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marissa [1.9K]
2 years ago
15

Solve the system of equations. ​ 2x−9y=14 x=−6y+7 ​

Mathematics
2 answers:
stepladder [879]2 years ago
8 0

Answer:

y = 0

x = 7

Step-by-step explanation:

2x − 9y = 14     ⇒  ( 1 )

x = − 6y +7      ⇒ ( 2 )

First, let us find the value of y.

<u>For that, replace x with ( - 6y + 7 ).</u>

<u>Let us take equation 1 for that.</u>

2x − 9y = 14

2 ( - 6y + 7 ) - 9y = 14

-12y + 14 - 9y = 14

21y = 14 - 14

21y = 0

<em>Divide both sides by 21.</em>

<u>y = 0</u>

<u>And now let us take equation 2 to find the value of x by replacing y with 0.</u>

2x − 9y = 14    

2x - 9 × 0 = 14

2x - 0 = 14

2x = 14

<em>Divide both sides by 2.</em>

<u>x = 7</u>

ipn [44]2 years ago
3 0

Step-by-step explanation:

put \: x \: into \: equation \: 1

2( - 6y + 7) - 9y = 14

- 12y + 14 - 9y = 14

- 21y + 14 = 14

- 21y = 14 - 14

- 21y = 0

\frac{ - 21y}{12}  =  \frac{0}{21}

y = 0

put \: y = 0 \: into \: equation \: 2

x = 6y + 7

x = 6(0) + 7

x = 0 + 7

x = 7

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anygoal [31]

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2 years ago
The distribution of lifetimes of a particular brand of car tires has a mean of 51,200 miles and a standard deviation of 8,200 mi
Orlov [11]

Answer:

a) 0.277 = 27.7% probability that a randomly selected tyre lasts between 55,000 and 65,000 miles.

b) 0.348 = 34.8% probability that a randomly selected tyre lasts less than 48,000 miles.

c) 0.892 = 89.2% probability that a randomly selected tyre lasts at least 41,000 miles.

d) 0.778 = 77.8% probability that a randomly selected tyre has a lifetime that is within 10,000 miles of the mean

Step-by-step explanation:

Problems of normally distributed distributions are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 51200, \sigma = 8200

Probabilities:

A) Between 55,000 and 65,000 miles

This is the pvalue of Z when X = 65000 subtracted by the pvalue of Z when X = 55000. So

X = 65000

Z = \frac{X - \mu}{\sigma}

Z = \frac{65000 - 51200}{8200}

Z = 1.68

Z = 1.68 has a pvalue of 0.954

X = 55000

Z = \frac{X - \mu}{\sigma}

Z = \frac{55000 - 51200}{8200}

Z = 0.46

Z = 0.46 has a pvalue of 0.677

0.954 - 0.677 = 0.277

0.277 = 27.7% probability that a randomly selected tyre lasts between 55,000 and 65,000 miles.

B) Less than 48,000 miles

This is the pvalue of Z when X = 48000. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{48000 - 51200}{8200}

Z = -0.39

Z = -0.39 has a pvalue of 0.348

0.348 = 34.8% probability that a randomly selected tyre lasts less than 48,000 miles.

C) At least 41,000 miles

This is 1 subtracted by the pvalue of Z when X = 41,000. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{41000 - 51200}{8200}

Z = -1.24

Z = -1.24 has a pvalue of 0.108

1 - 0.108 = 0.892

0.892 = 89.2% probability that a randomly selected tyre lasts at least 41,000 miles.

D) A lifetime that is within 10,000 miles of the mean

This is the pvalue of Z when X = 51200 + 10000 = 61200 subtracted by the pvalue of Z when X = 51200 - 10000 = 412000. So

X = 61200

Z = \frac{X - \mu}{\sigma}

Z = \frac{61200 - 51200}{8200}

Z = 1.22

Z = 1.22 has a pvalue of 0.889

X = 41200

Z = \frac{X - \mu}{\sigma}

Z = \frac{41200 - 51200}{8200}

Z = -1.22

Z = -1.22 has a pvalue of 0.111

0.889 - 0.111 = 0.778

0.778 = 77.8% probability that a randomly selected tyre has a lifetime that is within 10,000 miles of the mean

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2 years ago
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Greeley [361]

Answer:

None of these

Step-by-step explanation:

See attached image

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Maksim231197 [3]

Answer:

62.5

Step-by-step explanation:

2cm = 25mi

1cm = 12.5 (25/2)

5cm is 2 + 2 + 1

2 + 2 + 1 = 25 + 25 + 12.5 = 62.5

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Answer:

The scale factor is 2.

Step-by-step explanation:

Take the vertical sides of the 2 triangles.

Their length is 3 and 6 so the scale factor is 6/3 = 2.

Also we see than the horizontal lines are in the same ratio 4 : 2  = 2:1.

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2 years ago
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