Solve the system, by elimination please show all the steps!
-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

Answers

Answer 1

Answer:

x = 1 , y = 1 , z = 0

Step-by-step explanation:

Solve the following system:

{-2 x + 2 y + 3 z = 0 | (equation 1)

-2 x - y + z = -3 | (equation 2)

2 x + 3 y + 3 z = 5 | (equation 3)

Subtract equation 1 from equation 2:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x - 3 y - 2 z = -3 | (equation 2)

2 x + 3 y + 3 z = 5 | (equation 3)

Multiply equation 2 by -1:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+3 y + 2 z = 3 | (equation 2)

2 x + 3 y + 3 z = 5 | (equation 3)

Add equation 1 to equation 3:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+3 y + 2 z = 3 | (equation 2)

0 x+5 y + 6 z = 5 | (equation 3)

Swap equation 2 with equation 3:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y + 6 z = 5 | (equation 2)

0 x+3 y + 2 z = 3 | (equation 3)

Subtract 3/5 × (equation 2) from equation 3:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y + 6 z = 5 | (equation 2)

0 x+0 y - (8 z)/5 = 0 | (equation 3)

Multiply equation 3 by 5/8:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y + 6 z = 5 | (equation 2)

0 x+0 y - z = 0 | (equation 3)

Multiply equation 3 by -1:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y + 6 z = 5 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Subtract 6 × (equation 3) from equation 2:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y+0 z = 5 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Divide equation 2 by 5:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Subtract 2 × (equation 2) from equation 1:

{-(2 x) + 0 y+3 z = -2 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Subtract 3 × (equation 3) from equation 1:

{-(2 x)+0 y+0 z = -2 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Divide equation 1 by -2:

{x+0 y+0 z = 1 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Collect results:

Answer: {x = 1 , y = 1 , z = 0

Answer 2

Answer:

x= 1, y = 1, z=  0

Step-by-step explanation

-2x + 2y + 3z = 0

2x + 3y + 3z = 5

-2x - y + z = -3

2x + 3y + 3z = 5

(solving systems)

5y + 6z = 5

2y + 4z = 2

(rewriting)

z = 0

y = 1

-2x + 2 x 1 + 3 x 0

x=1


Related Questions

As x approaches infinity, for which function does f(x) approach negative infinity? Select all that apply. Select all that apply: f(x)=19x(3x+7)(x+12) f(x)=−23(x+4)(x−1)(x−5) f(x)=3x(x+4)(x+7)(x−9) f(x)=(4x−7)(3x+1)(2x−11) f(x)=−29x(2x+5)(2x−1)(x+8)(x−1)(x+4) f(x)=−45x(x+1)(x+5)(x+8)(2x+5)(2x−7)(4x+1)

Answers

Answer and explanation:

Please find answer and explanation attached

Ron Alotte and Dee Selerate ran a 20 km. Race. Dee made three 10 minute stops during the race to fix her shoes and rest and yet the two racers finished in a tie. If Ron ran the race at a constant speed of 8 km. Per hour, find Dee's average speed when running.

Answers

Answer:

10km/hr

Step-by-step explanation:

Given that:

Distance covered by both Dee and Ron= 20km

Ron's speed = 8km/hr

Dee made three 10 minute stops during the race.

Time it took Ron to cover 20km

Time = distance / speed

20km / 8km/hr = 2.5 hours = 150 minutes

Since they both tied ;

Running time of Dee = (150 - (3*10)) = 120 minutes = 2 hours

Ron's speed = distance / time

Speed = 20 km / 2hours

Speed = 10km/hr

A and \angle B∠B are supplementary angles. If m\angle A=(5x-19)^{\circ}∠A=(5x−19)

and m\angle B=(2x+10)^{\circ}∠B=(2x+10)

, then find the measure of \angle B∠B.

Answers

Answer: 52

Step-by-step explanation:

4x+8 = 5x-3 by the Vertical Angles Theorem that states the vertical angles are congruent.  

Subtract 4x from both sides and get:

8=1x -3

Add 3 to both sides:

11= 1x

if x =11, plug that in to angle A.  

4x+ 8 becomes 4(11)+8 =

44+ 8=

52

Mrs. Greene wants to plant a vegetable garden in her yard. She purchased a package containing 30 sections of fencing, each 1-foot long If she uses all 30 sections to create rectangular space, how many different arrangements are possible? What is the largest area she can enclose for her garden with this fencing?

