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

Answers

Answer 1

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


Related Questions

Which value from the list below, when substituted for x, would represent an acute triangle with side lengths x, x+ 4, and 20? Assume that the longest side of the triangle is of length 20 units.



Answers

just finished this question the answers: D / 14

The value of x could be 8<x<12.

What is Triangle Inequality?

According to the Triangle Inequality Theorem, any two triangle sides must add up to more than the third side's length.

Using Triangle Inequality

x+ x+4 > 20

2x+ 4 >20

2x > 16

x> 8

The angle across from the side with length 20 is the largest angle because it is the longest side length.

Therefore, x must be less than the value(s) that make that angle exactly 90 degrees. Simply determine the values of x for angles that are 90 degrees from the side with a length of 20.

Using Pythagorean theorem

x²+ (x+4)² = 20²

x² + x² +16 +8x = 400

2x² + 8x - 384= 0

x²+ 4x -192= 0

x= -16, 12

So, x has to be less than 12 i.e.,  x < 12

Hence, the value of x could be 8<x<12.

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Alisa, Mykia, and Martin decide to share the responsibility of walking their dog every
day. There are 365 days in a year, How many days each year does Alisa need to was
the dog?

Answers

Step-by-step explanation:

No of friends = 3

No of days = 365 days

Days Alisa needs to walk the dog = 365 ÷ 3 = 121. 66

A pre-paid cell phone company charges $10.4 as a monthly access fee and $0.18 per minute of calling time. Express the monthly cost C in terms of minutes of call time. What will the monthly cost be if you make 315 minutes of calls this month?

Answers

Answer:$67.10

Step-by-step explanation:

Using the first statement we can generate the equation c= 0.18m + 10.4  where c is the cost and m is the number of minutes. So if you make 315 minutes of call then input  that for m and solve for c.

c= 0.18(315) + 10.4

c= 67.10  

Customers of a phone company can choose between two plans for long distance calls. The first plan has a $17 monthly fee and charges an additional $0.08 for each minute of calls. The second plan has an $8 monthly fee and charges an additional $0.13 for each minute of calls. How many minutes of calls Will the costs of the two plans be equal?

Answers

Answer:

180 minutes of calls

Step-by-step explanation:

Let x represent the minutes of calls

The first plan's cost can be represented by 0.08x + 17

The second plan can be represented by 0.13x + 8

Set them equal to each other and solve for x:

0.08x + 17 = 0.13x + 8

17 = 0.05x + 8

9 = 0.05x

180 = x

So, it will take 180 minutes of calls for the plans to be equal.

It costs $109 per night to rent a motel room in Georgia. There is a one-time $30 non-refundable deposit required. How much will it cost your family to rent a room for a week in Hampton?

Answers

Answer:

$793.00

Step-by-step explanation:

109x7=763

763+30=793

109x7=763+30=793 dollars for one week

If HFG is complementary to ACB, then
A. ACB is complementary to DFH
B. ACBEZDFH
C. ACB is supplementary to DFH
D. ACBZHFG
Mark this and return

Answers

None of those are right

A color printer prints 11 pages in 4 minutes.
How many pages does it print per minute?

Answers

The printer prints 2.75 pages per minute

Solution: 11/4=2.75

Answer:

2.75

Step-by-step explanation:

11/4 = 2.75

Hoped I helped

How would you write the equation with a slope of 2/3 and a y-intercept of (0,-3)?

Answers

Answer:

y = (2/3)x - 3

Step-by-step explanation:

Slope-intercept form: y = mx + b

Note that:

y = (x , y)

m = slope

x = (x , y)

b = y-intercept.

The point is given to you. Note that:

(x , y) = (0 , -3) ∴

x = 0

y = -3

The slope = m = 2/3

Plug in the corresponding numbers to the corresponding variable:

y = mx + b

-3 = (2/3)(0) + b

-3 = 0 + b

b = -3

Plug in -3 for b in the equation:

y = mx + b

y = (2/3)x -3

y = (2/3)x - 3 is your equation.

~

What simplified common fraction is equivalent to $0.0\overline{57}$?

Answers

Answer:

0

Step-by-step explanation:

0/57 is going to be 0 since you have 0 out of 57 pizzas.

Answer:

90/330

Step-by-step explanation:

Aops Question

Compare and Contrast the following diagrams by creating a list of at least 5
complete sentences.

Answers

Answer:

Both diagrams describe the representation of an object in space.

Step-by-step explanation:

1. The first diagram is a 2-dimensional plane in space.

2. it has two axes, the x-axis and y-axis, which is the length and width of the plane.

