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Oksanka [162]
3 years ago
13

Given A = {18, 6, -3, -12} Determine all elements of set A that are in the solution of the inequality 2/3x + 3 < -2x -7

Mathematics
1 answer:
creativ13 [48]3 years ago
7 0
Plug in each value in the set into x, and evaluate both sides.
The values of x that make the inequality true are the answer.

Start with 18.
<span>2/3x + 3 < -2x -7
2/3(18) + 3 < -2(18) - 7
12 + 3 < -36 - 7
15 < -43 is false, so 18 does not work.

</span><span>Now do 6.
<span>2/3x + 3 < -2x -7
2/3(6) + 3 < -2(6) - 7
4 + 3 < -12 - 7
7 < -19 is false, so 6 does not work.

</span></span><span>Now do -3.
<span>2/3x + 3 < -2x -7
2/3(-3) + 3 < -2(-3) - 7
-2 + 3 < 6 - 7
1 < -1 is false, so -3 does not work.

</span></span><span><span>Now do -12.
<span>2/3x + 3 < -2x -7
2/3(-12) + 3 < -2(-12) - 7
-8 + 3 < 24 - 7
-5 < 17 is true, so -12 does not work.</span></span>

</span>
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3x+17 less than or equal to 2(1-x)​
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Answer:

x ≤ -5

Step-by-step explanation:

According to given condition:

3x + 17 ≤ 2(1 - x)

By simplifying:

3x + 17 ≤ 2 - 2x

Adding 2x - 17 on both sides we get:

3x + 2x ≤ 2 - 17

5x ≤ - 15

Dividing both sides by 5 we get:

x ≤ -5

i hope it will help you!

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3 years ago
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7 0
2 years ago
A. A group of twelve art students are visiting a local art museum for a field trip. The total cost of admission for the students
Shalnov [3]

Answer:

a) $10.42

b) 11 trips

c) 10 cookies

d) 12/125ths of a cheesecake (or 9.6%)

Step-by-step explanation:

a)  

Let x = the cost of admission for each student

Let y = the total cost of admission

⇒  y = 12x  

⇒  125 = 12x  

⇒  x = 125 ÷ 12  

⇒  x = 10.42

So the cost of admission for each student = $10.42

b)

Let x = the number of trips

Let y = the total number of passengers

⇒  y = 12x

⇒  125 = 12x  

⇒  x = 125 ÷ 12  

⇒  x = 10.42

Therefore, the van must make 11 trips in order to bring 125 passengers to the same location.  (If it took 10 trips, then it would only bring 120 passengers, hence why we have to round make 11 trips to bring the last 5 passengers).

c)

Let x = the number of cookies each neighbor will receive

Let y = the total number of baked cookies

⇒  y = 12x

⇒  125 = 12x  

⇒  x = 125 ÷ 12  

⇒  x = 10.42

Therefore, each neighbor will receive 10 cookies (we have to round it down, as if each neighbor received 11 cookies, we would need 132 in total).

d)

Let x = the number of cheesecakes purchased

Let y = the amount of cheescake each guest will receive

⇒  y = 125x

⇒  12 = 125x  

⇒  x = 12 ÷ 125

⇒  x = 12/125 = 0.096 = 9.6%

Therefore, each guest will receive 12/125ths of a cheesecake (or 9.6%).

6 0
2 years ago
A company is designing a new cylindrical water bottle. The volume of the bottle will be 205 cm to the square root of 3 cm. The h
Umnica [9.8K]

Answer:

19 cm

Step-by-step explanation:

Given :

Volume, V = 205 to the √3 = 205^√3

Height, h = 8.9

radius, r

Volume of cylinder:

V = πr²h

205 to the square root of 3 10094.275

company is designing a new cylindrical water bottle. The volume of the bottle will be 205 cm to the square root of 3 cm. The height of the water bottle is 8.9 cm. What is the radius of the water​ bottle?

10094.275 = π * r² * 8.9

10094.275 = 3.14 * 8.9 * r²

10094.275 = 27.946r²

r² = 10094.275 / 27.946

r² = 361.20643

r = √361.20643

r = 19 cm

8 0
3 years ago
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