Answers

Answer:

The largest area she can enclose for her garden with this fencing is [tex]56 ft^2[/tex]

Step-by-step explanation:

Suppose the rectangular space Mrs. Greene wants to plant has dimensions x feet and y feet.

Since each section of fencing is 1-foot long, both x and y must be integer numbers.

The perimeter of the rectangular space is calculated as:

P = 2x + 2y

And we know she uses all 30 sections of fencing, thus:

2x + 2y = 30, where x, y are integers and positive.

Simplifying by 2:

x + y = 15

Solve for x:

x = 15 - y

This equation doesn't have infinitely many solutions, since both numbers must be integers and positive. Suppose we start by setting y=1, then x=14. That is a possible arrangement for the garden.

Another valid option is for y=2, x=13

Continuing with these patterns, we find the maximum value for y is 7, x=8, because if we set y=8, x=7, this is the same condition as y=7, x=8.

Thus, from y=1 to y=7, there are 8 possible combinations for the arrangement of the garden.

The area of a rectangle is

[tex]A=x\cdot y[/tex]

Testing some possible arrangements:

y=1, x=14

[tex]A=1\cdot 14= 14 ft^2[/tex]

y=2, x=13

[tex]A=2\cdot 13= 26 ft^2[/tex]

y=3, x=12

[tex]A=3\cdot 12= 36 ft^2[/tex]

We can notice the combination y=7, x=8 has an area of:

[tex]A=7\cdot 8= 56 ft^2[/tex]

This is the largest possible area of all combinations, thus:

The largest area she can enclose for her garden with this fencing is [tex]56 ft^2[/tex]

The number 4 and the number 4/1 are
exactly the same. Explain why.

Answers

Step-by-step explanation:

Hey there!

It's obvious that 4 and 4/1 are exactly same.

Reason: something divided by 1 is always a a number same in a numerator.

Example;

1. 7/1 = 7

2. 5/1 = 5

Hope it helps..

I need help with this asap

Answers

Answer:

3\sqrt{3}

Step-by-step explanation:

look this up and it will give you the answer

pls mark brainliest

Answer:

The sqrt of 3 is an irrational number.

The sqrt of 9 is a rational number.

Step-by-step explanation:

An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 g of an alloy containing 12% copper with 78 g of an alloy containing 92% copper how many grams of copper are in the resulting mixture what percentage of the resulting mixture is copper

Answers

Given :

An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 g of an alloy containing 12% copper with 78 g of an alloy containing 92% copper.

To Find :

How many grams of copper are in the resulting mixture what percentage of the resulting mixture is copper.

Solution :

Mass of copper in 50 gm alloy = [tex]50\times 0.12 = 6\ gram[/tex].

Mass of copper in 78 gm alloy = [tex]78\times 0.98 = 76.44\ gram[/tex].

Total mass of copper, ( 6 + 76.44 ) gm = 82.44 gram.

Percentage of copper in resulting mixture :

[tex]\%=\dfrac{82.44}{50+78}\\\\\%=64.4\ \%[/tex]

Hence, this is the required solution.

The shampoo Eva likes to use costs $6 for a 24-ounce bottle. The conditioner she likes to use costs $12 for a 30-ounce bottle. How much more per ounce does her conditioner cost than her shampoo? $ per ounce

Answers

Answer:

0.15

Step-by-step explanation:

6 divided by 24 equals 0.25

12 divided by 30 equals 0.4

0.4 minus 0.25 is 0.15

$0.15 more per ounce does her conditioner cost than her shampoo.

Given that, the shampoo Eva likes to use costs $6 for a 24-ounce bottle.

What is the unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

The conditioner she likes to use costs $12 for a 30-ounce bottle.

Cost of shampoo per ounce =Total cost/Number of ounce

= 6/24

= $0.25 per ounce

Cost of conditioner per ounce =Total cost/Number of ounce

= 12/30

= $0.4 per ounce

Difference =0.4-0.25

= $0.15

Therefore, $0.15 more per ounce does her conditioner cost than her shampoo.

To learn more about the unitary method visit:

brainly.com/question/22056199.

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The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. A standard dartboard is
18 inches in diameter.
Suppose a standard dartboard is hung at standard height so that the bull's-eye is 11 feet from a wall to its left.
Samuel throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5.5 feet above the floor.
Does Samuel's dart land on the dartboard?