3. Both axes are perpendicular to each other.

4. The second diagram is a 3-dimensional plane with axis x, y and z representing the width, length and height of the plane respectively.

5. All three axes are perpendicular to each other like in the 2-dimensional plane.

18u^4w^6y^7+12u^9w^8

Answers

Answer:

[tex]6u^4w^6(3y^7+2u^5w^2)[/tex]

Step-by-step explanation:

[tex]18u^4w^6y^7+12u^9w^8[/tex]

we can only take common factor

18 and 12 have 6 as a common factor

in variables we have

[tex]u^4w^6y^7[/tex] and [tex]u^9w^8[/tex] so we see clearly that it is [tex]u^4w^6[/tex]

so we have

[tex]6u^4w^6(3y^7+2u^5w^2)[/tex]

as far as you can go

Without doing the calculations, determine whether -47-(-33) or -47+(-33) is greater

Answers

Answer:

-47-(-33) is greater

Step-by-step explanation:

the negative number and the subtraction end up to be addition

if f(x)=ln x then limx→2 f(x)= 1 2 Infinite Does Not Exist None of the above

Answers

Answer:

[tex]\lim_{x \to 2^{+}} f(x) = 2[/tex]

None of the above.

Step-by-step explanation:

f(x) = [x], in the graphing calculator, is f(x) = int(x).

This means we take the floor of x, or round down all the time.

The question is asking us to find the limit as x approaches 2 from the right. Since the graph from [2, 3) is going to be y = 2, we know that if we are approaching from the right of x → 2, we will approach y = 2 (shown in graph).

If we were to approach x → 2 from the left, then we would approach y = 1 (shown in graph).

If we were to approach from both the left and the right, then we would get DNE.

A bottle contains 2 liters of water. The bottle leaks 80 milliliters of water every 3 minutes. Will the bottle be empty in 1 hour? Explain why or why not. (1 liter = 1,000)

Answers

Answer:

No

Step-by-step explanation:

2 liters = 2,000

80/3 = 26.6

the bottle leaks 26.6 milliliters in a min

26.6 * 60 = 1596

1596 / 1000 = 1.596 ( to convert to liters)

the bottle will leak 1.596 an hour

No, the bottle will not empty in one hour because the bottle will leak 1.596 an hour.

What is Unitary Method?

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

Volume of bottle = 2 liters = 2,000 ml

For three  minutes bottle leaks = 80 ml

In one minute bottle leak= 80/3

                                   = 26.6 ml

In one minutes the bottle leak

=26.6 * 60

= 1596 ml

=1.596 liters

1596 / 1000 = 1.596 ( to convert to liters)

No, the bottle will not empty in one hour because the bottle will leak 1.596 an hour.

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Could anyone help me with this?

Answers

Complementary angles add to 90° and supplementary angles add to 180°, so angles ABC and CBD would be complementary.

To find x, subtract 37 from 90
90 - 37 = x
x = 53

A section of the theater has been reserved for 378 people . If each row in the theater seats 18 people, how many rows have been reserved

Answers

Answer:

21 reserved rows

Step-by-step explanation:

If A section of the theater has been reserved for 378 people and each row seats 18 then

378 divided by 18 = 21 reserved rows

Answer:

21 rows have been reserved

Step-by-step explanation:

You divide 378 by 18

Suppose that we have a pair of random variables X and Y with joint distribution
X
2 4 6
2 0.04 0.02 0.04
Y 4 0.12 0.06 0.12
6 0.24 0.12 0.24
(a) If we have M = max(X Y) the larger of the two observations, then calculate P{M = 6}.
(b) Show that X ami Y are independent.

Answers

Answer:

P (m=6)= 0.60

Marginal probability of y=  0.4 , 0.2 and 0.4

Marginal probability of x= 0.1  0.3 and 0.6

Step-by-step explanation:

The data given is

     X      2             4              6    

      2     0.04       0.02         0.04

y     4     0.12        0.06         0.12

     6      0.24      0.12          0.24

So the maximum value  M= max (X Y) is  (2,6) (6,4)(6,6)

We pick the larger value for each of the two observations

P (m=6) = 0.24+ 0.12+  0.24= 0.60

  X      2             4              6             Marginal

      2     0.04       0.02         0.04      0.1

y     4     0.12        0.06         0.12       0.3

      6      0.24      0.12          0.24      0.6

M.            0.4       0.2            0.4          1

The total is always equal to 1 .

X and Y are independent as the product of the marginal probability gives the joint probability.

