Select the correct answer. Which system of equations has a solution of (-2,-2,-2) ​

Select The Correct Answer. Which System Of Equations Has A Solution Of (-2,-2,-2)

Answers

Answer 1

Answer:

[B] [tex]\begin{bmatrix}x+2y=-6\\ y+2z=-6\\ x-y-z=2\end{bmatrix}[/tex]

Step-by-step explanation:

Going through all answer choice to find the solution:

[A]  [tex]\begin{bmatrix}x+y=0\\ y-z=-2\\ x+y-z=-4\end{bmatrix}[/tex]

[tex]\mathrm{Isolate\;x\;for\;x+y=0;x=-y}[/tex]

[tex]\mathrm{Substitute\:}x=-y[/tex]

[tex]\begin{bmatrix}y-z=-2\\ -y+y-z=-4\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}y-z=-2\\ -z=-4\end{bmatrix}[/tex]

[tex]\mathrm{Isolate\;z\;for\;-z=-4;z=4}[/tex]

[tex]\mathrm{Substitute\:}z=4[/tex]

[tex]\begin{bmatrix}y-4=-2\end{bmatrix}[/tex]

[tex]\mathrm{Isolate\;y\;for\;y-4=-2;y=2}[/tex]

[tex]\mathrm{For\:}x=-y[/tex]

[tex]\mathrm{Substitute\:}z=4,\:y=2[/tex]

[tex]x=-2[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=-2,\:z=4,\:y=2[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[B] [tex]\begin{bmatrix}x+2y=-6\\ y+2z=-6\\ x-y-z=2\end{bmatrix}[/tex]

[tex]\begin{bmatrix}y+2z=-6\\ z-y-z=2\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}y=-2[/tex]

[tex]\begin{bmatrix}-2+2z=-6\end{bmatrix}[/tex]

[tex]\mathrm{For\:}x=-6-2y[/tex]

[tex]\mathrm{Substitute\:}z=-2,\:y=-2[/tex]

[tex]x=-6-2\left(-2\right)[/tex]

[tex]x=-2[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=-2,\:z=-2,\:y=-2[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[C] [tex]\begin{bmatrix}3x-y=-8\\ y-3z=-8\\ x+y+z=-8\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}x=\frac{-8+y}{3}[/tex]

[tex]\begin{bmatrix}y-3z=-8\\ \frac{-8+y}{3}+y+z=-8\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}y-3z=-8\\ z+\frac{-8+4y}{3}=-8\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}y=-8+3z[/tex]

[tex]\begin{bmatrix}z+\frac{-8+4\left(-8+3z\right)}{3}=-8\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}\frac{15z-40}{3}=-8\end{bmatrix}[/tex]

[tex]\mathrm{For\:}y=-8+3z[/tex]

[tex]\mathrm{Substitute\:}z=\frac{16}{15}[/tex]

[tex]y=-8+3\cdot \frac{16}{15}[/tex]

[tex]y=-\frac{24}{5}[/tex]

[tex]\mathrm{For\:}x=\frac{-8+y}{3}[/tex]

[tex]\mathrm{Substitute\:}z=\frac{16}{15},\:y=-\frac{24}{5}[/tex]

[tex]x=\frac{-8-\frac{24}{5}}{3}=x=-\frac{64}{15}[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=-\frac{64}{15},\:z=\frac{16}{15},\:y=-\frac{24}{5}[/tex]

[tex]x=-\frac{64}{15}=-4.26666666667, z=\frac{16}{15}=1.06666666667,y=-\frac{24}{5}=-4.8[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[D] [tex]\begin{bmatrix}x-2y+z=0\\ 2y+9z=-20\\ x-y+z=0\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}y=\frac{-20-9z}{2}[/tex]

[tex]\begin{bmatrix}x-2\cdot \frac{-20-9z}{2}+z=0\\ x-\frac{-20-9z}{2}+z=0\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}x+20+10z=0\\ x+\frac{20+11z}{2}=0\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}x=-10z-20[/tex]

[tex]\begin{bmatrix}-10z-20+\frac{20+11z}{2}=0\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}\frac{20-9z}{2}-20=0\end{bmatrix}[/tex]

