Lastly, D is calculated as:

$D = Least + A$

So:

$D =21 + 28$

$D=49$

So, the function is:

$y = A \sin(Bx + C) + D$

$y = 28 \sin(\frac{\pi}{6} - \frac{2\pi}{3}) + 49$

8 0

3 years ago

How do you solve 5y+34=-2 (1-7y)

sergiy2304 [10]

You just kind of do it

6 0

3 years ago

Read 2 more answers

Let μ = 160 and σ = 16. find the z-score for the score, x = 150.

cricket20 [7]

Put the given values in the formula
$z=\dfrac{x-\mu}{\sigma}$
and evaluate.
z = (150 -160)/16 = -10/16
z = -5/8

The z-score for the score x=150 is -5/8 = -0.625.

8 0

3 years ago

Express as a trinomial. (3x+3)(2x−4)

Artyom0805 [142]

Use the FOIL method: First, Outside, Inside, Last

3x(2x) = 6x²

3x(-4) = -12x

3(2x) = 6x

3(-4) = -12

6x² -12x + 6x-12

Combine like terms

-12x + 6x = -6x

6x² - 6x - 12 is your answer

hope this helps

5 0

4 years ago

I need help, i don't understand it. thank you in advance.

Nadya [2.5K]

<em>Think of it as a riddle.</em>

You need to eliminate and match one city to one transport to one person in the end.

-----------------------------------------------------------------------------------------------

Take a look at my diagram!*

Use each clue to eliminate the rows and columns until you have narrowed it down.

Below is my work. It would be too hard to explain every step of the way; it will work differently for everyone. Maybe look up the game "Telepathy". The concept is similar!

-----------------------------------------------------------------------------------------------

<em>I first read the instructions, eliminating and boxing the possible and impossible options. </em>

<em>If I ever got down to one empty spot in a column or row, I'd make sure to circle that and frequently write it down.</em>

<em>If you're doing this right, you will </em><em>always be progressing</em><em>. </em><u><em>Don't doubt yourself; don't overthink it</em></u><em>. It's the game of </em><em>narrowing down and elimination</em><em>. If you find yourself stuck, </em><u><em>write what you know down.</em></u><em> </em><em>Use logic</em><em>. Make sure you </em><u><em>always</em></u><em> look for rows that you forgot to cross out, or empty spots that you missed. </em><em>Reread</em><em> the instructions! </em><u><em>You will get there</em></u><em>! </em>

-----------------------------------------------------------------------------------------------

*The "eliminated" part is a bit confusing, they weren't entirely eliminated. It's just my thought process! I didn't continue to use it. Just remember to group the right things together!

Don't be scared of looking up the cities and if you don't know, their states!

-----------------------------------------------------------------------------------------------

<u>Conclusion:</u>

John arrived by plane to Saint Louis meet up with his nephew.

John arrived by bus to Denver to visit his brother.

John came by train to Miami to visit his uncle.

John rode a cycle to Boston to meet up with his cousin.

John drove in a car to San Fransisco to visit his parents.

-----------------------------------------------------------------------------------------------

<em>Please let me know </em><u><em>if you have any questions</em></u><em>, or if this helped!</em>

6 0

4 years ago