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2 years ago

List three ways to express 3^5 as a product of powers

1 answer:

6 0

1) 3^2 × 3^3 = (3×3)×(3×3×3) = 9×27 = 243

2) 3^1 × (3^4) = 3×(3×3×3×3) = 3×81 = 243

3) 3^0 × (3^5) = 1×(3×3×3×3×3) = 243

You might be interested in

Factor each polynomial. Look for a GCF first

weeeeeb [17]

Answer:

20. $x\left(x-6\right)\left(x+8\right)$

22. $2\left(x+1\right)\left(x+4\right)$

24. $5m\left(m-1\right)\left(m+7\right)$

Step-by-step explanation:

20. $x^3+2x^{2} -48x$

The GCF is x, so you group it out of the equation first.

$x(x^{2} +2x-48)$

Then, you find 2 numbers that will equal to 2 when you add them and will equal to -48 when you multiply them.

$?+?=2\\?*?=-48$

The two numbers would be -6 and 8. You then differentiate the squares.

$x\left(x-6\right)\left(x+8\right)$

22. $2x^{2} +10x+8$

The GCF is 2, so you must group it out.

$2(x^{2} +5x+4)$

Find the two numbers that will equal to 5 when you add them and will equal to 4 when you multiply them.

$?+?=5\\?*?=4$

The two numbers would be 1 and 4. Finally, differentiate the squares.

$2\left(x+1\right)\left(x+4\right)$

24. $5m^{3} +30m^2-35m$

The GCF is 5m, so you must group it out.

$5m(m^2+6m-7)$

Find the two numbers that will equal to 6 when you add them and will equal to -7 when you multiply them.

$?+?=6\\?*?=-7$

The two numbers would be -1 and 7. Finally, differentiate the squares.

$5m\left(m-1\right)\left(m+7\right)$

7 0

2 years ago

Carlos is 33 years younger than Kristen. 2 years ago, Kristen's age was 2 times Carlos's age. How old is Carlos now?

ale4655 [162]

Answer:

Carlos is 35 years old now

Step-by-step explanation:

Assume that Carlos is x years old now

∵ Carlos is x years old now

∵ Carlos is 33 years younger than Kristen

- Kirsten's age is the sum of x and 33

∴ Kirsten is x + 33 years old now

2 years ago

∵ Carlos's age = x - 2

∵ Kristen's age = x + 33 - 2 = x + 31

∵ Kristen's age was 2 times Carlos's age

- Equate Kristen's age by 2 times Carlos's age

∴ x + 31 = 2(x - 2)

- Simplify the right hand side

∴ x + 31 = 2x - 4

- Subtract x from both sides

∴ 31 = x - 4

- Add 4 to both sides

∴ 35 = x

∵ x represents Carlos's age now

∴ Carlos is 35 years old now

6 0

3 years ago

Slope of (-7,-2) (9,4)

Olenka [21]

Answer:

m= $\frac{3}{8}$

Step-by-step explanation:

1. Use the slope equation to solve the problem

$\frac{y_{2} -y_{1}}{x_{2} -x_{1} }$

2. Plug in your values into the equation.

$\frac{4-(-2)}{9-(-7)}$

3. Simplify the equation.

m= $\frac{3}{8}$

4 0

2 years ago

Kia is printing packets of information. There are 23 pages in a packet, and she needs enough copies for 52 people. Each package

Andrew [12]

No she will not have enough paper because 200 times five is 1000 and if you multiply 23 by 52 is 1196 but I am not fully sure if this answer is right

6 0

2 years ago

Zoey made 6 1/2 cups of trail mix for a camping trip. She wants to divide the trail mix into 3/4 cup of servings. Twelve people

AlekseyPX

Answer:

Step-by-step explanation:

Given that:

Total number of cups of trail mix available for camping trip = $6\frac{1}{2}$

Amount of one serving contains = $\frac{3}{4}$ cups

Number of people at the trip = 12

To find:

Whether each person will be able to get the servings?

Solution:

Here, we can find the total number of servings by dividing the total number of cups of trail mix with the amount of one serving.

First of all, let us convert the mixed fraction into fractional number.

$6\dfrac{1}{2} = \dfrac{6\times 2+1}{2} = \dfrac{13}{2}$

Therefore, total number of servings available as per the given quantities:

$\dfrac{\frac{13}2}{\frac{3}4}\\\Rightarrow \dfrac{13\times 4}{2\times 3} \\\Rightarrow \dfrac{26}{3}\\\Rightarrow \approx 8$

So, With this type of servings Zoey will be able to serve only 8 people.

Therefore, there is not enough servings.

7 0

2 years ago