[tex]\mathrm{For\:}x=-10z-20[/tex]

[tex]\mathrm{Substitute\:}z=-\frac{20}{9}[/tex]

[tex]x=-10\left(-\frac{20}{9}\right)-20[/tex]

[tex]x=\frac{20}{9}[/tex]

[tex]\mathrm{For\:}y=\frac{-20-9z}{2}[/tex]

[tex]\mathrm{Substitute\:}x=\frac{20}{9},\:z=-\frac{20}{9}[/tex]

[tex]y=\frac{-20-9\left(-\frac{20}{9}\right)}{2}=0[/tex]

[tex]y=0[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=\frac{20}{9},\:z=-\frac{20}{9},\:y=0[/tex]

[tex]x=\frac{20}{9}=2.22222222222,\:z=-\frac{20}{9}-2.22222222222,\:y=0[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Kavinsky


Related Questions

Which expression shows 48 + 36 written as a product of two factors

Answers

Answer:

12(4+3)

Step-by-step explanation:

You need a 55% alcohol solution. On hand, you have a 50 mL of a 25% alcohol mixture. You also have 60% alcohol mixture. How much of the 60% mixture will you need to add to obtain the desired solution?

Answers

Answer:

  300 mL

Step-by-step explanation:

There is a simple diagrammatic way to solve mixture problems, illustrated in the attachment. In the left column are the available solution percentages. In the center is the percentage of the desired mix. In the column to the right of that are the diagonal differences between the desired value and the constituent values. Those differences represent the proportions of the constituents on the same horizontal line.

__

Here, that means 30 parts of 60% solution are needed for 5 parts of 25% solution. Since we have 50 mL of 25% solution, we can multiply these ratio values by 10 mL to find the quantities needed. That has been done here in the right-most column.

300 mL of 60% solution are needed to obtain the desired mixture.

__

Additional comment

If you want to write an equation, you can let x represent the quantity of high-concentration solution needed. Then the amount of alcohol in the mix is ...

  0.60x +0.25(50) = 0.55(x +50)

  0.05x = 0.30(50) . . . . . . . subtract 0.55x+0.25(50)

  x = 300 . . . . . . . . . . . . mL of 60% solution needed

Find the distance between the points (7,14) and (18,5).

Answers

Answer:

Exact distance = [tex]\sqrt{202}[/tex]

Approximate distance = 14.2127

==========================================================

Work Shown:

[tex](x_1,y_1) = (7,14) \text{ and } (x_2, y_2) = (18,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(7-18)^2 + (14-5)^2}\\\\d = \sqrt{(-11)^2 + (9)^2}\\\\d = \sqrt{121 + 81}\\\\d = \sqrt{202}\\\\d \approx 14.2127\\\\[/tex]

Note: I used the distance formula. Though you could plot the points, form a right triangle, and use the pythagorean theorem as an alternative route. The distance formula is effectively a modified version of the pythagorean theorem.

PLEASE HELP!!!!!
Abigail is studying for the school spelling bee. She already knows 204 words from the vocabulary list. Each day, she learns
24 additional words from the vocabulary list.
Which equation can be used to determine the total
number of words Abigail knows from the vocabulary list, y, over x days?
• A. y=24-204
•b y=24+204
• y=24(x+204)

Answers

Answer:

I think that it is y=24(x+204)

y= x24 + 204
okay so x is the number of days and you would multiply that by 24 because that’s how many words she learns each day and you would add 204 because that’s how many words she already knows. hope this helps

Skylar wanted to show the proportional relationship between the dollar value of the original investment, x, and its value after a 10% decrease, y. He creates the table of values shown. Does it model the relationship? Explain. Then, provide a correct equation for the relationship Skylar wants to model.

Answers

After checking the information of the table, it is to notice that the table fulfills the behavior of a direct relationship described by the linear equation y = 0.9 · x. #SPJ1

How to analyze a relationship between the two variables

Let be x and y the original investment and the value after applying the change, both in monetary units. A direct relationship is observed by following this model:

y = (1 + r/100) · x     (1)

Where r is change rate, in percentual units.