Answers

Answer:

Yes, Samuel dart does land on the dart board

Step-by-step explanation:

The given parameters are;

The height from the floor to the bulls eye = 5 feet 8 inches

The size of the standard board = 18 inches diameter

The distance of the bulls eye from the wall to the left = 11 feet

The distance the dart Samuel throws land from the left wall = 11.5 feet

The distance above the ground, the dart Samuel throws land = 5.5 feet

Whereby Samuel throws the dart directly at the dartboard, we have;

The location of the bulls eye = (11, 5.67)

The equation of the circle representing the dart board = (x - 11)² + (y - 5.67)² = 0.75² = 0.5625

The unit of the radius is in feet

The position of Samuel's dart is represented by the coordinate, (11.5, 5.5)

Plugging in the coordinates of the position of Samuel's dart into the equation of the circle of the dart board gives;

(11.5 - 11)² + (5.5 - 5.67)² = 0.2789 ≈ 0.528²

Therefore, given that the square of the distance of the position of Samuel's dart is less than the square of the radius of the dart board, we have;

Yes, Samuel dart does land on the dart board.

From the parameters given to find out if Samuel's dart landed on the dartboard, we can say that;

Samuel's dart does not land on the dartboard.

We are given;

Height from the floor to the bulls eye = 5 ft 8 in = 5.67 ft

Diameter of the standard dartboard = 18 in = 1.5 ft

Thus, radius; r = 1.5/2 = 0.75 ft

Distance of the bulls eye from the wall to the left = 11 ft

Distance of dart thrown by Samuel from the left wall = 11.5 ft

Height of dart thrown by Samuel above the ground = 5.5 ft

We know that general equation of a circle is;

(x - a)² + (y - b)² = r²

Since Height from the floor to the bulls eye is 5.67ft,then a = 5.67 ft

And also since Distance of the bulls eye from the wall to the left = 11 ft, then b = 11 ft

Thus;

(x - 11)² + (y - 5.67)² = 0.75²

(x - 11)² + (y - 5.67)² = 0.5625

Now, since he throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5.5 feet above the floor. Thus;

r² = (11.5 - 11)² + (5.5 - 5.67)²

r² = 0.2789

r² of 0.2789 gotten here is lesser than 0.5625 gotten earlier, we can conclude that Samuel's dart does not land on the dart board.

Read more at; https://brainly.com/question/18430680

x - 17 = 32 * linear equations

Answers

x= 49 hope this is what you needed!

Answer: x=49

x-17=32

Subtract 17 from both sides.

x=32+17

x=49

-2x + 7 = x-2
What is this ? In the most simplest steps possible

Answers

Answer:

Let's solve your equation step-by-step.

−2x+7=x−2

Step 1: Subtract x from both sides.

−2x+7−x=x−2−x

−3x+7=−2

Step 2: Subtract 7 from both sides.

−3x+7−7=−2−7

−3x=−9

Step 3: Divide both sides by -3.

−3x /−3      −9 /−3

Answer:

x=3

                                            Hope this helps

                                                     (>'-'<)    

x2 + 6 x+8 = 0
What is the factors

Answers

Answer:

Step-by-step explanation:

Write a sentence as an equation using the given information in each problem.

1. Write the sentence as an equation.
the product of 371 and ​d​ is the same as 52

2. Write the sentence as an equation. n​ decreased by 320 is equal to 139

3. Write the sentence as an equation. 317 is equal to ​k​ plus 110

4. Write the sentence as an equation.
the total of 374 and ​k​ is the same as 305

5. Write the sentence as an equation. 398 is the same as ​d​ plus 6

Answers

Answer:

1. 371 × d = 52

2. n - 320 = 139

3. 317 = k + 110

4. 374 + k = 305

5. 398 = d + 6

Step-by-step explanation:

1. 371 × d = 52

d = 52/371

d = 0.14016172506

2. n - 320 = 139

n = 139 + 320

n= 459

3. 317 = k + 110

k = 317 - 110

k = 207

4. 374 + k = 305

k = 305 - 374

k = -69

5. 398 = d + 6

d = 398 - 6

d = 392

Which sequences of transformations confirm the congruence of shape II and shape I?

a reflection of shape I across the x-axis followed by a 90° clockwise rotation about the origin
a reflection of shape I across the x-axis followed by a 90° counterclockwise rotation about the origin
a reflection of shape I across the y-axis followed by a 90° counterclockwise rotation about the origin
a reflection of shape I across the y-axis followed by a 90° clockwise rotation about the origin
a reflection of shape I across the x-axis followed by a 180° rotation about the origin

Answers

A,B,C

Step-by-step explanation:

Answer:

A, B and C

Step-by-step explanation:

Can someone Answer this please!

