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Paraphin [41]
3 years ago
6

Solve the absolute value inequality: |x + 12| + 5 < 27 Isolate the absolute value by subtracting 5 from both sides.

Mathematics
2 answers:
Feliz [49]3 years ago
8 0

Answer:

- 34 < x < 10

Step-by-step explanation:

Inequalities of the type | x | < a, always have a solution of the form

- a < x < a

given | x + 12 | + 5 < 27 ( subtract  5 from both sides )

| x + 12 | < 22, then

- 22 < x + 12 < 22 ( subtract 12 from all 3 intervals )

- 34 < x < 10


SSSSS [86.1K]3 years ago
3 0

Answer:

-34 < x < 10

Step-by-step explanation:

We have to solve absolute value inequality which means that we have to find the value of x.

| x+12 | +5 < 27

Adding -5 to both sides of above inequality,we get

| x+12 | +5-5 < 27-5

| x+12 | +0 < 22

| x+12 |  < 22

Since, we know that

| x | < a  ⇔ -a< x< a where a is any constant.

hence,

-22 < x+12 < 22

Adding -12 to each side of above inequality,we get

-22-12 < x+12-12 < 22-12

-34 < x+0 < 10

-34 < x < 10 which is solution of given inequality.

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Answer:

-3/4 pi radians

Step-by-step explanation:

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Hence, -<em>135° = -135/180 pi radians</em>

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2 years ago
Consider the sequence 100, 95, 90, 85, 80, 75 ...<br> What is the value of f(8)?
MAVERICK [17]

Answer:

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Step-by-step explanation:

Find a pattern in the sequence. It might be an <u>arithmetic sequence</u> (always adds or subtract by a certain number), or a <u>geometric sequence</u> (always multiplies or divides by a certain number).

To find a pattern in this decreasing sequence, we find either the common difference or the common divisor of each pair of consecutive numbers.

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Now, we know that this is an <u>arithmetic sequence</u>, and the common difference is <u>5</u>.

To calculate f(8), we find the 8th term in the sequence. We can do that by counting the terms in the sequence and using the common difference, 5, that we found, to continue the sequence.

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Step-by-step explanation:

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