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Alekssandra [29.7K]
3 years ago
5

Sonia ran 6 miles more than twice as far as Brian if the total number of milesso you ran 6 miles more than twice as far as Brian

if the total numbers of Miles run by both is 33 how far did each one run.
​
Mathematics
1 answer:
melamori03 [73]3 years ago
3 0

Answer: Brian ran 9 miles

Sonia ran 24 miles

Step-by-step explanation:

Let's Brian's distance be represented by x.

Since Sonia ran 6 miles more than twice as far as Brian. This will be:

= (2 × x) + 6

= 2x + 6

Therefore,

x + 2x+6 = 33

3x + 6 = 33

3x = 33 - 6.

3x = 27

x = 27/3

x = 9

Brian ran 9 miles

Sonia ran = 2x+6 = 2(9).+ 6 = 18+6 = 24 miles

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The following dataset represents the math test scores for a class of 20 students. 90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80
neonofarm [45]

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3 years ago
In a G.P the difference between the 1st and 5th term is 150, and the difference between the
liubo4ka [24]

Answer:

Either \displaystyle \frac{-1522}{\sqrt{41}} (approximately -238) or \displaystyle \frac{1522}{\sqrt{41}} (approximately 238.)

Step-by-step explanation:

Let a denote the first term of this geometric series, and let r denote the common ratio of this geometric series.

The first five terms of this series would be:

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First equation:

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Second equation:

a\, r^3 - a\, r = 48.

Rewrite and simplify the first equation.

\begin{aligned}& a\, r^4 - a \\ &= a\, \left(r^4 - 1\right)\\ &= a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) \end{aligned}.

Therefore, the first equation becomes:

a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) = 150..

Similarly, rewrite and simplify the second equation:

\begin{aligned}&a\, r^3 - a\, r\\ &= a\, \left( r^3 - r\right) \\ &= a\, r\, \left(r^2 - 1\right) \end{aligned}.

Therefore, the second equation becomes:

a\, r\, \left(r^2 - 1\right) = 48.

Take the quotient between these two equations:

\begin{aligned}\frac{a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right)}{a\cdot r\, \left(r^2 - 1\right)} = \frac{150}{48}\end{aligned}.

Simplify and solve for r:

\displaystyle \frac{r^2+ 1}{r} = \frac{25}{8}.

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Calculate the sum of the first five terms:

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Calculate the sum of the first five terms:

\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= \frac{1522\sqrt{41}}{41} \approx 238\end{aligned}.

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