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aleksandr82 [10.1K]
3 years ago
12

1. Solve the system of equations by substitution and check your solution.

Mathematics
1 answer:
dedylja [7]3 years ago
6 0

Answer:

x = 7 and y = −2

(7, -2)

Step-by-step explanation:

x = 1 - 3y

3x + 3y = 15

Substitute −3y + 1 for x in 3x + 3y = 15:

3(1 - 3y) + 3y = 15

3 - 9y + 3y = 15

3 - 6y = 15

-3           -3

-6y = 12

/-6     /-6

y = -2

Now we solve for x. Substitute −2 for y in x = −3y + 1:

x = 1 - 3y

x = 1 + (-3)(-2)

x = 1 + 6

x = 7

Now we check our solution.

x = 1 - 3y

7 = 1 + (-3)(-2)

7 = 7 ✅

3x + 3y = 15

3(7) + 3(-2) = 15

21 - 6 = 15

15 = 15 ✅

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A _________________is a numerical value that describes a population.
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Answer:

A parameter is a numerical value that describes a population.

Step-by-step explanation:

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3 years ago
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What does h(40) = 1700 mean in terms of the problem?
ipn [44]

Answer:

40 hours of training=h(40)

Monthly Pay=1700

Step-by-step explanation:

For 40 hours of training, you will receive $1700 for the month.

7 0
2 years ago
If y varies directly as x, and y=6 as x=-1, find y for the x-value of 5
Tema [17]

Answer:

y=-30

Step-by-step explanation:

we are given

y varies directly as x

so, we can write equation as

y=kx

where

k is constant of proportionality

We have

at x=-1 , y=6

so, we can use it to find k

6=k(-1)

so, we get

k=-6

now, we can plug it back

y=-6x

now, we can plug x=5

and we get

y=-6\times 5

y=-30

6 0
3 years ago
John works two jobs. As a security guard he earns $8.50 per hour. As a landscaper he earns $14 per hour. One week John worked a
Rashid [163]

Answer:

John work as a security guard job <u>27 hours</u> and as a landscaper <u>33 hours</u>.

Step-by-step explanation:

Given:

John works two jobs.

As a security guard he earns $8.50 per hour and as a landscaper he earns $14 per hour.

One week John worked a total of 60 hours and earned $691.50.

Now, to find hours he work at each job.

Let the job of security guard be x hours.

And the job of landscaper be y hours.

So, the total hours John worked in a week:

x+y=60.

⇒ y=60-x.............( 1 )

<em>Now, the money earned by John in a week:</em>

8.50x+14y=691.50

<em>Putting the equation ( 1 ) in the place of y:</em>

⇒ 8.50x+14(60-x)=691.50

⇒ 8.50x+840-14x=691.50

<em>Moving variables on one side and the other we get:</em>

⇒ 840-691.50=14 x-8.50x

⇒148.50=5.50x

<em>Dividing both sides by 5.50 we get:</em>

⇒ 27=x

<u>As a security guard job he worked 27 hours</u><u>.</u>

Putting the value of in x equation ( 1 ) we get:

y=60-27

⇒ y=33.

<u>As a landscaper he worked 33 hours</u>.

Therefore, John work as a security guard job 27 hours and as a landscaper 33 hours.

5 0
3 years ago
At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 36 m
Degger [83]

The probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes is 59.81%

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Z score is given by:

z = (raw score - mean) / standard deviation

Given mean of 36 minutes and a standard deviation of 3 minutes.

For x = 32:

z = (32 - 36)/3 = -1.33

For x = 37:

z = (37 - 36)/3 = 0.33

P(-1.33 < z < 0.33) = P(z < 0.33) - P(z < -1.33) = 0.6179 - 0.0198 = 0.5981

The probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes is 59.81%

Find out more on equation at: brainly.com/question/2972832

#SPJ1

7 0
2 years ago
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