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4 years ago

9

A=(1/2)h(b1+b2) solve for h

1 answer:

pshichka [43]4 years ago

6 0

Answer:

$\large\boxed{h=\dfrac{2A}{b_1+b_2}}$

Step-by-step explanation:

$A=\dfrac{1}{2}h(b_1+b_2)\qquad\text{multiply both sides by 2}\\\\2A=2\!\!\!\!\diagup\cdot\dfrac{1}{2\!\!\!\!\diagup}h(b_1+b_2)\\\\2A=h(b_1+b_2)\qquad\text{divide both sides by}\ (b_1+b_2)\\\\\dfrac{2A}{(b_1+b_2)}=\dfrac{h(b_1+b_2)}{(b_1+b_2)}\qquad\text{cancel}\ (b_1+b_2)\\\\\dfrac{2A}{b_1+b_2}=h\to h=\dfrac{2A}{b_1+b_2}$

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Solve<br> 3(2x - 5) = 9(10 - x)

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Answer:

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Step-by-step explanation:

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Find the 13th term of the arithmetic sequence -3x – 1,42 + 4,112 + 9, ...

Strike441 [17]

Answer:

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

Step-by-step explanation:

We are given the arithmetic sequence:

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

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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lisov135 [29]

Answer:

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Step-by-step explanation:

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