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3 years ago

Solve the three variable system. (I was just introduced to these)

Mathematics

2 answers:

sladkih [1.3K]3 years ago

8 0

First we have to get down to a system of two equations, then we can work from there. adding the first and third equation together, we get

$x - y + (y - 2z) = 2 + ( - 3) \\ x - 2z = - 1$
now multiply the second equation by 2, and add it to our new equation

$6x + 2z = 22 \\ 6x + 2z + (x - 2z) = 22 - 1 \\ 7x = 21 \\ x = 3$

now plug x into the second equation

3(3) + z = 11

z = 2

and plug it into the first equation

3 - y = 2

y = 1

Elanso [62]3 years ago

4 0

So basically you do two of the equations first and then solve for the last equation. Please Refer To The Picture

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Which situation could be represented by the graph?

Ymorist [56]

The correct option which resembles with the given graph is $\fbox{\begin\\\ optionA and optionC\\\end{minispace}}$ .

Further explanation:

From the given graph the it is observed that the interval is $[8,11)$ which is a half open interval or it can be said that it is a half closed interval.

A half closed or a half open interval is an interval in which one end point of the interval is included but the other point is not included.

For example:

In an interval of the form $[a,b)$ the point $a$ is included in the set but the point $b$ is not included in the set.

Similarly, in the interval $[8,11)$ the point $8$ is included in the set but the point $11$ is not included in the set.

In order to determine the correct option which resembles with given graph form interval for each option.

Option A:

As per the statement in option A the age of the student must be at least $8$ years and not more than $11$ years that is the age of the student is either $8$ years or greater than $8$ years and less than $11$ years.

As per the above statement the interval formed is $\fbox{\begin\\\ [8,11)\\\end{minispace}}$ in which $8$ is included in the set and $11$ is not included which means it is a half closed or half opoen interval.

Therefore, $\fbox{\begin\\\ optionA\\\end{minispace}}$ is a correct option.

Option B:

As per the statement in option B the amount of money the babysitter can earn is between $\$8$ and $\$11$ per hour.

As per the above statement the interval formed is $\fbox{\begin\\\ (8,11)\\\end{minispace}}$ in which both of the end points are not included in the set which means that it is an open interval.

Therefore, $\fbox{\begin\\\ optionB\\\end{minispace}}$ is an incorrect option.

Option C:

As per the statement in option C the time required to complete a program in college cannot be less than $8$ hours and the time must be less than $11$ hours.

From the above statement it is concluded that the time required can be $8$ hours or more than $8$ hours but it has to be less than $11$ hours.

So, as per the above the statement the interval formed is $\fbox{\begin\\\ [8,11)\\\end{minispace}}$ .

Therefore, $\fbox{\begin\\\ optionC\\\end{minispace}}$ is a correct option.

Option D:

As per the statement in option D the age of the dogs is either $8$ years old or below $8$ years and age of the dog must be greater than $11$ tears.

As per the above statement the interval formed is $\fbox{\begin\\\ (-\infty,8) \bigcup(11,\infty)\\\end{minispace}}$ .

Therefore, the $\fbox{\begin\\\ optionD\\\end{minispace}}$ is an incorrect option.

So, $\fbox{\begin\\\ optionA and optionC\\\end{minispace}}$ are the correct options which resembles with the given graph.

Learn more:

A problem on composite function brainly.com/question/2723982
A problem to find radius and center of circle brainly.com/question/9510228
A problem to determine intercepts of a line brainly.com/question/1332667

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Sets

Keywords: Interval, set, open interval, closed interval, half open interval, half closed interval, set theory, program, community college, babysitters, veterinary clinic, ages, students.

5 0

3 years ago

Read 2 more answers

Find area and perimeter

alisha [4.7K]

Answer:

Perimeter

P = P1+P2

P1 = 4a P2=2(a+b)

P1=4*5 P2=2(3+5)

P1=20 P2=2*8

P2=16

P = 20+16

P=36

Area

A=A1+A2

A1= $a^{2}$ A2=a*b

A1= $5^{2}$ A2=3*5

A1=25 A2=15

A=25+15

A=40

5 0

3 years ago

The expression -2(x-4) is the same as?

Tomtit [17]

Answer:

-2x + 8

Step-by-step explanation:

I applied the distribution technique to the original question.

5 0

2 years ago

A local restaurant is offering a special deal in which customers can receive one appetizer, one entree, and one dessert for a fi

Dmitriy789 [7]

There are105 different choices.
For 1 appetizer, there are 15 different combinations of entrees and desserts. 1 dessert has 5 entrees you can mix, and since there are 3 desserts, there are 15 choices. It goes the same for every appetizer until there is 7x15. 7Ax15choices equals 105 options.
The customer has 105 meal choices.

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3 years ago

Hi. What is the smallest number that can be written in 6 ways as the sum of the squares of 3 primes? Also, please list them as w

Fed [463]

2019 is the smallest number.

Here are the ways:

$7^2+11^2+43^2$