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Allisa [31]
3 years ago
9

bought a soccer ball for 19.95 and bought a pair of sneakers that cost three times the as much as the ball she had 7.80 left how

did she have when she purchase
Mathematics
1 answer:
lilavasa [31]3 years ago
8 0

Answer:$87.69

Step-by-step explanation:

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The sum of four consecutive terms of an arithmetic progression is 32 and the ratio of product of the first and the last term to
OverLord2011 [107]

The four consecutive terms are 2,6,10,14.

Explanation:

Let the four consecutive terms of an arithmetic progression be (a - 3d), (a - d),(a + d), (a + 3d)

It is given that the sum of four consecutive terms is 32.

Thus, adding all the four consecutive terms, we have,

\begin{array}{r}{a-3 d+a-d+a+d+a+3 d=32} \\{4 a=32} \\{a=8}\end{array}

Thus, the value of a is 8.

It is also given that the ratio of the product of first and last term to the product of the two middle terms is 7:15. Thud, we have,

\frac{(a-3d)(a+3d)}{(a-d)(a+d)} =\frac{7}{15}

Simplifying the terms, we have,

$\begin{aligned} \frac{a^{2}-9 d^{2}}{a^{2}-d^{2}} &=\frac{7}{15} \\ 15\left(a^{2}-9 d^{2}\right) &=7\left(a^{2}-d^{2}\right) \\ 15 a^{2}-135 d^{2} &=7 a^{2}-7 d^{2} \\ 8 a^{2} &=128 d^{2} \end{aligned}$

Now, substituting a = 8, we have,

$\begin{aligned} 8(64) &=128 d^{2} \\ 512 &=128 d^{2} \\ 4 &=d^{2} \\ 2 &=d \end{aligned}$

Thus, the value of d is 2.

Now, we shall substitute the value of a and d in the terms (a - 3d), (a - d),(a + d), (a + 3d), we get, the four consecutive terms.

Thus, the four consecutive terms are 2,6,10,14.

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3 years ago
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Answer:the first one

Step-by-step explanation:

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</span>
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Answer:

factor:

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100x^2+10x+(10x+1)

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