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2 years ago

2. x + 12 =23 3. X-6 = 13 4. X-9 = 14 5. 2x = 12 6. 3x = 30

Mathematics

2 answers:

levacccp [35]2 years ago

4 0

Answer:

2. x = 11

3. x = 19

4. x = 23

5. x = 6

6. x = 10

Step-by-step explanation:

2. x + 12 =23

x = 23 - 12

x = 11

3. x - 6 = 13

x = 13 + 6

x = 19

4. x - 9 = 14

x = 14 + 9

x = 23

5. 2x = 12

x = 12/2

x = 6

6. 3x = 30

x = 30/3

x = 10

tekilochka [14]2 years ago

4 0

2. 23 - 12 = 11
x = 11
3. 13 + 6 = 19
x = 19
4. 14 + 9 = 23
x = 23
5. 12/2 = 6
x = 6
6. 30/3 = 10
x = 10

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

laila [671]

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 then a<b or 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

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x ≤ -2

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

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2 years ago

Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain.

djyliett [7]

An=a1+d(n-1)
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a1=first term, when n=1
d=common differnce=amount each term increases by
n=which one

so
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so a1=40
it seems to increas by 7 each time

an=40+7(n-1)
explicit formula is expanded
an=40+7n-7
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the domain is natural numbers because you can't have the -3rd term or the 0th term or the 3.24th term

domain is natural numbers
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3 years ago

At 3pm, the length of the shadow of a thin vertical pole standing on level ground is the same as the height of the pole. A while

aliya0001 [1]

Answer: The height of the pole is 175.97 ( approx )

Step-by-step explanation:

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Also, let the angle of elevation of the sun to the pole at 3 pm is $\theta$

Thus, by the question,

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Aleonysh [2.5K]

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