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3 years ago

What are 3 exponents that equal 216 except for 6 to the 3rd power?

1 answer:

7 0

Answer: First find the prime factorization of 216, then piece it back together in different ways. We are going to us multiple exponents.

216 = 6 x 6 x 6 = 2 x 3 x 2 x 3 x 2 x 3

Therefore, we could write it as:

(2^3)(3^3)

or

(6^1)(2^2)(3^2)

or

(6^2)(2^1)(3^1)

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What is the slope of the line

lidiya [134]

Answer:

c is the correct answer

Step-by-step explanation:

because i worked it out

8 0

2 years ago

Read 2 more answers

Free points insta: (jqyneii) giving Brainliest to the first person :D make sure to get outside its good for you ily <3

kiruha [24]

Answer:

THANKS FOR THE POINTS

Step-by-step explanation:

3 0

2 years ago

Help. The problem is in the picture

inn [45]

Answer:

The answer to your question is y = 2/3x + 4

Step-by-step explanation:

Data

Equation y = 2/3 x + 5

New line = ?

Process

Two lines are parallel if the have the same slope. The slope is the coefficient of the x.

1.- Get the slope of the original line

y = 2/3x + 5

slope = 2/3

2.- Two find the equation of a parallel line we need to point I will use (0, 4)

Use the point slope formula

y - y1 = m(x - x1)

y - 4 = 2/3(x - 0)

y - 4 = 2/3 x

y = 2/3x + 4

6 0

3 years ago

Convert the decimal to a fraction in simplest form:

Shkiper50 [21]

Answer:

Decimal 0.333 to a fraction in simplest form is: $\frac{333}{1000}$

Step-by-step explanation:

Given the decimal

$0.333$

Multiply and divide by 10 for every number after the decimal point.

There are three digits to the right of the decimal point, therefore multiply and divide by 1000.

Thus,

$0.333=\frac{0.333\cdot \:\:1000}{1000}$

$=\frac{333}{1000}$ ∵ 0.333×1000 = 333

Let us check if we can reduce the fraction $\frac{333}{1000}$

For this, we need to find a common factor of 333 and 1000 in order to cancel it out.

But, first, we need to find the Greatest Common Divisor (GCD) of 333, 1000

<u>Greatest Common Divisor (GCD) : </u>

The GCD of a, b is the largest positive number that divides both a and b without a remainder.

Prime Factorization of 333: 3 · 3 · 37

Prime Factorization of 1000: 2 · 2 · 2 · 5 · 5 · 5

As there is no common factor for 333 and 1000, therefore, the GCD is 1.

Important Tip:

As GCD is 1, therefore the fraction can not be simplified.

Therefore, decimal 0.333 to a fraction in simplest form is: $\frac{333}{1000}$

4 0

3 years ago

Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as: