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3 years ago

Find the value of x. B X+5 4 D E 2x 3 А x = [?]

Mathematics

1 answer:

Greeley [361]3 years ago

5 0

Answer:

x = 3

Step-by-step explanation:

Δ BDE and Δ BAC are similar triangles, thus the ratio of corresponding sides are equal, that is

$\frac{BD}{BA}$ = $\frac{BE}{BC}$ , substitute values

$\frac{x+5}{3x+5}$ = $\frac{4}{7}$ ( cross- multiply )

4(3x + 5) = 7(x + 5) ← distribute parenthesis on both sides )

12x + 20 = 7x + 35 ( subtract 7x from both sides )

5x + 20 = 35 ( subtract 20 from both sides )

5x = 15 ( divide both sides by 5 )

x = 3

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Find the sum of the first five terms using the geometric series formula for the sequence 1/2, -1,2,-4…

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<h3>How to determine the sum?</h3>

The series is given as:

1/2, -1,2,-4…

Calculate the common ratio of the series using

r = -4/2

Evaluate

r = -2

The sum is then calculated as:

$S_n = a\frac{1 - r^n}{1 - r}$

This gives

$S_n = \frac{1}{2} * \frac{(1 - (-2)^5}{1 + 2}$

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Hence, the sum of the first five terms is 11/2