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blagie [28]
3 years ago
15

Which of the options is a solution for the following system of inequalities?

Mathematics
2 answers:
creativ13 [48]3 years ago
3 0
For it to be a solution, it has to satisfy both inequalities.

using (5,-2)...x = 5 and y = -2

4x + y > 3
4(5) - 2 > 3
20 - 2 > 3
18 > 3.....correct

x - y > 2
5 - 2 > 2
3 > 2....correct

 solution is (5,-2)



marishachu [46]3 years ago
3 0

Answer:

Option D.

Step-by-step explanation:

The given system of inequalities are

4x+y>3

x-y>2

We need to find a solution for the following system of inequalities.

Check each point by these inequalities.

For (-2,-2)

4(-2)+(-2)>3\Rightarrow -10>3 False

So, (-2,-2) is not included in the solution set.

For (1,-5)

4(1)+(-5)>3\Rightarrow -1>3 False

So, (1,-5) is not included in the solution set.

For (0,0)

4(0)+(0)>3\Rightarrow 0>3 False

So, (0,0) is not included in the solution set.

For (5,-2)

4(5)+(-2)>3\Rightarrow 18>3 True

(5)-(-2)>2\Rightarrow 7>2 True

Both inequalities are true for the point (5,-2). So, the point (5,-2) is a solution for the following system of inequalities

Therefore, the correct option is D.

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An investment of ​$100 comma 000 was made by a business club. The investment was split into three parts and lasted for one year.
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Answer:

  • $54000 was invested at​ 8% interest
  • $36000 was invested at​ 6% interest
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Step-by-step explanation:

Total Investment = ​$100,000

The investment was split into three parts (say x, y and z)

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Simple Interest = Principal X Rate/100 X Time

The first part of the investment earned​ 8% interest

Interest on the first part = 0.08x

The second part of the investment earned​ 6% interest

Interest on the second  part = 0.06y

The third part of the investment earned​ 9% interest

Interest on the third part = 0.09z

Total interest from the investments = $ 7380.

Therefore:

0.08x+0.06y+0.09z=7380

The interest from the first investment was 2 times the interest from the second.

0.08x=2 X 0.06y

0.08x=0.12y

Substituting we have:

0.12y+0.06y+0.09z=7380

0.18y+0.09z=7380

From 0.08x=0.12y

x=1.5y

Substituting x=1.5y into x+y+z=100000

1.5y+y+z=100000

2.5y+z=100000

z=100000-2.5y

Substituting z=100000-2.5y into 0.18y+0.09z=7380

0.18y+0.09(100000-2.5y)=7380

0.18y+9000-0.225y=7380

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Divide both sides by -0.045

y=36000

Recall: x=1.5y

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Therefore:

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