After checking the information of the table, it is to notice that the table fulfills the behavior of a direct relationship described by the linear equation y = 0.9 · x. #SPJ1

Remark

The table of the change in investment with respect to initial investment is missing and is now introduced below:

(x₁, y₁) = (75, 7.5), (x₂, y₂) = (100, 10), (x₃, y₃) = (200, 20), (x₄, y₄) = (300, 30), (x₅, y₅) = (400, 40)

To learn more on direct relationships, we kindly invite to check this: https://brainly.com/question/14293770 #SPJ1

a food server at harpers restaurant earns 5 dollars plus a 15% tip on the money made on each table he serves. Sam worked as a food server for six hours last friday and his tables earned $600. How much money did Sam make that day?

Answers

Answer:

The answer is given in the picture

Step-by-step explanation:

Do you remember me calista

I am alvena

Answer:

$70

Step-by-step explanation:

$5 x 6 hours = $30

$600 ÷ 15% = $40

$30 + $40 = $70

Do these for me pls

Answers

Answer:

1) C or B

2) J

3) C

4) J

Step-by-step explanation:

1) I am not sure but I think you start with the x so that is -5 then y which is 7 so y= 5/7x - 5 or y= 7/5x - 5

2) The graph always starts at the origin (0.0) that where the line should be put
3) 39 in + 78 in = 117 in

4)

2/3.5 = 0.57

4/7 = 0.57

6/9 = 0.57

7/12 = 0.57

Two consecutive numbers have a sum of 107. What is the larger of the two numbers?

Answers

Answer:

54

Step-by-step explanation:

54 + 53 = 107

54

[tex] \: \: \: \: \: \: \: \: \: \: \: \bold{54 + 53 = 107}[/tex]

Note : To solve a problem like this, all we have to do is find a number that matches the result, in this case it is [tex]\bold{54}[/tex] and [tex]\bold{53}[/tex]

[tex]\therefore[/tex] it gives us a result of [tex]\bold{107.}[/tex]

The radius of a circle is 7 m. Find its circumference in terms of \piπ

Answers

Answer:

I think its 43.98 or 44 I think its one of those

Step-by-step explanation:

C=2πr=2·π·7≈43.9823

=2π(7)=2⋅722⋅7=2⋅22=44 cm.


Please use cofunction or even odd identities to solve this problem!

50 points !

Answers

Answer:

  cot(θ) = -1.45

Step-by-step explanation:

The identity applicable to this problem is ...

  tan(π/2 -θ) = cot(θ)

__

Substituting for tan(π/2 -θ), you have the desired cotangent value:

  cot(θ) = -1.45

Using the recurrence relation s(1) = 2 and s(2)=3, s(k) =s(k-1)+2s(k-2)+6, find the fourth term

Answers

Recurrence functions are used to preedict the subsequent value in a sequence. The fourth term of the sequence based on the recurrence relation is 25

How to find the recurrence relation of a function?

Given the recurrence relations according to the question

s(1) = 2 and

s(2)=3

s(k) =s(k-1)+2s(k-2)+6

If s(1) = 2, hence;

s(3) =s(3-1)+2s(3-2)+6

s(3) = s2 + 2s1 + 6
s(3) = 3 + 2(2) + 6
s(3) = 13

Determine the fourth term:

s(4) =s(4-1)+2s(4-2)+6

s(4) = s3 + 2s2 + 6
s(4) = 13 + 2(3) + 6
s(4) = 25

Hence the fourth term of the sequence based on the recurrence relation is 25

Learn more on recurrence relation here: https://brainly.com/question/10636530

What is the surface area of this triangular pyramid? 3 m 3 m 3 m 3 m 2.6 m​

Answers

[tex]\stackrel{\textit{3 standing triangles}}{3\left[\cfrac{1}{2}(\stackrel{b}{3})(\stackrel{h}{3}) \right]}~~ + ~~\stackrel{\textit{triangular base}}{\cfrac{1}{2}(3)(2.6)}\implies 13.5~~ + ~~3.9\implies 23.4~m^2[/tex]

Which graph represents the function f(x) = 1/3|x|?​

Answers

Answer:

The answer is D.

Step-by-step explanation:

You pick a card at random.
1 2 3 4
567
What is P(not even)?
Write your answer as a fraction or whole number.

