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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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Nostrana [21]

Answer:

B

Step-by-step explanation:

The formula for the area of a triangle is given as:

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If we know the area (A) and the base, to find the height, the following would be done:

Divide both sides by b

A/b = h/2

Multiply both sides by 2

\frac{A}{b} * 2 = h

As we can see here, to find the base, we would divide the area by the vase, then multiply what we get by 2.

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3 years ago
In a political science class, test scores were determined to be 20 times the number of hours, h, the student studied plus 3.
V125BC [204]

Answer:

S = 20h + 3

Step-by-step explanation:

It is seen in a political science class that the test score were determined to be 20 times the number of hours, h, the student studied plus 3.

Hence, the condition can be modeled by the equation

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where, S represents the score of a particular student who studied h hours before the test. (Answer)

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3 years ago
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Alexandra [31]
In my opinion, ur right
4 0
3 years ago
(1/27)^x-6=27<br><br>Could I please have a step by step as well? Much appreciated! ​
Andrei [34K]

Answer:

x = 7

Step-by-step explanation:

1) Use Division Distributive Property: (x/y)^a = x^a/y^a.

\frac{1}{ {27}^{x - 8} }  = 27

2) Multiply both sides by 27^x - 8.

1 =  {27} \times 27^{1 + x  - 8}

3) Use the product rule: x^a x^b = x^a+b.

1 =  {27}^{1 + x - 8}

4) Simplify 1 + x - 8 to x - 7.

1  =  {27}^{x - 7}

5) Use Definition of Common Logarithm: b^a = x if and only if log<u>b</u><u> </u>(x) = a.

log_{27}1 = x - 7

6) Use Change of Base Rule.

\frac{ log_1  }{  log{27} }  = x - 7

7) Use rule of 1: log 1 = 0.

\frac{0}{ log_{27}}  = x - 7

8) Simplify 0/log_27 to 0.

0 = x - 7

9) Add 7 to both sides.

7 = x

10) Switch sides.

x = 7

<u>Therefor</u><u>,</u><u> </u><u>the</u><u> </u><u>answer</u><u> </u><u>is</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>7</u><u>.</u>

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