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Virty [35]
3 years ago
12

On a piece of paper, graph this system of inequalities. Then determine which region contains the solution to the system.

Mathematics
2 answers:
Mashutka [201]3 years ago
3 0

we have

y\leq \frac{1}{4}x+3 ----> inequality 1

The solution of the inequality 1 is the shaded area below the solid red line

The solution is the region D and region C

y\geq-x+5 -----> inequality 2

The solution of the inequality 2 is the shaded area above the solid blue line

The solution is the region B and region C

The solution of the system is the common area

so

The solution is the region C

see the attached figure

therefore

the answer is the option C

Region C

konstantin123 [22]3 years ago
3 0

Answer:

Region C of  the graph will contains the solution to the given system

Step-by-step explanation:

 Consider the given system of equation

y\le\frac{1}{4}x+3

and y\ge-x+5

We have to choose the region of the graph that contains the solution to the given system.

Since, to determine the region choose  a test point in each region and then then check the values of inequality at that point and for the test point that satisfies both the inequality  will contains the solution to the given system.

On region A)

Let (0, 4)  be the test point that lies in region A

Then put the value of x = 0 and y= 4 in given system,

we have,

4\le\frac{1}{4}(0)+3 \Rightarrow 4\le 3 (false)

and 4\ge(0)+5 \Rightarrow 4\ge 5 (false)

On region B)

Let (0, 8)  be the test point that lies in region B

Then put the value of x = 0 and y= 8 in given system,

we have,

8\le\frac{1}{4}(0)+3 \Rightarrow 8\le 3 (false)

and 8\ge(0)+5 \Rightarrow 8\ge 5 (true)

On region C)

Let (8,0)  be the test point that lies in region C

Then put the value of x = 8 and y= 0 in given system,

we have,

0\le\frac{1}{4}(8)+3 \Rightarrow 0\le 5 (true)

and 0\ge(-8)+5 \Rightarrow 0\ge -3 (true)

On region D)

Let (0,0)  be the test point that lies in region D

Then put the value of x = 0 and y= 0 in given system,

we have,

0\le\frac{1}{4}(0)+3 \Rightarrow 0\le 3 (false)

and 0\ge(0)+5 \Rightarrow 0\ge 5 (false)

Thus, only (8,0)  be the test point that lies in region C satisfies both inequality.

Thus, region C of  the graph will contains the solution to the given system

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Answer:

believe the answer is

y =  \frac{3}{4} x - 5

Step-by-step explanation:

Hope this helps!

3 0
3 years ago
Nathan went shopping for a new camera because of a sale. The store was offering a 40% discount. If the price on the tag was $35,
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Answer:

The price after the discount but before the tax is $21

Step-by-step explanation:

Here, we are told there is a price off of 40% on an item that costs $35.

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We proceed by finding 40% of $35

Mathematically, that would be;

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Step-by-step explanation:

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What is 3x + 77 = 4x + 54
loris [4]

Answer:

Simplifying

3x + 77 = 4x + 54

Reorder the terms:

77 + 3x = 4x + 54

Reorder the terms:

77 + 3x = 54 + 4x

Solving

77 + 3x = 54 + 4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4x' to each side of the equation.

77 + 3x + -4x = 54 + 4x + -4x

Combine like terms: 3x + -4x = -1x

77 + -1x = 54 + 4x + -4x

Combine like terms: 4x + -4x = 0

77 + -1x = 54 + 0

77 + -1x = 54

Add '-77' to each side of the equation.

77 + -77 + -1x = 54 + -77

Combine like terms: 77 + -77 = 0

0 + -1x = 54 + -77

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Combine like terms: 54 + -77 = -23

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Divide each side by '-1'.

x = 23

Simplifying

x = 23

Step-by-step explanation:

I hope its helps

8 0
2 years ago
Read 2 more answers
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