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Andrej [43]
3 years ago
10

Which ordered pairs are in the solution set of the system of linear inequalities?

Mathematics
1 answer:
Anastaziya [24]3 years ago
8 0
<h3>Answer: Choice A.  (2,2), (3,1), (4,2)</h3>

==========================================================

Explanation:

The graph of y \ge -\frac{1}{3}x+2 has the boundary y = (-1/3)x+2 which is a solid line. This line goes through (0,2) and (3,1). We shade above the boundary because of the "greater than" sign.

The graph of y < 2x+3 has a dashed boundary line of y = 2x+3, and we shade below the boundary because of the "less than" sign.

The two regions overlap in the upper right corner where it's shaded in the darkest color. The points (2,2), (3,1) and (4,2) are in this upper right corner region. If we plug the coordinates of each point into each inequality, then we'll get true statements.

For instance, let's try (x,y) = (2,2) into the first inequality

y \ge -\frac{1}{3}x+2\\\\2 \ge -\frac{1}{3}(2)+2\\\\2 \ge -\frac{2}{3}+2\\\\2 \ge -\frac{2}{3}+\frac{6}{3}\\\\2 \ge \frac{-2+6}{3}\\\\2 \ge \frac{4}{3}\\\\2 \ge 1.33\\\\

Which is true since 2 is indeed larger than 1.33, so that confirms (2,2) is in the shaded region for y \ge -\frac{1}{3}x+2\\\\

Let's check the other inequality as well

y < 2x+3\\\\2 < 2(2)+3\\\\2 < 4+3\\\\2 < 7\\\\

That works too. So (2,2) is in BOTH shaded regions at the same time; hence, it's a solution to the system. You should find that (3,1) and (4,2) work for both inequalities also. This will confirm choice A is the answer.

--------------------------------

Extra info (optional section)

A point like (3,-1) does not work for the first inequality as shown below

y \ge -\frac{1}{3}x+2\\\\-1 \ge -\frac{1}{3}(3)+2\\\\-1 \ge -1+2\\\\-1 \ge 1\\\\

Since -1 is neither equal to 1, nor is -1 larger than 1 either. The false statement at the end indicates (3,-1) is not a solution to that inequality.

Based on the graph, the point (3,-1) is not above the blue solid boundary line. All of this means we can rule out choice B.

You should find that (1,-2) is a similar story, so we can rule out choice C. Choice D can be ruled out because (2,0) is not a solution to the first inequality.

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a recipe calls for a total of 3 2/3 cups of flour and sugar. it the recipe calls for 1/4 cup of sugar, how much flour is needed?
zavuch27 [327]

Answer:

This is very detailed as I wish to make some principles about fractions clear.

3

5

12

Explanation:

This question boils down to  

3

2

3

−

1

4

A fractions structure is that of:

count

size indicator of what you are counting

→

numerator

denominator

You can not directly add or subtract the counts (numerators) unless the size indicators (denominators) are the same.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider  

3

2

3

Write as  

3

+

2

3

Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way something looks without changing its true value

[

3

×

1

]

+

2

3

[

3

×

3

3

]

+

2

3

 

9

3

   

+

2

3

 

=

 

11

3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Putting it all together

3

2

3

−

1

4

 

→

 

11

3

−

1

4

But the size indicators are not the same. I chose to make them become 12

11

3

−

1

4

 

→

 

[

11

3

×

1

]

−

[

1

4

×

1

]

               

→

 

[

11

3

×

4

4

]

−

[

1

4

×

3

3

]

               

→

     

44

12

     

−

 

3

12

Now we may subtract the counts

               

→

 

44

−

3

12

 

=

 

41

12

But this is the same as  

12

12

+

12

12

+

12

12

+

5

12

                         

=

 

1

2

+

2

1

2

+

2

1

2

+

5

12

 

=

 

3

5

12


Step-by-step explanation:


5 0
3 years ago
Read 2 more answers
X=6<br> is a solution to the inequality x−5≤ 10<br><br> True or False?
vekshin1

Answer:

  • \boxed{\sf{FALSE}}
  • \boxed{\sf{x\leq 15}}

Step-by-step explanation:

Isolate the term of x from one side of the equation.

<h3>x-5≤10</h3>

<u>First, add by 5 from both sides.</u>

\sf{x-5+5\leq10+5}

<u>Solve.</u>

<u>Add the numbers from left to right.</u>

\sf{10+5=15}

\Longrightarrow: \boxed{\sf{x\leq 15}}

  • <u>Therefore, the solution is x≤15, which is our answer.</u>

I hope this helps you! Let me know if my answer is wrong or not.

6 0
2 years ago
Read 2 more answers
If CD= EF and EF = GH, then
Dmitry [639]
GH=CD i think im not really super outrageous with math 
6 0
3 years ago
Write an equation of a line that passes through the point (-5,3) and is parallel to the line y = -2x + 5.
zimovet [89]

Answer:

Step-by-step explanation:

y = -2x+5

slope of line is -2.

slope of parallel to line is also -2

point-slope equation for line of slope -2 that passes through (-5,3):

y-3 = -2(x+5)

8 0
2 years ago
What percent of 1/2 is 2/5
eimsori [14]
1/2= 50%
2/5=40% is the answer
4 0
3 years ago
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