I need help with solving a system of equations using elimination

<img src="https://tex.z-dn.net/?f=12x%20%5E%7B2%7D%20%20%2B%204x%20%2B%2020" id="TexFormula1" title="12x ^{2} + 4x + 20" alt="1

Nesterboy [21]

<h3>Answer: </h3>

The GCF is 4

The polynomial factors to $4(3x^2+x+5)$

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Further explanation:

Ignore the x terms

We're looking for the GCF of 12, 4 and 20

Factor each to their prime factorization. It might help to do a factor tree, but this is optional.

12 = 2*2*3
4 = 2*2
20 = 2*2*5

Each factorization involves "2*2", which means 2*2 = 4 is the GCF here.

We can then factor like so

$12x^2 + 4x + 20\\\\4*3x^2 + 4*x + 4*5\\\\4(3x^2 + x + 5)$

The distributive property pulls out that common 4. We can verify this by distributing the 4 back in, so we get the original expression back again.

The polynomial inside the parenthesis cannot be factored further. Proof of this can be found by looking at the roots and noticing that they aren't rational numbers (use the quadratic formula).

4 0

2 years ago

For the following telescoping series, find a formula for the nth term of the sequence of partial sums

gtnhenbr [62]

I'm guessing the sum is supposed to be

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}$

Split the summand into partial fractions:

$\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}$

$1=a(5k+4)+b(5k-1)$

If $k=-\frac45$ , then

$1=b(-4-1)\implies b=-\frac15$

If $k=\frac15$ , then

$1=a(1+4)\implies a=\frac15$

This means

$\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}$

Consider the $n$ th partial sum of the series:

$S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)$

The sum telescopes so that

$S_n=\dfrac2{14}-\dfrac2{5n+4}$

and as $n\to\infty$ , the second term vanishes and leaves us with

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17$

7 0

3 years ago

The geometric mean of 8 and 2 is<br><br> 5<br> 3<br> 4<br> 16

igomit [66]

Answer:5

Step-by-step explanation:

<h3><u>(8 + 2)</u> <u>sum of values </u> = <u>10</u> = 5</h3><h3> 2 number of values 2</h3><h3 />

There is equal spacing between the mean and the extremes

8 - 5 = 3

5 - 2 = 3

5 0

3 years ago

The Law of Large Numbers states that as the number of trials of an experiment increases, the experimental probability of an even

Lena [83]

The law of large number states that , if number of trials increases in an experiment , in a fair trial where each outcome has same chance of occurring or having equal probabilities,when total number of trials goes higher and higher the probabilities of each single outcome becomes approximately equal.→→In case of Experimental Probability

The Coin Possessed by Jake is a Magic coin.

Now Outcomes received by jake when he tosses the coin certain number of times.He flipped it 100 times, and found that it came up heads 64% of the time. He flipped it another 500 times, and it came up heads 57% of the time. He then flipped it 1000 times, and it came up heads 58% of the time. Then, he flipped it 1500 times, and it came up heads 62% of the time.

Based on the information provided , it appears that coin is not fair . It is Unbiased.So , if we apply law of large numbers here after number of trials will go higher and higher , the chances of coming head will be more than tail i.e theoretical probability of the magic coin coming up heads is> 50%.

To test my hypothesis i have used the information provided by Jake, which shows that coin is not fair. The probability of head has more than tail i.e by 14%, 7%,8% and 12%.

8 0

3 years ago

Susan's stylist has done a great job of coloring her hair. She wants to leave a 20 percent tip. If the bill was $150, how much s

Schach [20]

She should leave $30. Hope it helps! If you could vote me brainiest, that would be awesome!

8 0

3 years ago

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