Answers

Answer:

I think the answer is A because Irrational numbers cannot be written in as a fraction but the do repeat at the point

if a2+b2+c2=ab+bc+ca find a+b/b​

Answers

Answer:

Step-by-step explanation:

a² + b² + c² = ab + bc + ca

On multiplying both sides by “2”, it becomes

2 ( a² + b² + c² ) = 2 ( ab + bc + ca)

2a² + 2b² + 2c² = 2ab + 2bc + 2ca

a² + a² + b² + b² + c² + c² – 2ab – 2bc – 2ca = 0

a² + b² – 2ab + b² + c² – 2bc + c² + a² – 2ca = 0

(a² + b² – 2ab) + (b² + c² – 2bc) + (c² + a² – 2ca) = 0

(a – b)² + (b – c)² + (c – a)² = 0

=> Since the sum of square is zero then each term should be zero

⇒ (a –b)² = 0, (b – c)² = 0, (c – a)² = 0

⇒ (a –b) = 0, (b – c) = 0, (c – a) = 0

⇒ a = b, b = c, c = a

∴ a = b = c.

hence

a+b/b​

a+a/a= (since a=b)

2a/a=

a....

10 Brynlee's monthly cell phone bill
is $60 a month plus $2.50 per
gigabyte used. Raylin's cell phone bill is $450
per month plus $3.25 per gigabyte used.
Determine after how many gigabytes used
would the cell phone plans cost the same
for the month what is the answer??

Answers

Answer:

20 gigabytes

Step-by-step explanation:

Let n represent the amount of gigabytes used.

First make an equation for each senario, Brynlee's would be 60+2.50n and Raylin's would be 45+3.25n.

Set them to equal each other, 60+2.50n=45+3.25n.

Then isolate for n.

60-45=3.25n-2.50n

15=0.75n

Divide both sides by 0.75 to get 20

Which equation shows an example of the associative property of addition?

A. (–4 + i) + 4i = –4 + (i + 4i)
B. (–4 + i) + 4i = 4i + (–4i + i)
C. 4i × (–4i + i) = (4i – 4i) + (4i × i)
D. (–4i + i) + 0 = (–4i + i)

Answers

Answer:

I am pretty it's A

Step-by-step explanation:

Basically the Associative Law of Addition means that the order that the numbers are added does not matter.

Answer:

A. (–4 + i) + 4i = –4 + (i + 4i)

Step-by-step explanation:

edge2020

Have a great day y'all :)

Does 3 times 48 equal 4 times 36

Answers

Answer:

Yes

Step-by-step explanation:

3 x 48 = 144

4 x 36 = 144

They are equal.

Answer:

3 * 48 is 144 4 x 36 is also 144 so yes they are equal

Given: ΔABC, where AB = BC Prove: m∠BAC = m∠BCA Statement Reason 1. Let ΔABC be an isosceles triangle with AB = BC. given 2. Create point D on side so bisects ∠ABC. constructing an angle bisector 3. M∠ABD = m∠CBD definition of angle bisector 4. BD = BD Reflexive Property of Equality 5. ΔABD ≅ ΔCBD 6. M∠BAC = m∠BCA Corresponding angles of congruent triangles have equal measures. What is the reason for statement 5 in this proof? A. ASA B. SSS C. AAS D. SAS

Answers

Answer:

D. SAS

Step-by-step explanation:

Given: ΔABC

Bisecting <ABC to create point D implies that BD is a common side to  ΔABD and ΔCBD.

Also,

m<ABD = m<CBD (angle bisector)

BA = BC (given property of the isosceles triangle)

Therefore,

ΔABD ≅ ΔCBD (Side Angle Side)

The reason for statement 5 in this proof is that ΔABD ≅ ΔCBD by SAS (Side-Angle-Side) relations of the congruent triangles.

