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dalvyx [7]
3 years ago
13

Can you please help me with 1-12? Thank you

Mathematics
1 answer:
Marysya12 [62]3 years ago
6 0

Answer:

1. 18.84 in

2. 56.52 cm

Step-by-step explanation:

The circumference of a circle is the distance around the circle. Its found using the formula C = πd or C=2πr. The variable d represents the diameter or the distance from one edge of the circle to the other through the cent. The variable r represents the radius of a circle or the distance from one edge to the center. Use the formula by substituting a diameter or radius then simplify.

1. C = πd = π(6) = 3.14(6) = 18.84 in

2. C = 2πr = 2(3.14)(9) = 56.52 cm

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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

2x ≤-2

x ≤ (-2)÷2

x ≤ -2

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

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Step-by-step explanation:

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Step-by-step explanation:

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Which system of linear inequalities is graphed?
ANEK [815]

To determine the system of inequality that has been graphed, we need to be very smart.


Observe that all the equations are the same.


Also note that all the lines are solid. This should tell you that the inequities should involve.


\ge \:or\: \le



Therefore the answer is between option A and B.



So we choose a point in the solution region to discriminate between A and B.


Let us choose the origin since that is easy to evaluate.


We substitute into option A to get.

y\le 3x-1\:and\: x+ 3y \ge 6




0\le 3(0)-1\:and\: 0+ 3(0) \ge 6




0\le -1\:and\: 0\ge 6


The above statements are false



We now substitute into option B



y\ge 3x-1\:and\: x+ 3y \le 6




0\ge 3(0)-1\:and\: 0+ 3(0) \le 6




0\ge-1\:and\: 0 \le 6


Both statements are true, therefore the correct answer is option B.




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3 years ago
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mafiozo [28]

to replace 2x we need +6x-4x

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