1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Murrr4er [49]
3 years ago
5

Solve the following System of Three Equations: x−3y+z=−15 2x+y−z=−2 x+y+2z=1

Mathematics
1 answer:
jeyben [28]3 years ago
6 0

Answer:

x = -3 , y = 4 , z = 0

Step-by-step explanation:

Solve the following system:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for z:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Solve for z.

Subtract x - 3 y from both sides:

{z = 3 y + (-x - 15)

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Perform a substitution.

Substitute z = -15 - x + 3 y into the second and third equations:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

x + y + 2 (-15 - x + 3 y) = 1

Hint: | Expand the left hand side of the equation x + y + 2 (-15 - x + 3 y) = 1.

x + y + 2 (-15 - x + 3 y) = x + y + (-30 - 2 x + 6 y) = -30 - x + 7 y:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for x:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Isolate terms with x to the left hand side.

Subtract 15 - 2 y from both sides:

{z = -15 - x + 3 y

3 x = 2 y - 17

-30 - x + 7 y = 1

Hint: | Solve for x.

Divide both sides by 3:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

-30 - x + 7 y = 1

Hint: | Perform a substitution.

Substitute x = (2 y)/3 - 17/3 into the third equation:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Choose an equation and a variable to solve for.

In the third equation, look to solve for y:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Isolate terms with y to the left hand side.

Add 73/3 to both sides:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 = 76/3

Hint: | Solve for y.

Multiply both sides by 3/19:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

y = 4

Hint: | Perform a back substitution.

Substitute y = 4 into the first and second equations:

{z = -x - 3

x = -3

y = 4

Hint: | Perform a back substitution.

Substitute x = -3 into the first equation:

{z = 0

x = -3

y = 4

Hint: | Sort results.

Collect results in alphabetical order:

Answer: {x = -3 , y = 4 , z = 0

You might be interested in
Some scientists believe alcoholism is linked to social isolation. One measure of social isolation is marital status. A study of
frez [133]

Answer:

1) H0: There is independence between the marital status and the diagnostic of alcoholic

H1: There is association between the marital status and the diagnostic of alcoholic

2) The statistic to check the hypothesis is given by:

\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}

3) \chi^2 = \frac{(21-33.143)^2}{33.143}+\frac{(37-41.429)^2}{41.429}+\frac{(58-41.429)^2}{41.429}+\frac{(59-46.857)^2}{46.857}+\frac{(63-58.571)^2}{58.571}+\frac{(42-58.571)^2}{58.571} =19.72

4) df=(rows-1)(cols-1)=(3-1)(2-1)=2

And we can calculate the p value given by:

p_v = P(\chi^2_{2} >19.72)=5.22x10^{-5}

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.72,2,TRUE)"

Since the p value is lower than the significance level so then we can reject the null hypothesis at 5% of significance, and we can conclude that we have association between the two variables analyzed.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

                    Diag. Alcoholic   Undiagnosed Alcoholic    Not alcoholic    Total

Married                     21                              37                            58                116

Not Married              59                             63                            42                164

Total                          80                             100                          100              280

Part 1

We need to conduct a chi square test in order to check the following hypothesis:

H0: There is independence between the marital status and the diagnostic of alcoholic

H1: There is association between the marital status and the diagnostic of alcoholic

The level os significance assumed for this case is \alpha=0.05

Part 2

The statistic to check the hypothesis is given by:

\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}

Part 3

The table given represent the observed values, we just need to calculate the expected values with the following formula E_i = \frac{total col * total row}{grand total}

And the calculations are given by:

E_{1} =\frac{80*116}{280}=33.143

E_{2} =\frac{100*116}{280}=41.429

E_{3} =\frac{100*116}{280}=41.429

E_{4} =\frac{80*164}{280}=46.857

E_{5} =\frac{100*164}{280}=58.571

E_{6} =\frac{100*164}{280}=58.571

And the expected values are given by:

                    Diag. Alcoholic   Undiagnosed Alcoholic    Not alcoholic    Total

Married             33.143                       41.429                        41.429                116

Not Married     46.857                      58.571                        58.571                164

Total                   80                              100                             100                 280

And now we can calculate the statistic:

\chi^2 = \frac{(21-33.143)^2}{33.143}+\frac{(37-41.429)^2}{41.429}+\frac{(58-41.429)^2}{41.429}+\frac{(59-46.857)^2}{46.857}+\frac{(63-58.571)^2}{58.571}+\frac{(42-58.571)^2}{58.571} =19.72

Part 4

Now we can calculate the degrees of freedom for the statistic given by:

df=(rows-1)(cols-1)=(3-1)(2-1)=2

And we can calculate the p value given by:

p_v = P(\chi^2_{2} >19.72)=5.22x10^{-5}

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.72,2,TRUE)"

Since the p value is lower than the significance level so then we can reject the null hypothesis at 5% of significance, and we can conclude that we have association between the two variables analyzed.

7 0
3 years ago
30 POINTS!!! WILL MARK BRAINLIEST! : )
TiliK225 [7]
1. <span>C) Inverse Property of Multiplication
2. </span><span>B) Inverse Property of Addition
3. </span><span>C) Inverse Property of Multiplication
</span>4. Your answer is not listed (The answer is Associative Property of Multiplication)
3 0
3 years ago
Read 2 more answers
Could you please check my answers and let me know if they are right?
ANTONII [103]

Answer:

11 is correct

12 should be 51°

Step-by-step explanation:

15/sin(104) = 12/sin(J)

J = 50.917°

8 0
3 years ago
V
KATRIN_1 [288]

Answer:

sorry no idea hhcchuucghhf

5 0
2 years ago
36x+9 equals what<br> big blak vjndjgd
Yuki888 [10]

We can conclude that the equation 36x + 9 equals -1/4.

<h3>What exactly is an equation?</h3>
  • An equation, in its most basic form, is a mathematical statement demonstrating that two mathematical expressions are equal.
  • 3x + 5 = 14, for example, is an equation in which the expressions 3x + 5 and 14 are separated by a 'equal' sign.

So,

  • 36x + 9
  • 36x + 9 = 0
  • 36x = -9
  • x = -9/36
  • x = -1/4

Therefore, we can conclude that the equation 36x + 9 equals -1/4.

Know more about equations here:

brainly.com/question/2972832

#SPJ9

6 0
1 year ago
Other questions:
  • Find the value of each variable. <br> I need help only on 3 please
    9·2 answers
  • Write an expression to show how you could calculate the total amount David paid.
    15·2 answers
  • The temperature in a greenhouse should be 68 degrees or higher. One​ morning, the heater stopped working. The temperature droppe
    10·1 answer
  • A dog's weight increased by 50% in 3 years. by the end of 3 years, the dog weighed 45 pounds. how much did the dog weigh 3 years
    7·2 answers
  • I just want people to tell me if this correct for the first question
    8·2 answers
  • Mimi uses a 7.5-gal bucket to fill a wading pool. She pours 12 buckets full of water into the pool, which can hold up to 138 gal
    10·1 answer
  • Walter's family plays a quick game together every night after dinner. Walter draws names out of a hat to determine which kind of
    13·2 answers
  • What fraction is 20 min of 3 hours? Answer in simplest form
    7·1 answer
  • Daniel works at a nearby electronic store he makes 15% on everything he sells if he Sells a laptop for 293.00 how much money doe
    14·1 answer
  • 3. The MPG (Miles per Gallon) for a mid-size car is normally distributed with a mean of 32 and a standard deviation of .8. What
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!