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Serga [27]
3 years ago
14

What is the value of X in the figure below? In this diagram.

Mathematics
1 answer:
kipiarov [429]3 years ago
3 0
<h3>Answer:  E.  45/4</h3>

===========================================

Work Shown:

Because we have similar triangles, we can form the proportion below to isolate x.

(AC)/(BC) = (CD)/(AC)

(15)/(20) = (x)/(15)

15*15 = 20x .... cross multiply

225 = 20x

20x = 225

x = 225/20

x = (5*45)/(5*4)

x = 45/4

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Step-by-step explanation:

1.\sum_{i=1}^{5}3i

The simplest method is "brute force".  Calculate each term and add them up.

∑ = 3(1) + 3(2) + 3(3) + 3(4) + 3(5)

∑ = 3 + 6 + 9 + 12 + 15

∑ = 45

2.\sum_{k=1}^{4}(2k)^{2}

∑ = (2×1)² + (2×2)² + (2×3)² + (2×4)²

∑ = 4 + 16 + 36 + 64

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3.\sum_{k=3}^{6}(2k-10)

∑ = (2×3−10) + (2×4−10) + (2×5−10) + (2×6−10)

∑ = -4 + -2 + 0 + 2

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4. 1 + 1/4 + 1/16 + 1/64 + 1/256

This is a geometric sequence where the first term is 1 and the common ratio is 1/4.  The nth term is:

a = 1 (1/4)ⁿ⁻¹

So the series is:

\sum_{j=1}^{7}(\frac{1}{4})^{j-1}

5. -5 + -1 + 3 + 7 + 11

This is an arithmetic sequence where the first term is -5 and the common difference is 4.  The nth term is:

a = -5 + 4(n−1)

a = -5 + 4n − 4

a = 4n − 9

So the series is:

\sum_{j=1}^{5}(4j-9)

5 0
3 years ago
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