Solve the following system of equations using substitution or elimination. 4x-2y+3z=1
x+3y-4z=-7
3x+y+2z=5
PLEASE HELP !!!

Answers

Answer 1

[1]   4x - 2y + 3z = 1

[2]   x + 3y - 4z = -7

[3]   3x + y + 2z = 5

Add -4 [2] to [1], and add -3 [2] to [3] to eliminate x :

-4 (x + 3y - 4z) + (4x - 2y + 3z) = -4 (-7) + 1

-4x - 12y + 16z + 4x - 2y + 3z = 28 + 1

[4]   -14y + 19z = 29

-3(x + 3y - 4z) + (3x + y + 2z) = -3 (-7) + 5

-3x - 9y + 12z + 3x + y + 2z = 21 + 5

-8y + 14z = 26

[5]   -4y + 7z = 13

Add 2 [4] to -7 [5] to eliminate y :

2 (-14y + 19z) - 7 (-4y + 7z) = 2 (29) - 7 (13)

-28y + 38z + 28y - 49z = 58 - 91

-11z = -33

z = 3

Plug this into either [4] or [5] to solve for y :

-4y + 7 (3) = 13

-4y + 21 = 13

-4y = -8

y = 2

Plug both of these solutions into either of [1], [2], or [3] to solve for x :

x + 3 (2) - 4 (3) = -7

x + 6 - 12 = -7

x = -1


Related Questions

3.99 x 10^-2 - 1.5 10^-3


put it in scientific notation

Answers

Answer:

its 3.45 x 10^5

Step-by-step explanation:

The solution of the given expression will be 3.84 x 10⁻².

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 3.99 x 10⁻² - 1.5 x 10⁻³. The expression will be solved as below:-

E = 3.99 x 10⁻² - 1.5 x 10⁻³

E = ( 3.99 x 0.15 ) x 10⁻²

E = 3.85 x 10⁻²

Therefore, the solution of the expression is 10⁻².

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6 is added to three-fifths of p

Answers

Answer:

Is that the question? I don't think it is

I’m confused ? Is that the question ?

hello please help will give brainliest!

Answers

Answer:

420

Step-by-step explanation:

Answer:

A. 420

Step-by-step explanation:

nice

A $55 pair of shoes was discounted 15% making a sale price $46.79 the discounted price was sent us Canada game by 10% explain how you would find the final price of the shoes?

Answers

Answer:

A $55 pair of shoes was discounted 15% making a sale price $46.79 the discounted price was sent us Canada game by 10% explain how you would find the final price of the shoes?

-1/2(-2x+4y) someone expand this pls

Answers

Answer:

-1/2(-2x+4y)=

x-2y

The college tutoring center staff are considering whether the center should increase the number of math workshops they offer to help students improve their performance in math classes. Faculty would like to know if requiring student attendance at these math workshops will improve overall passing rates for their students in their math classes. They plan to use the number of workshops attended to predict the final exam score and regression analysis to determine the effectiveness of the mandatory workshop attendance policy.

For each of the following classify the variable as explanatory, response, or neither.

a. Whether the student attended a workshop.
b. Number of workshops attended
c. Whether the student passes the course

Answers

Answer:

a. Whether the student attended a workshop.   Neither

b. Number of workshops attended.  Explanatory variable

c. Whether the student passes the course. Response variable

Step-by-step explanation:

In a given experiment, the response variable addresses the core of the question that was asked. In the experiment above, we are trying to determine the passing rate. That is the response variable. The explanatory variable provides an explanation for the response.

The number of workshops attended by the students would provide an explanation of their passing rates.  Whether the student attended a workshop is not a consideration in the experiment, because it is believed that they would attend the workshop.