We find the marginal probability by adding the rows and columns and then check if their product equal the given joint distribution which is true.



Can someone help me find the angle measurements

Answers

Answer:

12. 50 degrres

13. 90 degrees

14. 40 degrees

15. 50 degrees

16. 130 degrees

17. 90 degrees

Step-by-step explanation:

12. Angle UAY is equal to 50 degrees as it is stated in the graph

13. Angle YAZ is 90 degrees, as there is a square at the angle, meaning that the angle is a right angle.

14. Angle ZAX + Angle UAY + Angle YAZ = 180, as it is supplementary.

We know Angle UAY and Angle YAZ, so we can find Angle ZAX

Angle ZAX = 180 - UAY - YAZ = 180 - 50 - 90 = 40 degrees

15. Angle XAW = 50 degrees, as it is vertical angles with Angle UAY.

16. Angle WAU = Angle YAX = Angle YAZ + Angle ZAX = 90 + 40 = 130 degrees

17. Angle ZAW and Angle YAZ are supplementary, so they add up to 180 degrees.

Angle YAZ = 90 degrees, so Angle ZAW must also equal 90 degrees.

Answer & Explanation:

9. 50° (given)

10. 90° (90° angle is shown)

11. 40° (the line WAZ must equal 180° so 90° + 50° = 140 -> 180° - 140° = 40°)

12. 50° (same explanation as #11)

13. 130° (if the line WAZ must be 180°, then 180°- 50° = 130°)

14. 90° (right angle)

please mark as brainest if this hopefully helps!

x(z + 3) + 1 + 3 − y; use x = 6, y = −5, and z = 2

Answers

Answer: 39

Step-by-step explanation:

x(z+3)+1+3-y

plug in the values given for each variable

6(2+3)+1+3-(-5)

use pemdas to solve

6(5)+1+3+5

30+1+3+5

31+8

39

Answer: 39

Step-by-step explanation:

Given: x=6, y=-5, z=2

To solve this problem, plug all the variables in.

--------------------------------------------------------------------

 x(z+3)+1+3-y

Plug in

=(6)[(2)+3]+1+3-(-5)

Take off parentheses

=6(2+3)+1+3+5

Add 2 and 3, and also add 1 and 3

=6(5)+4+5

Multiply 6 and 5, and add 4 and 5

=30+9

Add 30 and 9

=39

Hope this helps!! :)

Please let me know if you have any question

Any help would be appreciated!

Answers

Answer:

this might help you....

Answer:

See below.

Step-by-step explanation:

In the figure above, ∠WXY and ∠YXZ are a linear pair.

What is a Linear Pair?

A Linear Pair is 2 angles that are adjacent, and form a straight line when combined. A Linear Pair contains 2 Supplementary Angles, angles that add up to 180°.

Their measures add up to 180°.

In order to find y, because they're a linear pair, we can set up an equation with the 2 angles equal to 180°.

[tex]4y+6y+30=180[/tex]

Combine Like Terms:

[tex]10y+30=180[/tex]

Subtract 30 from Both Sides:

[tex]10y=150[/tex]

Divide by 10:

[tex]\frac{10y}{10} = \frac{150}{10} \\y = 15.[/tex]

The value of y is 15.

Now since we know the value of y, we can substitute 15 into each angle to find their measure.

Substitute:

[tex]4(15)=60\\6(15)+30=120[/tex]

The measure of ∠WXY is 60° and the measure of ∠YXZ is 120°.

add the fractions and simplify the answer:2 1/4+5 5/6+3 2/3​

Answers

Look at the lower part of the fractions. 4, 6, and 3 can all be multiplied by something to equal 60 (there’s probably a lower number, it’s just the first one I thought of). Multiply 1/4 by 15, and you’ll get 15/60. Multiply 5/6 by 10, and you’ll get 50/60. Multiply 2/3 by 20, and you’ll get 40/60. Add them all together and you will get 105/60, or 1 45/60. If we add that to the whole numbers which are remaining, then we’ll get 11 and 45/60. Lastly, we need to simplify. This part is easy, because 45/60 is simply 3/4. Meaning the answer is 11 and 3/4.

Which of these is not a technique that can be used to randomly assign students to a treatment group?

Answers

Answer:

A. Winning an election for class president.

Step-by-step explanation:

It would not be fair because in an election you have to vote and having people vote into what group to be in, would not be randomly assigned and it would not be fair.

Answer:

A

Step-by-step explanation:

Did it already

A 6 inch personal pizza has 630 calories, with 240 of those from fat. A 12 inch pizza is cut into 8 slices. Estimate the number of calories in one slice of a 12 inch pizza.

