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Eduardwww [97]
2 years ago
6

Which of the following is the solution to the following system of inequalities? Let the green region represent the answer region

.
x+2y ≤ 4
3x-y ≤ 2

Mathematics
2 answers:
netineya [11]2 years ago
6 0
We are given with two inequalities and is asked to determine the solution to the given inequalities. x+2y ≤ 43x-y ≤ 2we can multiply equation 1 by -3 and add the two equations then. y is equal to 10/7 while x is equal 8/7. In this case, the region of domain is numbers less than 8/7 and that of range is numbers less than 10/7
VMariaS [17]2 years ago
4 0

Answer:

Step-by-step explanation:

One of the two inequalities have been given as x + 2y ≤ 4, which is represented by the region below the red line drawn on graph.

Second inequality is 3x - y ≤ 2, which is represented by the region on the left of the blue line.

Solution region will be the green which is common in both the regions.

Hence all the solutions of the system of inequalities will lie in the green region.

By solving these inequalities we can get the domain and range of the solution region of this system of inequalities.

We multiply x + 2y ≤ 4 by 3 and subtract it by 3x - y ≤ 2

(3x - y) - 3(x + 2y) ≤ 2 -12

3x - y - 3x - 6y ≤ -10

-7y ≤ -10

y\leq \frac{10}{7}

Now we put the value of y in (x + 2y) ≤ 4

x+2(\frac{10}{7})\leq 4

x+\frac{20}{7}\leq  4

x\leq 4-\frac{20}{7}

x\leq \frac{8}{7}

So the domain and range of the green region will be x\leq \frac{8}{7} and y\leq \frac{10}{7}.

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I need this asap ty:p
Anastasy [175]

Answer:

(a) x = -2y

(c) 3x - 2y = 0

Step-by-step explanation:

You can tell if an equation is a direct variation equation if it can be written in the format y = kx.

Note that there is no addition and subtraction in this equation.

Let's put these equations in the form y = kx.

(a) x = -2y

  • y = x/-2 → y = -1/2x
  • This is equivalent to multiplying x by -1/2, so this is an example of direct variation.

(b) x + 2y = 12

  • 2y = 12 - x
  • y = 6 - 1/2x
  • This is not in the form y = kx since we are adding 6 to -1/2x. Therefore, this is <u>NOT</u> an example of direct variation.

(c) 3x - 2y = 0

  • -2y = -3x
  • y = 3/2x
  • This follows the format of y = kx, so it is an example of direct variation.

(d) 5x² + y = 0

  • y = -5x²
  • This is not in the form of y = kx, so it is <u>NOT</u> an example of direct variation.

(e) y = 0.3x + 1.6

  • 1.6 is being added to 0.3x, so it is <u>NOT</u> an example of direct variation.

(f) y - 2 = x

  • y = x + 2
  • 2 is being added to x, so it is <u>NOT</u> an example of direct variation.

The following equations are examples of direct variation:

  • x = -2y
  • 3x - 2y = 0
7 0
3 years ago
Read 2 more answers
Which ordered pair is a solution to the equation? y=x3/4
Leni [432]

Answer:

(8,6)

Step-by-step explanation:

y=x3/4

y=8(3/4)

y=24/4

y=6

when you input 8 for x, you get 6 for y.

6 0
3 years ago
Read 2 more answers
What is the square root of 5x^2 = 300
vesna_86 [32]

So, values of x are: x=2\sqrt{15},\,\,x=-2\sqrt{15}

Step-by-step explanation:

We need to find the square root of 5x^2 = 300

Writing in mathematical form:

5x^2=300

Divide both sides by 5

\frac{5x^2}{5}=\frac{300}{5}

x^2=60

Taking square root on both sides

\sqrt{x^2}=\sqrt{60}

x=\pm (\sqrt{2\times 2\times 3\times 5})

x=\pm (\sqrt{2^2 \times 3\times 5})

x=\pm (2\sqrt{3\times 5})

x=\pm (2\sqrt{15})

x=2\sqrt{15},\,\,x=-2\sqrt{15}

So, values of x are: x=2\sqrt{15},\,\,x=-2\sqrt{15}

Keywords: Square root

Learn more about square root at:

  • brainly.com/question/3511750
  • brainly.com/question/4034547

#learnwithBrainly

7 0
3 years ago
Find a value for each variable:<br>1. -3(x – 7) – 11 = 28​
11111nata11111 [884]

Answer: x=-6

Step-by-step explanation: I gtg to my next hour so cya

7 0
3 years ago
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Solve the equation using elimination
Romashka-Z-Leto [24]

Answer:

1 1/3

Step-by-step explanation:

you would take 3x+2y=7 and put y=-3x+11 in place of y so it would be 3x+2×-3x+11=7

5 0
2 years ago
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