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3 years ago

Solve the compound inequality |3x-9|≤15 and |2x-3|≥5. Give answer in interval notation.

Mathematics

1 answer:

laila [671]3 years ago

6 0

Answer:

The solution of |3x-9|≤15 is [-2;8] and the solution |2x-3|≥5 of is (-∞,2] ∪ [8,∞)

Step-by-step explanation:

When solving absolute value inequalities, there are two cases to consider.

Case 1: The expression within the absolute value symbols is positive.

Case 2: The expression within the absolute value symbols is negative.

The solution is the intersection of the solutions of these two cases.

In other words, for any real numbers a and b,

if |a|> b then a>b or a<-b
if |a|-b

So, being |3x-9|≤15

Solving: 3x-9 ≤ 15

3x ≤15 + 9

3x ≤24

x ≤24÷3

x≤8

or 3x-9 ≥ -15

3x ≥-15 +9

3x ≥-6

x ≥ (-6)÷3

x ≥ -2

The solution is made up of all the intervals that make the inequality true. Expressing the solution as an interval: [-2;8]

So, being |2x-3|≥5

Solving: 2x-3 ≥ 5

2x ≥ 5 + 3

2x ≥8

x ≥8÷2

x≥8

or 2x-3 ≤ -5

2x ≤-5 +3

2x ≤-2

x ≤ (-2)÷2

x ≤ -2

Expressing the solution as an interval: (-∞,2] ∪ [8,∞)

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Ne4ueva [31]

Look at the picture.

Use the Pythagorean theorem:

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substitute

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Answer: $\sin45^o=\dfrac{\sqrt2}{2}$

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3 years ago

When a particular mass-spring system is started by stretching the spring 3 cm, one complete oscillation takes 4 seconds.

11Alexandr11 [23.1K]

Answer:

A. 5.16 s.

B. 5.66 s.

Step-by-step explanation:

For a simple harmonic motion,

T = 2pi (sqrt * (l/g))

Given:

L1 = 3 cm

T1 = 4 s

L2 = 5 cm

T2 = ?

4 = 2pi*sqrt(3/g)

g = 7.4

At, L2,

T2 = 2pi*sqrt(5/7.4)

= 5.16 s.

M1 = M1

M2 = 2*M1

For a simple harmonic motion,

T = 2pi (sqrt * (m/k))

4 = 2pi (sqrt * (M1/k))

M1/k = 0.405

Inputting the above values,

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3 years ago

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jenyasd209 [6]

Keywords:

Cookies, boxes, sale, profit, unit cost

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Let $"x"$ be the number of boxes of cookies:

So, to know the number of boxes we divide 702 cookies among 18:

$x = \frac {702} {18}\\x = 39$

So, we have Tyler sold 39 boxes of cookies

Now, let $"y"$ be the cost of each box of cookies, to know the unit cost or sale price of the cookie boxes, we divided 136.50 dollars among 39 boxes of cookies, then:

$y = \frac {136.50} {39}\\y = 3.5$

Thus, the cost of each box was 3.5 dollars.

Answer:

The cost of a box is 3.5 dollars

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3 years ago

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elena55 [62]

Answer:

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