Answers

Answer:

p7

Step-by-step explanation:

If it includes 4 then 0.8, if not then 0.6.

Find the area of the shaded region

Answers

Answer:

Area of square - area of circle

Step-by-step explanation:

ALEKS Knowlege Check:

Evaluate the expressions. ​

Answers

Answer:

1, -1

Step-by-step explanation:

(-2/3)⁰

Anything that is raised to the power of 0 automatically becomes the value 1. Knowing this, apply the exponent.

(-2/3)⁰ = 1

-(7)⁰

Now using what we know, apply the exponent to the 7.

-(7)⁰ = -1

Notice that the negative is NOT inside the parenthesis and therefore does NOT get affected by the power.

13 yd
10 yd
8 yd
What is the area in square yards

Answers

Answer:520 yd

Step-by-step explanation:

multiply 13 x 10 x 8 then divide by 2


I think

QUICK HELP PLEASEEEE SOMEBODY PLEASE HELP

Answers

Answer:

Infinite answers is the correct answer

Step-by-step explanation:

Infinitely Many Solution Is the answer

A number is chosen at random from 1 to 50. Find the probability of selecting numbers with a last digit of 9.

Answers

Answer:

10%

Step-by-step explanation: There are 5 numbers between 5 and 50 that end in 9. 5 is 10 percent of 50. Pls give brainliest.

5 aplicaciones de notación científica en la vida cotidiana

Answers

Answer:

In scientific notation:

The first number in the mathematical equation is called the "coefficient." The coefficient must be greater than or equal to one and less than 10. For example to create the scientific notation for the number 256, the coefficient would be 2.56.

The second number in the equation is a power of 10, written as 10 with an exponent, like 102 which stands for 10 x 10.

Combining these two numbers would create this scientific notation equation for 256 - 2.56 x 102.

A negative exponent shows the decimal is moved that many places to the left and a positive exponent shows the decimal is moved that many places to the right.

Scientific Notation Examples

Here are examples of scientific notation:

1 = 100

10 = 1 x 10¹

100 = 1 x 10²

1000 = 1 x 10³

10000 = 1 x 104

100000 = 1 x 105

42,000,000 = 4.2 x 107

676,000,000,000 = 6.76 x 1011

0.1 = 1 x 10-1

0.01 = 1 x 10-2

0.001 = 1 x 10-3

0.0001 = 1 x 10-4

0.00001 = 1 x 10-5

0.00000078 = 7.8 x 10-7

0.000000000000000 = 3.56 x 10-13

Real Life Examples of Scientific Notation

Explore how scientific notation is used to express large numbers.

7 x 109 = Population of the world is around 7 billion written out as 7,000,000,000

1.08 x 109 = Approximate speed of light is 1080 million km per hour or 1,080,000,000 km per hour

2.4 x 105 = Distance from the Earth to the moon is 240 thousand miles or 240,000 miles

9.3 x 107 = Distance from the Earth to the sun is 93 million miles or 93,000,000 miles

3.99 x 1013 = Distance from the sun to the nearest star (Proxima Centauri) is 39,900,000,000,000 km

9.4605284 × 1015 = Distance light travels in a year is less than 9.5 trillion kilometers, or exactly 9,460,528,400,000,000 km

1.4 x 108 = Amount of water surface area on the Earth is 140 million square miles or 140,000,000 square miles

1.0 x 1014 = Approximate number of cells in the human body is 100 trillion or 100,000,000,000,000

1.332 x 10-3 = Density of oxygen is 1332 millionths g per cc or .001332 g per cc

2.4 x 10-3 = Diameter of a grain of sand is 24 ten-thousandths inch or .0024 inch

7.53 x 10-10 = Mass of a dust particle is 0.000000000753 kg

9.1093822 × 10-31 = Mass of an electron is 0.00000000000000000000000000000091093822 kg

4.0 x 10-7 = Length of the shortest wavelength of visible light (violet) is 0.0000004 meter

!!!!PLEASE HELP HAS TO BE DONE TODAY!!!!

What is the LCD of
45
015
03
05
8
15
-
ن
and 2/3/?

Answers

The answer would be B: 15.

NO LINKS!!

