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Levart [38]
3 years ago
8

Consider the diagram showing the path Joel biked. Joel biked 9 miles east and then 12 miles north. If he biked back to his start

ing point using the most direct route, how many miles would he ride all together? Joel’s starting point is x

Mathematics
2 answers:
natulia [17]3 years ago
7 0

Using the Pythagorean theorem:

The direct distance back would be:

√(9^2 + 12^2)

√(81 + 144)

√225

15 miles

The total miles would be the sum of the 3 sides:

15 + 9 +12 = 36 total miles.

Andrej [43]3 years ago
5 0

Answer:

36 miles

Step-by-step explanation:

Consider the diagram showing the path Joel biked. Joel biked 9 miles east and then 12 miles north. If he biked back to his starting point using the most direct route, he would have ride 36 miles all together. Joel’s starting point is x.

In order to solve this, we must use the Pythagorean theorem.

The amount of miles would be found by adding the 3 sides together to find the sum or answer.

15 + 9 + 12 = 36 miles

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Find the 13th term of the arithmetic sequence -3x – 1,42 + 4,112 + 9, ...
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The 13th term is 81<em>x</em> + 59.

Step-by-step explanation:

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\displaystle -3x -1, \, 4x +4, \, 11x  + 9 \dots

And we want to find the 13th term.

Recall that for an arithmetic sequence, each subsequent term only differ by a common difference <em>d</em>. In other words:

\displaystyle \underbrace{-3x - 1}_{x_1} + d = \underbrace{4x + 4} _ {x_2}

Find the common difference by subtracting the first term from the second:

d = (4x+4) - (-3x - 1)

Distribute:

d = (4x + 4) + (3x + 1)

Combine like terms. Hence:

d = 7x + 5

The common difference is (7<em>x</em> + 5).

To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:

\displaystyle x_n = a + d(n-1)

Where <em>a</em> is the initial term and <em>d</em> is the common difference.

The initial term is (-3<em>x</em> - 1) and the common difference is (7<em>x</em> + 5). Hence:

\displaystyle x_n = (-3x - 1) + (7x+5)(n-1)

To find the 13th term, let <em>n</em> = 13. Hence:

\displaystyle x_{13} = (-3x - 1) + (7x + 5)((13)-1)

Simplify:

\displaystyle \begin{aligned}x_{13} &= (-3x-1) + (7x+5)(12) \\ &= (-3x - 1) +(84x + 60) \\ &= 81x + 59 \end{aligned}

The 13th term is 81<em>x</em> + 59.

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3 years ago
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