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4 years ago

3 (4x+4)+(x+8)=7x-2 (-3x+11) what does x equal?

Mathematics

1 answer:

Yanka [14]4 years ago

5 0

jedimath on iPad will teach you step by step

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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

3 years ago

The length of the rectangle is 8cm longer than the width.

masya89 [10]

The length of the rectangle is 8cm longer than the width.
l=w+8
If the length of the original rectangle is increased by 6cm and the width is increased by 3cm the perimeter is 76cm.
p=76=((l+6)+(w+3))*2=(l+6+w+3)*2=(l+w+9)*2

to solve this substitute l=w+8 into the p= equation:
p=76=((w+8)+w+9)*2=
76=(2w+17)*2
76=4w+34
42=4w
10.5=w

l=w+8=10.5+8=18.5

4 0

4 years ago

An amount of $48,000 is borrowed for 12 years at 3% interest, compounded annually. If the loan is paid in full at the end of tha

Marianna [84]

Answer:

soory this is for points

Step-by-step explanation:

8 0

3 years ago

Give each answer as mixed number in simplest form

allochka39001 [22]

Answer:

3 7/18

Step-by-step explanation:

2 1/6 + 1 2/9 (- cancels with the - to give us +)

Convert to simple fraction: 13/6 +11/9

Find the common denominator: 13x 3/6x3 + 11 x 2/9 x 2

39/18 + 22/18

Now that the denominators are same, conduct the given operation.

39 + 22/ 18

61/18

Convert into mixed fraction: 3 7/18

Final answer: 3 7/18

7 0

2 years ago

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What is 2340 divided by 53?

Jet001 [13]

44.1 is the answer to that

4 0

3 years ago

Read 2 more answers