Answers

Answer:

157.5.

Step-by-step explanation:

If the 6-inch pizza has 630 calories, the 12-inch pizza has double.

6 x 2 = 12.

Therefore, the 12-inch pizza has 1,260.

630 x 2 = 1,260.

There are 8 slices in a pizza, making the answer 1,260 / 8.

1,260 / 8 = 157.5

An estimation could be 150 if you round 630 to 600.

Hope this helps!

The number of calories in one slice of a 12-inch pizza would be 157.5.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

We have been given that the 6-inch pizza has 630 calories,

Therefore, the 12-inch pizza has double i.e. 1,260 calories.

To determine the number of calories in one slice of a 12-inch pizza.

We have to apply the division operation in 1,260 between 8,

⇒ 1,260 / 8.

⇒  157.5

If we round 630 to 600, an estimate would be 150.

Hence, the number of calories in one slice of a 12-inch pizza would be 157.5.

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How much is the total cost to mail this package?

Answers

Answer:

19.44

Step-by-step explanation:

Here is the scale model of a fountain at a museum the scale is 1:30 how many boulders are in the real fountain

Answers

Answer:

When we do a scale model of something (like a building, a house, or whatever) al the properties of the original thing must also be in the model.

So for example, you want to do a model of a house, and in the backyard of the house there are 4 trees, then in the model of the house you also need to put 4 trees in the backyard (indifferent of the scale of the model).

Then the number of boulders in the really fountain should be the same as the number of boulders in the scale model of the fountain.

Answer:

c. 10

Step-by-step explanation:

i just took the test

Simplify by factoring. √1350x^4

Answers

Answer:

 15[tex]x^{2}[/tex][tex]\sqrt{6}[/tex]

Step-by-step explanation:

√1350x^4= √2*5*5*3*3*3x^4 = 5*3x^2√2*3 =5[tex]x^{2}[/tex][tex]\sqrt{6}[/tex]

Shawna reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. The plot shows a strong positive correlation.
Shawna recalls that correlation does not imply causation. In this example, Shawna sees that increasing the number of cars per household would not cause members of her community to purchase health insurance.
Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.
A) Average income per household
B) The number of cars on the road
C) The number of citizens in the United States
D) Average mileage per vehicle

Answers

Answer:

The correct answer is:

A) Average income per household

Step-by-step explanation:

Correlation of variables is the statistical relationship between two variables. A correlation is positive if both variables move in the same direction (e.g both are increasing, or both are decreasing), and negative if the variables move in different directions - as one variable increases, the other decreases.

Correlation does not imply causation: This means that one can not legitimately associate a cause-and-effect relationship between the two variables, especially when there is a third variable (lurking) that has an effect on the outcomes that is not included as an explanatory or response variable.

In this example, it cannot be legitimately shown that increasing the number of cars per household would cause members of the community members to purchase health insurance, but when we bring in the lurking variable, which is the increase in average income per household, we can see that this possibility might cause more people to buy more health insurance even after they have purchased cars, because they have more money to spend.

The midpoint of AB is M(6, -1). If the coordinates of A are (4,-4), what are the
coordinates of B?

Answers

Answer:

(8, 2)

Step-by-step explanation:

(x, y)=(6, -1)

(x1+x2)/2=6

(y1+y2)/2=-1

------------------

(4+x2)/2=6

4+x2=6*2

4+x2=12

x2=12-4

x2=8

---------------

(-4+y2)/2=-1

-4+y2=-1*2

-4+y2=-2

y2=-2-(-4)

y2=-2+4

y2=2

(x2, y2)=(8, 2)

Nico earns $32.50 for each hour he works. last week Nico warned $1,300, and this week he earned $1,040. how many more hours did nick work last week than this week?

Answers

Answer:

8 hours

Step-by-step explanation:

$1,300/$32.50 = 40

$1,040/$32.50 = 32

40-32=8

Answer:

8 hours

Step-by-step explanation:

First, find the difference in the money

1300-1040=260

Then divide by 32.5

260/32.5=2600/325

8

So he worked for 8 more hours

The midpoint of (-4,15) and (22,3)

Answers

Answer:

(9, 9)

Step-by-step explanation:

midpoint of (-4,15) and (22,3)

[tex] = \bigg( \frac{ - 4 + 22}{2}, \: \: \frac{15 + 3}{2} \bigg) \\ \\ = \bigg( \frac{18}{2}, \: \: \frac{18}{2} \bigg) \\ \\ = ( 9, \: \: 9) \\ \\ [/tex]

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