I need help with homework in GoMath, 5th Grade, Lesson 2.5

Answers

Can you show a photo of the lesson you need help with

4 divied by 217 long divisions

Answers

Answer:

Step-by-step explanation:

Answer: 0.018 or not simplified: 0.01843317972

     0. 0 1 8

2 1 7 4. 0 0 0

   − 0      

     4 0    

   −   0    

     4 0 0  

   − 2 1 7  

     1 8 3 0

   − 1 7 3 6

         9 4

Homer sold cupcakes and cookies yesterday. Each cupcake sold for $2.25 and each cookie sold for $0.25. At the end of the day, Homer has sold $55.50 worth of cookies and cupcakes. If he sold 54 cupcakes and cookies combined, how many cupcakes were sold and how many cookies were sold

Answers

Answer: 21 cupcakes and 33 cookies were sold.

Step-by-step explanation:

Let x= Number of cupcakes

y = Number of cookies

As per given,

x+y= 54       (i)

Cost: 2.25x+0.25y=55.50          (ii)

Multiply 0.25 to (i0, we get

0.25x+0.25y = 0.25(54)

⇒0.25x+0.25y = 13.5         (iii)

subtract (iii) from (ii), we get

2x=42

Divide both sides by 2, we get x= 21

Put this in (i) , we get 21+y =54 ⇒ y= 54-21= 33

Hence, 21 cupcakes and 33 cookies were sold.

The graph of a linear function is given below.

What is the zero of the function
A. -5
B.2/5
C.2
D.5/2

Answers

Answer:

A. - 5

Step-by-step explanation:

Since, line is intersecting x-axis at - 5, therefore zero of the function is - 5.

The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in minutes since the coffee was put on the counter.
a) Is f'(t) positive or negative? Why?
b) What are the units of f'(35)?
c) Suppose that |f'(35)| = 1.5 and f(35) = 68. Fill in the blanks (including units where needed) and select the appropriate terms to complete the following statement about the temperature of the coffee in this case.
At ____ minutes after the coffee was put on the counter, its temperature is ____ and will ____ by about ____ in the next 30 seconds.

Answers

Answer:

a

    f'(t) is  negative

b

 The  unit is degC/min

c

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.          

Step-by-step explanation:

From the question we are told we are told that  

   The  equation for the temperature of a cup of coffee place on a counter is

         [tex]H= f(t)[/tex]

Here  t is the time in minutes the  coffee was put on the counter

Generally  f(t)'  is the derivative of  f(t) at it represents the change of the temperature of the cup of coffee with respect to time

 Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence  f(t)' is  negative

Generally the unit of the temperature is in degrees Celsius while that of time is  in minutes

  So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e  degC/min)

  From the question we are told that

        [tex]|f(35)'| =  1.5[/tex]

i.e  the rate of change of temperature after 35 minutes is  1.5

and

         [tex]|f(35)| =  68[/tex]

i.e the temperature of the cup of coffee after 35 minutes is  67 degC

Now after another   t=  30  seconds =  [tex]\frac{30}{60}= 0.5 \ minutes[/tex] the  rate  of change of the temperature of the cup of  coffee is  

          [tex]R =  |f(35)'| *  t[/tex]

=>        [tex]R = 1.5  *  0.5 [/tex]

=>        [tex]R = 0.75  [/tex]    

So

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.  

     

The value of f'(t)  is negative because as the cup of coffee is placed on the counter there is a loss of heat from the cup of coffee to the surroundings as t increases hence f'(t) is negative.

The units of  f'(35) = degC/min.

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.    

Given

The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in minutes since the coffee was put on the counter.

1. The value of f'(t)  is negative because as the cup of coffee is placed on the counter there is a loss of heat from the cup of coffee to the surroundings as t increases hence f'(t) is negative.

2. What are the units of f'(35)?

The units of  f'(35) = degC/min.

3. At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.    

At ║f'(35)║ = 1.5 and f'(35) = 68

|f'(35)| = 1.5 represents the rate of change of temperature every 35 minutes = 1.5.

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4z-10=14 *
I can’t get the answer please help

Answers

Answer:

z = 6

Step-by-step explanation:

4z - 10 = 14

    + 10   +10

4z = 24

24 ÷ 4 = 6

n = 6

There are six wires which need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determine which order would be fastest for the robot to use.