Answer:

Option D is correct trust me

Step-by-step explanation:

The formula for the volume of a rectangular prism is V = lwh. Which is the equivalent equation solved for h?​

Answers

Answer:

V /(lw) = h

Step-by-step explanation:

V = lwh

Divide each side by lw

V/ ( lw) = lwh/(lw)

V /(lw) = h

V /(lw) = h

V = lwh

Divide each side by lw

V/ ( lw) = lwh/(lw)

V /(lw) = h

If B = 3x^2-x+3and A=x-6, find an expression that equals 2B+3A in standard form?

Answers

Answer:

[tex]6x^{2} +x-12[/tex]

Step-by-step explanation:

All you need to do is multiply equation B by 2 and multiply equation A by 3, then put an addition sign between them and combine like terms after you've distributed what you needed for each one.

Someone please help! Asap

Answers

4x + 3 + 9x + 5 = 47
13x + 8 = 47
13x = 39
X = 3

9(3) + 5

Answer: 32
Answer :
X=3

Steps :

4x+3 + 9x+5
= 13x+8

Then
13x+8 = 47

X=3

Which of the following is a possible value for X

Answers

Answer:

E)3

Step-by-step explanation:

4/3-1=2

3+1/2=2

First, You cross multiply.

(x - 1)(x + 1) = 8

x^2 - 1 = 8

Now subtract 8 from both sides.

x^2 - 9 = 0

x^2 - 9 is a difference between 2 squares.

(x + 3)(x - 3) = 0

For an equation with only multiplying to be equal to 0, one of its factors must be 0.

So either x + 3 = 0 or x - 3 = 0.

So x could be -3 or 3.

The answer is (E).

Hope this helps!

When electrons flow with little resistance through a conductor it is called a

Answers

Answer:

The answer is free electrons

Step-by-step explanation:

When electrons flow with little resistance through a conductor, then it is called a Electricity.

What are electrons?

"The electron is a subatomic particle whose electric charge is negative one elementary charge."

What is resistance?

"Resistance is a measure of the opposition to current flow in an electrical circuit."

What is conductor?

"A conductor, or electrical conductor, is a substance or material that allows electricity to flow through it. "

What is Electricity?

The steady flow of electrons through a conductor is called electricity

Hence , if electrons are flowing that means they conducts electricity.

Learn more about electricity here

https://brainly.com/question/8971780

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W(-5,1) reflect it across x=-3

Answers

Answer:

(-1,1)

Step-by-step explanation:

Someone plz help me thank you.

Answers

Answer:

there are 438 blue marbles and 162 red marbles

Step-by-step explanation:

If we were doing it out of 100 there would be 73 blue marbles and 27 red marbles add 73 to 27 and you get 100 so multiply 73 by 6 and you get 438 and then multiply  27 by 6 and you get 162 and 438 to 162 and you get 600. Therefore your answer is 438 blue marbles and 162 red marbles.

hope this helps

Janessa,has 18$. She buys a ticket to a movie and a smoothie. How much money dose she have left? Ticket: $8.75
Celery Sticks: $3.75
Smoothie: $2.85
What do you need to find before you can solve the​ problem?
A. The total amount of money Janessa has in her bank account.
B. The cost of a smoothie
C.The total amount of money Janessa had spent
D. The total amount of money Janessa has left.

Answers

Answer:

B. The cost of a smoothie

Step-by-step explanation:

The answer to the problem: 8.75 + 2.85 = $11.60

But to solve the problem you have to know the price of a smoothie.

Simplify the following expression.
(5^3)^5

Answers

Answer:

5 ^15

Step-by-step explanation:

(5 ^3)^5 =5 ^(3×5)=5 ^15

Answer:  5^15

The rule used is (a^b)^c = a^(b*c)

If you raise some exponential expression to another exponent, then you multiply the exponents. You keep the base the same.

In this case, a = 5, b = 3, c = 5.

Using a calculator,

5^15 = 30,517,578,125

But it's likely your teacher will want you to keep the answer in exponential form since it's easier to work with.

Nool is a computer repairman, To fix a computer,
he charges a customer X per hour, plus a fired
lee of $15 for the service call, as represented by
the equation below
y = 40x + 15
In the equation, what is represented by the variable
A the number of hours Noel worked
the amount Noel charged per hour
C, the fixed fee for the service call
D. the total cost of the repair job
Can someone

Answers

i’m pretty sure it’s B, the amount Noel charged per hour :)
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