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sergiy2304 [10]
3 years ago
11

|2x| ≤ x + 3

Mathematics
2 answers:
Korolek [52]3 years ago
5 0

Let's solve your inequality step-by-step.

|2x|≤x+3

Solve Absolute Value.

|2x|≤x+3

Let's find the critical points of the inequality.

|2x|=x+3

We know either2x=x+3or2x=−(x+3)

2x=x+3(Possibility 1)

2x−x=x+3−x(Subtract x from both sides)

x=3

2x=−(x+3)(Possibility 2)

2x=−x−3(Simplify both sides of the equation)

2x+x=−x−3+x(Add x to both sides)

3x=−3

3x

3

=

−3

3

(Divide both sides by 3)

x=−1

Check possible critical points.

x=3(Works in original equation)

x=−1(Works in original equation)

Critical points:

x=3 or x=−1

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x≤−1(Doesn't work in original inequality)

−1≤x≤3(Works in original inequality)

x≥3(Doesn't work in original inequality)

Answer:

−1≤x≤3

r-ruslan [8.4K]3 years ago
3 0

Answer:

[-1,3]

Step-by-step explanation:

|2x|<x+3

calculate the absolute value

2*|x|<x+3

move < to left

2*|x|-x<3

split into possible cases

2x-x<3, x<0

2*(-x)-x<3, x<0

solve inequalities

[0,3]

[-1,0]

find union

[-1,3]

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HELP!!! if a hospital patient is given 50 milligrams of medicine, which leaves the bloodstream at 10% per hour, how many milligr
kipiarov [429]

Answer:

I also got 27.44 mg.

Step-by-step explanation:

Use the function given to you:

A(t)=le^rt

l: Initial Amount (50)

r: Rate (-.1) (Negative because the medicine is exiting the bloodstream at 10% per hour

t: 6 (the specific time value you are evaluating the function at.

A(6)=50e^-.1(6)=27.44

8 0
3 years ago
What is the 40th term of the arithmetic sequence 13, 26, 39, 52
Diano4ka-milaya [45]

Answer:

your answer would be 520

Step-by-step explanation:

13 x 40 = 520

7 0
2 years ago
Please help i don’t understand this
swat32

Similar polygons only differ by a scaling factor. In other words, two polygons are similar if one is the scaled version of the other.

In particular, this implies that the angles are preserved, and the correspondent sides are in proportion.

These two polygons are both rectangles, so the angles are preserved. We must check the sides, and we have to check if the smaller sides are in the same proportion as the bigger sides.

So, the two rectangles are similar if the following is true.

4\div 5 = 11\div 12

In any proportion, the product of the inner terms must be the same as the product of the outer terms:

4\cdot 12 = 5\cdot 11 \iff 48=55

This is clearly false, and thus the two rectangles are not similar.

5 0
3 years ago
Joe went on holiday to Spain.
Hunter-Best [27]
Answers:

a. £2,090
b. My answer would be less because my total in euros would be divided by a greater number when converting euros to pounds.

Work for part a:

Apartment: 560•3= 1680 euros

Car: 20.16•15= 302.4 euros

1680+302.4=1982.4

1982.4/1.12 = £x/1

1982.4 / 1.12= £1,770

£1,770 + £320 = £2,090 total

Work for part b:
Example:
(instead of 1.12 I put 2 to see what would happen with a greater number)
1982.4 / 2 = 991.2

991.2 is less than 1,770 (the answer I got with 1.12)

Let me know if you need any clarification! :)
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3 years ago
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