Simplify using exponent rules:3^3×3^4/3^10

Answers

Answer 1

Answer:

$\bf ~\hspace{7em}\textit{negative exponents} \n\n a^(-n) \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^(-n)} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^(-m)\implies a^(n-m) \n\n[-0.35em] \rule{34em}{0.25pt}\n\n \cfrac{3^3 \cdot 3^4}{3^(10)}\implies \cfrac{3^3 \cdot 3^4\cdot 3^(-10)}{1}\implies 3^(3+4-10)\implies 3^(-3)\implies \cfrac{1}{3^3}\implies \cfrac{1}{27}$

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Find the output, h, when the input, x, is - 18. h=17+ x/6

Determine the time needed to deliver 72 papers at rate of 9 papers in 18 minutes.

Answers

Answer: The required time needed to deliver 72 papers is 2 hours 24 minutes.

Step-by-step explanation: Given that 9 papers are delivered in 18 minutes.

We are to determine the time needed to deliver 72 papers.

We will be using the UNITARY method to solve the problem.

We have

Time needed to deliver 9 papers = 18 minutes.

So, time needed to deliver 1 minute will be

$(18)/(9)=2~\textup{minutes}.$

Therefore, time needed to deliver 72 papers is given by

$2*72=144~\textup{minutes}=(120)/(60)~\textup{hours},24~\textup{minutes}=2~\textup{hours}~24~\textup{minutes}.$

Thus, the required time needed to deliver 72 papers is 2 hours 24 minutes.

So you need to find out time. What you do is divide 72 by 9 to get 8. Once you get 8, you have to multiply it by 18. Your answer is then 144 Papers

Is 5
/12 bigger than 3/7

Answers

You can figure out if two fractions are bigger by just cross multiplying the numerator and denominator of each fraction.

$(5)/(12) (3)/(7)$

Multiply the 5 and 7, and then the 3 and 12. Be sure to start with the numerator of the first fraction.
$(5)/(12) (3)/(7)$
5 * 7 = 35, 3 * 12 = 36
So $(3)/(7)$ is bigger.

5/12 is not bigger than 3/7

Find the value of x. Write your answer in simplest form.
x=

Answers

The value of x is 7 cm, as it's a 45-45-90 triangle, also known as an isosceles right triangle, where sides opposite the 45° angles are equal in length.

In this case, we're dealing with a 45° angle, which is part of a 45-45-90 special triangle, often referred to as an isosceles right triangle.

We know that in a 45-45-90 triangle, the sides are in the ratio of 1:1:√2.

Knowing this, we can easily find the length of the unknown side (BC), which we dubbed as 'x'.

In a triangle with a 45° angle and hypotenuse of 7 cm (side AC), the length of the other side (BC) would be the same as the side adjacent to the 45° angle because it is an isosceles triangle.

Therefore, 'x' in this instance is also 7 cm.

Learn more about triangle here:

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The answer is 7 √2

A shortcut for a 45 45 90 right triangle is that the hypotenuse is √2 * short leg.

So you do 7 * √2

Which would equal to 7 √2 or 9.89949493661167

What division problem does this model represent? 24

Answers

A division problem which this model represent include the following: 24 ÷ 8 = 3.

How to evaluate and solve the given expression?

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.

Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Note: Let the variable x represent each of the boxes.

Based on the model provided below, we have the following mathematical expression:

x + x + x = 24

3x = 24

x = 24/3

x = 8

Therefore, the division problem is given by;

24 ÷ 8 = 3.

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Complete Question:

What division problem does this model represent?

24÷8=3 24÷6=4 24÷4=6 24÷24=1 24÷3=8 24÷12=2

Dave wants to install carpet in his room. The room is rectangular in shape with a length of 16 feet and a width of 12 feet. If the total cost of installing the carpet is $288, what is the unit price of carpet per square foot?

Answers

Hello there!

If you multiply 12 by 16, you get 192. Divide 288 by 192 ( being the total amount of square feet. ) and you get 1.5, essentially being $1.50 per square foot.

To check this, multiply 192 by 1.5 and you will get 288.

Ok so the width is 12 and the length is 16 so we will multiply those: 12 x 16=192 so now we divide 288 by 192= 1.5 or %1.50 so the answer is %1.50 per square foot Hope this helped!!

There are 28 less blue coffee mugs than green coffee mugs. There are 16 blue coffee mugs. How many green coffee mugs are there?

Answers

Answer:

44 coffee mugs

Step-by-step explanation:

Think of 28 + 16

That should tell you how many blue coffee mugs there are because ,it's less than and if you take that 28 and add it by the amount of blue mugs you get your answer.

There are 44 green mugs

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