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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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In an isosceles triangle, the vertex angle is 112 degrees. What is the measure of each base.
jeka94

Answer:

A

Step-by-step explanation:

The base angles of an isosceles triangle are congruent

The sum of the 3 angles in a triangle = 180°, hence

180° - 112° = 68°

base angle = \frac{68}{2} = 34°

Thus each base angle equals 34° → A




8 0
3 years ago
7. Jena has a triangular garden with a perimeter that can be represented by 25r ^ 2 - 9r + 14 . The sum of two sides of the gard
galben [10]

Answer: 15r^2-21r+5

Step-by-step explanation:

Given: Perimeter of triangular garden = 25r^2 - 9r + 14

The sum of two sides of the garden = 10r^2 + 12r + 9

Perimeter is the sum of all sides of a triangle.

Third side = Perimeter of triangular garden - sum of two sides of the garden

=25r ^ 2 - 9r + 14-(10r ^ 2 + 12r + 9)\\\\=25r ^ 2 - 9r + 14-10r ^ 2 - 12r - 9\\\\=15r^2-21r+5

The expression represent the third side = 15r^2-21r+5.

5 0
3 years ago
Which is true of a population in a statistical survey?​
Verizon [17]

Answer:

The population of a statistical survey is chose at random, so it's not believed to be biased.

3 0
3 years ago
What is the distance between the points (21 , 13) and (3 , 13) in the coordinate plane?
Oxana [17]

Answer:

\displaystyle d = 18

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

  • Coordinates (x, y)

<u>Algebra II</u>

  • Distance Formula: \displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

Point (21, 13)

Point (3, 13)

<u>Step 2: Find distance </u><em><u>d</u></em>

Simply plug in the 2 coordinates into the distance formula to find distance <em>d</em>

  1. Substitute in points [Distance Formula]:                                                         \displaystyle d = \sqrt{(3-21)^2+(13-13)^2}
  2. [√Radical] (Parenthesis) Subtract:                                                                   \displaystyle d = \sqrt{(-18)^2+(0)^2}
  3. [√Radical] Evaluate exponents:                                                                       \displaystyle d = \sqrt{324+0}
  4. [√Radical] Add:                                                                                                 \displaystyle d = \sqrt{324}
  5. [√Radical] Evaluate:                                                                                          \displaystyle d = 18
5 0
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