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Simora [160]
2 years ago
7

Help me with the 2 problems

Mathematics
2 answers:
denpristay [2]2 years ago
7 0
Yes because 484 + 484 equals 964
And equation you should always do the opposite of the sign you get to find your answer so he got minus he should use Addition
Vlad1618 [11]2 years ago
6 0

9.

no

he has to put -484 to the left of the equal sign too

z + 484 -484 = 964 - 484

z = 480

10.

a.

310,000 + x = 465,000

x = 465,000 - 310,000

x = 155,000

b.

310,000x = 930,000

x = 930,000 ÷ 310,000

x = 3

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Luba_88 [7]

Answer:

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Step-by-step explanation:

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3 years ago
<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}

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\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}

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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?

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2 years ago
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Roman55 [17]

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Step-by-step explanation:

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3 years ago
Genesis’ basketball team won 32% of the games that they played this year and if they won 16 games, how many games they play this
ANTONII [103]

Answer:

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Step-by-step explanation:

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Answer:

The discount is $0.8d.

Step-by-step explanation:

Given that,

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Discount is applied to the original cost.

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Discount = 0.8 d

Hence, the discount is $0.8d.

8 0
3 years ago
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