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3 years ago

Which statement is true about this equation? -9(x + 3) + 12 = -3(2x + 5) − 3x

Mathematics

1 answer:

Alenkasestr [34]3 years ago

4 0

Answer:

Any value of "x" makes the equation true

Step-by-step explanation:

(-∞,∞)

All real numbers

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What is the prime factorization for 50 using exponents?

galina1969 [7]

Answer:

Either way, it gives us the prime factorization for 50 that is 5 x 5 x 2. The prime factorization of 50 can be expressed using exponents as 5^2 x 2.

Step-by-step explanation:

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2 years ago

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5000 is 1/10 of what

VikaD [51]

50,000 is the answer because if you multiply 5,000 and 10 you get 50,000. And if you divide 50,000 by 10 you get 5,000. Which is 1/10 of 50,000.

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2 years ago

How to you get the radical form?

Over [174]

Answer:

Note: this answer is kind of long so jump to picture to see a visual process.

In order to find the simplest radical form of a square root, you need prime factorize the number. In order to do this, you take a number and divide it by different prime numbers until all of its factors are now prime. We will use 24 as our example. 24 divided by 2 (which is prime) is 12. 12 divided by 2, is 6. 6 divided by 2 is 3. Therefor, our prime factorization of 24 is 2^3 * 3, which basically means 8 * 3. Then, take take out pairs of the same number and put on the OUTSIDE of the root. However, make sure that it is NEXT to the square root and not inside the mini hook that the square root makes. This means that that number is multiplying the square root of the number. Now, the only pair in this prime factorization is 2, so take two out of the prime factorization and that leaves us with square root 6 times 2, which is the answer.

Also, when taking out pairs, only take one number from the pair (in this case 2) and put it on the outside. If there is another pair, multiply that number by the other number. So if there was a pair of 3 and a pair of 2, take out 1 three and 1 two and multiply them and put on the outside.

Step-by-step explanation:

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2 years ago

A number written in expanded form is written has the sum of each blank write 39,005 in expanded form

evablogger [386]

When expanding number, we should separate the numbers according to the places like the number 275 written in expanded form 200+70+5. So, in this question we must likely done like this. The number is 39,005 the sum that is written on expanded form is 30,000+9,000+5.

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3 years ago

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Does the series converge or diverge? If it converges, what is the sum? Show your work. ∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1

Mekhanik [1.2K]

Answer:

Step-by-step explanation:

Given the series,

∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1

I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)

So,

∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞

There are different types of test to show if a series converges or diverges

So, using Ratio test

Lim n → ∞ (a_n+1 / a_n)

Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))

Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))

Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)

Lim n→ ∞ (-1/2)^(n-n+1)

Lim n→ ∞ (-1/2)^1 = -1/2

Since the limit is less than 0, then, the series converge...

Sum to infinity

Using geometric progression formula

S∞ = a / 1 - r

Where

a is first term

r is common ratio

So, first term is

a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1

a_1 = -4

Common ratio r = a_2 / a_1

a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2

a_2 = 2

Then,

r = a_2 / a_1 = 2 / -4 = -½

S∞ = -4 / 1--½

S∞ = -4 / 1 + ½

S∞ = -4 / 3/2 = -4 × 2 / 3

S∞ = -8 / 3 = -2⅔

The sum to infinity is -2.67 or -2⅔

Check attachment for better understanding

3 0

3 years ago