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2 years ago

For the geometric sequence x, (2x + 1), (4x + 10), ... the value of x, to the nearest

Mathematics

1 answer:

mel-nik [20]2 years ago

6 0

Answer:

x ≈ 0.17

Step-by-step explanation:

There is a common ratio r between consecutive terms in a geometric sequence, that is

r = $\frac{a_{2} }{a_{1} }$ = $\frac{a_{3} }{a_{2} }$ , substitute values

$\frac{2x+1}{x}$ = $\frac{4x+10}{2x+1}$ ( cross- multiply )

x(4x + 10) = (2x + 1)² ← expand using FOIL

4x² + 10x = 4x² + 4x + 1 ( subtract 4x² + 4x from both sides )

6x = 1 ( divide both sides by 6 )

x = $\frac{1}{6}$ ≈ 0.17 ( to the nearest hundredth )

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The average value of two positive numbers is 30% less than one of the two numbers. By which percentage is average value bigger t

Viefleur [7K]

Answer:

75% bigger

Step-by-step explanation:

Let the first number be x and the second be y.

So:

$Average = \frac{x + y}{2}$

And:

$Average = (1 - 30\%) * x$ -----30% less than x

Substitute $Average = (1 - 30\%) * x$ in $Average = \frac{x + y}{2}$

$\frac{x + y}{2} = (1 - 30\%) * x$

$\frac{x + y}{2} = (1 - 0.30) * x$

$\frac{x + y}{2} = 0.70 * x$

$\frac{x + y}{2} = 0.70x$

Cross multiply

$x + y = 0.70x * 2$

$x + y = 1.40x$

Collect like terms

$1.40x - x = y$

$0.40x = y$

Make x the subject

$x = \frac{y}{0.40}$

$x = 2.50y$

So, the average is:

$Average = (1 - 30\%) * x$

$Average = (1 - 30\%) * 2.50y$

$Average =0.70 * 2.50y$

$Average =1.75y$

Rewrite as:

$Average =(1 + 0.75)y$

Express as percentage

$Average =(1 + 75\%)y$

This means that the average is 75% bigger than the second number

6 0

2 years ago

37% of what number is 99.9?

siniylev [52]

Answer:

270

Step-by-step explanation:

37 % of a number is the same as divide by 100 and multiply by 37. To get this number we do the opposite: divide 99.9 by 37 which gives us 27 and then multiply by 100 which will give us 270.

if we check this: 270 /100 *37 = 99,9

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3 years ago

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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