Required:
Use the multiplication rule of counting to determine the number of possible sequences of assembly that must be tested.

Answers

Answer:

There are 720 possible sequences of assembly that must be tested.

Step-by-step explanation:

We are given that;

No. of wires needed to be attached to a circuit board = 6

We want to find the number of possible sequences of the assembly that must be tested.

From multiplication rule of counting;

Number of possible sequences of the assembly = 6!

1st selection of wire = 6 possible choices

2nd selection of wire = 5 possible choices

3rd selection of wire = 4 possible choices

4th selection of wire = 3 possible choices

5th selection of wire = 2 possible choices

6h selection of wire = 1 possible choice

Thus,

number of possible sequences = 6 × 5 × 4 × 3 × 2 × 1 = 720

Thus, there are 720 possible sequences of assembly that must be tested.

Calvin is starting a new job this summer. He has created a table to represent his earnings, which are dependent on the number of hours he works. Write an equation to represent y, Calvin’s total earnings based on x the number of hours he works. * PLEASE HELPPP!!!!!!

Answers

Answer:

I think its 232.5

Step-by-step explanation:

Divide 3 by one then multiply that by 15.

Answer:

how much does he make in a hour

Step-by-step explanation:

An insurance policy sells for $800. Based on past data, an average of 1 in 50
policyholders will file an $8,000 claim, an average of 1 in 100 policyholders will file
a $20,000 claim, and an average of 1 in 250 policyholders will file a $50,000 claim. Find
the expected value to the company per policy sold.

Answers

Answer: i needed this question too!

help me pleeeaseeee​

Answers

Answer:

-2

Step-by-step explanation:

Heather wants to purchase an electric guitar the price of the guitar with tax is $2,240.if she can save $90 per month how linf will it take her to save up for the guitar

Answers

Answer:

25

Step-by-step explanation:

F(4) for the function f(x)=2x+5

Answers

Answer:

= 13

Step-by-step explanation:

Use direct substitution:

2(4)+5 = 13

angles 2 and angle 7 are ??? angles​

Answers

Answer:

D alternate exterior angle

Step-by-step explanation:

Answer:

vertical angles

vertical angles are congruent angles located diagonally opposite each other.

complete the pattern 444 4440 44,400 444,000 ______ _______ what goes on does 2 spots

Answers

Answer:

4440,000 and 44.400,000

Step-by-step explanation:

All you do is add another zero to the end

The number of kilograms of water in a human body varies directly as the mass of the body. An 84-kg person contains 56 kg of water. How many kilograms of water are in a 63-kg person?
kg of water are in a 63-kg person.

Answers

Answer:

42

Step-by-step explanation:

To find the amount of water in a 63-kg person you must first find the unit rate in an 84-kg person.

84 ÷ 56 = 1.5

1.5 is how much human body weight there is as a unit rate over 1-kg of water.

1.5 x 56 = 84, so this shows we are correct.

84 ÷ 1.5 = 56, so that goes even further to prove you are correct.

Now, what's the amount of water in a 63-kg person?

1.5 is the unit rate we found out was used, so it should still be proportional.

63 ÷ 1.5 = 42.

Indeed, it is proportional. You are correct.

The answer is 42.

There is 42 kg of water in a 63 kg person.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 4 is an equation.

We have,

The number of kilograms of water in a human body varies directly with the mass of the body.

This means,

W ∝ M

Where W is the kg of water and M is the mass of the body.

Now,

W = KM

W = 56 kg

M = 84 kg

So,

56 = 84K

K = 56/84

Now,

For M = 63,

W = KM

W = 56/84 x 63

W = 42

Thus,

There is 42 kg of water.

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solve for n: 10/60 =n/84

Answers

Answer:

n=14

Step-by-step explanation:

Is this relation a function? Justify your answer.

Please help me!! 5:45pm est! Answer as soon as you can!

Answers

Answer:

D

Step-by-step explanation:

Two side of a triangle have the following measures. Find the range of possible measures for the third side.