Determine if each statement is always, sometimes, or never true​

Answers

Answer:

sometimessometimesalways

Step-by-step explanation:

These questions can be answered by reference to the formulas for the volume of a cone, cylinder, and sphere.

__

Cone

  V = 1/3πr²h . . . volume depends on height as well as radius

Cones with the same radius will sometimes have the same volume. (When they have the same height.)

__

Cylinder

  V = πr²h . . . volume depends on height as well as radius

Cylinders with the same radius will sometimes have the same volume. (When they have the same height.)

__

Sphere

  V = 4/3πr³ . . . volume depends only on radius

Spheres with the same radius will always have the same volume.

SometimesSometimesAlways

Lets note the formulas first to make clear.

For cone

V=1/3πr²h

For cylinder

V=πr²h

For sphere

V=4/3πr³

We can see

for first two

the volume depends upon the height hence if they have same radius then their volume may or may not be same

For sphere

volume depends upon radius so if radius is same the volume is same

Nine of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 are to be put in two groups so that the sum of the numbers in each group is a multiple of four.

What is the largest number that could be left out?

Answers

Answer:

13,62,75,48,1092

Step-by-step explanation:

1+3=4, 6+2=8, 7+5=12, 4+8=12& 1+0+9+2=12.

Determine the equation for a circle in standard form with a radius of 18, and center (18,-18).

Answers

Answer:

(x-18)²+(y+18)²=18².

Step-by-step explanation:

1) the formula is: (x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - coordinates of the centre, r - the length of the radius;

2) according to the formula above:

(x-18)²+(y+18)²=18².

Find the area of the figure.

(50 POINTS On Last post)

Answers

Answer:

173,056,00

Step-by-step explanation:

f(x) = 2x + 3 and g(x) = 24 – X.

Solve the equation f(x) = g(14).

Answers

Answer:

x = 3.5

Step-by-step explanation:

f(x) = 2x + 3

g(x) = 24 – x

-> g(14) = 24 - 14

-> g(14) = 10

f(x) = g(14) (Given)

-> 2x + 3 = 10

-> 2x = 10 - 3

-> 2x = 7

-> x = 7/2

-> x = 3.5

Pls help me in this khan academy exercise

Answers

Answer:

x= 180° - (103°+33°)

x= 180° - 136°

x= 44°

help me pwesssssssssss

Answers

Answer:

858 Remainder 4

Step-by-step explanation:

A triangle has an angle that measures 44.3 and another that measures 52.4" What is the measure of the third angle​

Answers

83.3, because all the angles have to add up to 180
180-44.3-52.4= 83.3

The measure of the third angle, if the other angles measure 44.3 and 52.4, is 83. 3 degrees.

How to determine the angle?

To determine the angle, we need to know the following;

The sum of the interior angles of a triangle is 180 degreesAlternating angles are equalCorresponding angles are equalSupplementary angles sum up to 180 degreesComplementary angles sum up to 90 degrees

Then, from the information given, we have that;

A triangle has an angle that measures 44.3 and another that measures 52.4"

Then, we get; x + 52.4 + 44.3 = 180

collect the like terms'

x = 180 - 96.7

x = 83. 3 degrees

Learn about angles at: https://brainly.com/question/25716982

#SPJ2

The ceiling of Stacy's living room is a square that is 22 ft long on each side. Stacy knows the diagonal of the ceiling from corner to corner must be longer than 22 ft, but she doesn't know how long it is.

Solve for the length of the diagonal of Stacy's ceiling in two ways:

(a) Using the Pythagorean Theorem.

(b) Using trigonometry.

Round each answer to the nearest whole number and make sure to show all your work. (Hint: the answers should be the same!)

Answers

Answer:

I don't understand trig very well but I do get pythagorean theorem, which I can help with. Your final answer will end up being 31.

Step-by-step explanation:

First off the formula for pythagorean theorem is a^2 + b^2 = c^2

We know that C stands for the hypotenuse so we want to know what C is.

A and B are both 22 so our equation turns into 22^2 + 22^2 = c^2

22 squared is 484 which leads to 484 + 484 = c^2

484 + 484 = 968

968 is our C^2 but we still need to find the square root

The square root of 968 is 31.11269837... and a whole lot of other numbers

You round that out to 31 and get the length of your diagonal

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