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elena-s [515]
2 years ago
10

What is 20 xy -35xyz + 15x?

Mathematics
2 answers:
Ber [7]2 years ago
8 0
5x(4y-7yz+3)______________
Lisa [10]2 years ago
4 0

Answer:

5x(−7yz+4y+3)

Step-by-step explanation:

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<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B
riadik2000 [5.3K]

Let

S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n

where we assume |r| < 1. Multiplying on both sides by r gives

r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}

and subtracting this from S_n gives

(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}

As n → ∞, the exponential term will converge to 0, and the partial sums S_n will converge to

\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}

Now, we're given

a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a

a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}

We must have |r| < 1 since both sums converge, so

\dfrac{15}a = \dfrac1{1-r}

\dfrac{150}{a^2} = \dfrac1{1-r^2}

Solving for r by substitution, we have

\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)

\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}

Recalling the difference of squares identity, we have

\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}

We've already confirmed r ≠ 1, so we can simplify this to

\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15

It follows that

\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12

and so the sum we want is

ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0
2 years ago
Aaron has $4,500 saved to pay for an ATV that costs $7,500.
Komok [63]

Answer:

i think its 0.9994225

Step-by-step explanation:

just subtract the 8.75136.24 bye 7.75193. and there you go.

6 0
3 years ago
Write the expression in simplest form.<br> (11 + 3) – 2(- 4 1 - 1) =<br> NIO
Aleksandr-060686 [28]

Answer:

11+3=14

-41-1=-42

14-2(-42)

-2(-42)

14+84

98

I hope this is good enough:

5 0
2 years ago
Lori want to distribute 35 peaches equally into baskets. she will use more than 1 but fewer than 10 baskets how many basket Lori
Hunter-Best [27]
Unless this is a trick question, I think 7 baskets. If you have 7 baskets then you can put 5 peaches in each basket. Hope this is right.
7 0
3 years ago
Eric writes 1/3 of a page in 1/5 of a minute. How much time, in minutes, does it take him to write a full page? Type your answer
Sholpan [36]

Answer:hello

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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