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mina [271]
3 years ago
7

Write the following inequality in slope-intercept form. −6x + 2y ≤ 42

Mathematics
2 answers:
zubka84 [21]3 years ago
7 0
Add the 6x to both sides. Then divide both sides by 2 to get y by itself.

y <= 6x + 42

Note: if it were a -2y, you’d have to flip the inequality sign when dividing by that negative 2.

:)
jeyben [28]3 years ago
7 0

Answer:  The required slope-intercept form is y\leq 3x+21..

Step-by-step explanation:  We are given to write the following inequality in slope-intercept form :

-6x+2y\leq 42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

We know that

the slope-intercept form of an inequality of the given form is as follows :

y\leq mx+c, where m is the slope and c is the y-intercept.

From inequality (i), we have

-6x+2y\leq 42\\\\\Rightarrow 2y\leq6x+42\\\\\Rightarrow y\leq\dfrac{6}{2}x+\dfrac{42}{2}\\\\\Rightarrow y\leq 3x+21.

Thus, the required slope-intercept form is y\leq 3x+21..

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Answer:

3. 2

4. f(n) = 3 + 4(n - 1)

Step-by-step explanation:

3. The general term of the arithmetic sequence is given by:

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To find the ninth term of this arithmetic sequence, just put $ n = 9 $ in the general term.

∴ A(9) = - 14 + (9 - 1)(2) = - 14 + 8(2) = -14 + 16 = 2.

Therefore the ninth term in the arithmetic sequence is two.

4. To know which expression represents the given sequence, substitute different values for $ n $ to conclude.

In Option A, f(n) = 4 + 3(n - 1). Substitute n = 1.

We get f(1) = 4 + 3(0) = 4. This is not the first term in the sequence and can be eliminated.

In Option B, f(n) = 4 + 3n. Substitute n = 1.

We get f(1) = 4 + 3(1) = 7, not 3 so can be eliminated.

Similarly in Option C, we get 7 and could be eliminated.

In Option D, f(n) = 3 + 4(n - 1). Substitute n = 1.

We get f(1) = 3 + 4(1 - 1) = 3, which is the first term in the sequence.

Similarly, f(2) = 3 + 4(2 - 1) = 3 + 4 = 7.

Substitute n = 3, 4 to get other terms as well.

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a_sh-v [17]
8z = 64
divide both sides with 8

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z = 8.
7 0
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olga nikolaevna [1]

Answer:

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Step-by-step explanation:

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We get:

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Simplifying, we have:

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