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Lina20 [59]
3 years ago
15

Solve the inequality. 2(4+2x)25x+5

Mathematics
1 answer:
Inessa [10]3 years ago
6 0

Answer:

x ≤ 3

Step-by-step explanation:

Given

2(4 + 2x) ≥ 5x + 5 ← distribute parenthesis on left side

8 + 4x ≥ 5x + 5 ( subtract 4x from both sides )

8 ≥ x + 5 ( subtract 5 from both sides )

3 ≥ x , hence

x ≤ 3

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An angle measures 156° less than the measure of its supplementary angle. What is the measure of each angle?
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12° and 168°

Step-by-step explanation:

If x is the angle, and y is the supplementary angle, then:

x + y = 180

x = y − 156

Solve the system of equations using substitution:

y − 156 + y = 180

2y = 336

y = 168

Plug back into either equation to find x:

x = 12

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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.

3 0
3 years ago
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