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Fiesta28 [93]
3 years ago
12

3m+3n=36 8m+5n=31 Using the process of elimination

Mathematics
1 answer:
amm18123 years ago
6 0

Answer:

m=-29/3 and n=65/3

Step-by-step explanation:

The given system has equations:

3m+3n=36

8m+5n=31

Multiply the top equation by 5 and bottom equation by 3 to get:

15m+15n=180

24m+15n=93

Subtract the top equation from the bottom equation to get:

9m=-87

Divide both sides by 9

m =  -  \frac{29}{3}

We substitute this value into the first equation to get:

3( -  \frac{29}{3} ) + 3n = 36

3n = 36 + 29

3n = 65

n =  \frac{65}{3}

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The graph of y > 1 2 x - 2 is shown. Which set contains only points that satisfy the inequality? A) {(6, 1), (-1, -3), (4, 4)
Kaylis [27]

Answer:

Option B) {(1, -1), (-3, -3), (2, 4)}

Step-by-step explanation:

<u><em>The correct inequality is </em></u>

y>\frac{1}{2}x-2

The solution of the inequality is the shaded area above the dashed line y=\frac{1}{2}x-2

see the attached figure to better understand the problem

we know that

If a ordered pair satisfy the inequality, then the ordered pair must lie in the shaded area of the solution

<u><em>Verify each case</em></u>

case A) {(6, 1), (-1, -3), (4, 4)}

ordered pair (6,1)

For x=6, y=1

substitute in the inequality

1>\frac{1}{2}(6)-2

1>1 ---> is not true

therefore

The point not satisfy the inequality

case B)  {(1, -1), (-3, -3), (2, 4)}

ordered pair (1,-1)

For x=1, y=-1

substitute in the inequality

-1>\frac{1}{2}(1)-2

-1>-1.5 ---> is true

so

The point satisfy the inequality

ordered pair (-3,3)

For x=-3, y=3

substitute in the inequality

3>\frac{1}{2}(-3)-2

3>-3.5 ---> is true

so

The point satisfy the inequality

ordered pair (2,4)

For x=2, y=4

substitute in the inequality

4>\frac{1}{2}(2)-2

4>-1 ---> is true

so

The point satisfy the inequality

therefore

The set contains only points that satisfy the inequality

case C) {(1, -1), (-3, -3), (4, -2)}

ordered pair (4,-2)

For x=4, y=-2

substitute in the inequality

-2>\frac{1}{2}(4)-2

-2>0 ---> is not true

therefore

The point not satisfy the inequality

case D) {(-1, -3), (-3, -3), (2, 4)}

ordered pair (-1,-3)

For x=-1, y=-3

substitute in the inequality

-3>\frac{1}{2}(-1)-2

-3>-2.5 ---> is not true

therefore

The point not satisfy the inequality

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3 years ago
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IRINA_888 [86]

Answer: 1.893 Welcome

Step-by-step explanation:

7 0
3 years ago
The popping-times of the kernels in a certain brand of microwave popcorn are
Lynna [10]

Answer:

The z-score for this kernel is -2.3

Step-by-step explanation:

* Lets revise how to find the z-score

- The rule the z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- The popping-times of the kernels in a certain brand of microwave

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- The standard deviation is 10 seconds

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∵ z-score = (x - μ)/σ

∵ x = 127

∵ μ = 150

∵ σ = 10

∴ z-score = (127 - 150)/10 = -23/10 = -2.3

* The z-score for this kernel is -2.3

7 0
3 years ago
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