8, 9



_______ < x < _______

Answers

Answer:

8<x<9

Step-by-step explanation

Help me ASAP please !!!! I attached a pic

Answers

x^3 would be equivalent to that expression!

let f(r) be the number of riders on a bus r hours after 8 am. Explain the meaning of the statement f(5)=23.

Answers

Answer:

See explanation

Step-by-step explanation:

Given

f(r) => Number of people in the bus after 8am

Required

Interpret f(5) = 23

Going by the analysis in the question, the interpretation goes this:

5 hours after 8 am, there are 23 riders on a bus

We can also interpret as:

There are 23 riders on a bus at 1 pm

Since 1 pm = 5 hours after 8am

what is 1555 times 67

Answers

Answer:

104185

Step-by-step explanation:

Answer:

104,185

Step-by-step explanation:

Help my daughter please k gtg

Answers

Answer:

5.7, 4.6, 5.6, 6.7

Step-by-step explanation:

Answer:

2.63+3.07= 5.7

9.4-4.8= 4.6

3.92+1.68= 5.6

8.5-1.8= 6.7

The points Q, R, S and T all lie on the same line segment, in that order, such that the
ratio of QR:RS: ST is equal to 1:4:5. If QT = 40, find RS.

Answers

Answer:

RS=3

Step-by-step explanation:

Solve for x:

6x+3x+x=10

All parts add up to whole

10x=10

Combine like terms

x=1

Use x to solve for segment lengths:

QR=6x=6(1)=6

RS=3x=3(1)=3

ST=x=1

Therefore RS=3

The length of the line segment RS will be 16 units.

What are collinear points?

An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points are transparently collinear. If the points are in a line, then the points are collinear points.

Let Q, R, S, and T be the collinear points. Then the condition of the collinear will be

QR + RS + ST = QT

The points Q, R, S, and T all lie on the same line segment, in that order, such that the ratio of QR:RS: ST is equal to 1:4:5. If QT = 40.

Let QR / 1 = RS / 4 = ST / 5 = x

QR = x

RS = 4x

ST = 5x

Then the value of the variable x will be

QR + RS + ST = QT

x + 4x + 5x = 40

10x = 40

x = 4

Then the length of the line segment RS will be

RS = 4x

RS = 4 (4)

RS = 16

Then the length of the line segment RS will be 16 units.

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We would like to know the velocity of the block when it reaches some position x. Finding this requires an integration. However, acceleration is defined as a derivative with respect to time, which leads to integrals with respect to time, but the force is given as a function of position. To get around this, use the chain rule to find an alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx.

Answers

Answer:

An alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex] is [tex]a_x=v_x \frac{dv_x}{dx}[/tex]

Step-by-step explanation:

We know that :

[tex]a_x=\frac{dv_x}{dt}[/tex]

Now we are supposed to find an alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex]

So, We will use chain rule over here :

[tex]a_x=\frac{dv_x}{dt}\\a_x=\frac{dv_x}{dt} \times \frac{dx}{dx}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt} [\frac{dx}{dt}=v_x]\\a_x=\frac{dv_x}{dx} \times v_x\\a_x=v_x\frac{dv_x}{dx}[/tex]

Hence an alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex] is [tex]a_x=v_x \frac{dv_x}{dx}[/tex]

The alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx is [tex]a_x = v_x \frac{dv_x}{dx}[/tex]

Chain rule:

Here we used the chain rule:

It is the basic method for differentiating a composite function. Here the first factor on the right, Df(g(x)), represents that the derivative of f(x) is first found and then x, wherever it arises, is replaced by the function g(x).

So,

[tex]a_x = \frac{dv_x}{dt}\\\\ = \frac{dv_x}{dt} \times \frac{dx}{dx}\\\\= \frac{dv_x}{dx} \times \frac{dx}{dt}\\\\ = \frac{dv_x}{dx} \times \frac{dx}{dt} (\frac{dx}{dt} = v_x)\\\\ = \frac{dv_x}{dx} \times v_x\\\\= v_x\frac{dv_x}{dx}[/tex]

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