How to solve the equation

The solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

The system of equations is given as

2x - y + 2z = -6

-3y + z = -2

2x - 3z = -4

Subtract 2x - 3z = -4 from 2x - y + 2z = -6

This is represented as

(2x - y + 2z = -6) - (2x - 3z = -4)

This gives

- y + 5z = -2

Multiply - y + 5z = -2 by 3

-3y + 15z = -6

Subtract -3y + 15z = -6 from -3y + z = -2

This is represented as

(-3y + z = -2) - (-3y + 15z = -6)

This gives

-14z = 4

Divide by -14

z = -2/7

Substitute z = -2/7 in - y + 5z = -2

- y - 5 * 2/7 = -2

This gives

- y - 10/7 = -2

Rewrite as:

y = 2 - 10/7

Evaluate

y = 4/7

Substitute z = -2/7 in 2x - 3z = -4

2x - 3 * 4/7 = -4

This gives

2x - 12/7 = -4

So, we have:

2x = 12/7 - 4

Evaluate

2x = -16/7

Divide by 2

x = -8/7

Hence, the solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

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2/5 get dumps out of the box from 4 and 7/10 pounds of candy then weight of the candy left in the box  is 2 and [tex]\frac{41}{50}[/tex] pounds.

As given,

Total weight of the candy =  4 and 7/10 pounds =  [tex]\frac{47}{10\\}[/tex] pounds

pound is the  imperial unit of weight generally written as lb.

one pound = 0.4535 kilograms = 453.5 gm.

[tex]\frac{2}{5}[/tex] th of candy is dumps out of the box.

1- [tex]\frac{2}{5}[/tex] = [tex]\frac{3}{5}[/tex] th of the total candy is left in the box.

weight of the candy left in the box = [tex]\frac{3}{5}[/tex] * [tex]\frac{47}{10}[/tex] = [tex]\frac{141}{50}[/tex] pounds.

now 141= 50*2 + 41

[tex]\frac{141}{50}[/tex] pound = 2 and [tex]\frac{41}{50}[/tex] pounds

Hence, weight of the candy left in the box= 2 and [tex]\frac{41}{50}[/tex] pounds.

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Using the shell method, the volume is

[tex]\displaystyle 2\pi \int_0^1 (2-x) \cdot 8x^3 \, dx = 16\pi \int_0^1 (2x^3 - x^4) \, dx[/tex]

Each cylindrical shell has radius [tex]2-x[/tex] (the horizontal distance from the axis of revolution to the curve [tex]y=8x^3[/tex]); has height [tex]8x^3[/tex] (the vertical distance between a point on the [tex]x[/tex]-axis in [tex]0\le x\le1[/tex] and the curve [tex]y=8x^3[/tex]).

Compute the integral.

[tex]\displaystyle 16 \pi \int_0^1 (2x^3 - x^4) \, dx = 16\pi \left(\frac{x^4}2 - \frac{x^5}5\right) \bigg|_{x=0}^{x=1} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 16\pi \left(\frac12 - \frac15\right) \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{24}5\pi = \boxed{4.8\pi}[/tex]

Answer:

Step-by-step explanation:

Let x be the sweater

Let y be the shirt

Equation1:    x+4y=47

Equation2:    4x+3y=84

Now solve for x in the first equation:

x+4y=47

x=47-4y

Now that we've solved for x, substitute the value for x which is 47-4y into Equation2 as follows:

4x+3y=84

4(47-4y)+3y= 84

188-16y+3y= 84

188-13y= 84

-13y= 84-188

-13y= -104

y= -104/-13

y= 8

Now plug in the value for y which is 8 into Equation 1 and solve for x:

x+4y=47

x+4(8)=47

x+32=47

x=47-32

x=15

You can perform a check by plugging in the x and y values into equations 1 and 2 which should yield true statements.

The answer is: 1 sweater costs $15 and 1 shirt costs $8

Answer:

Step-by-step explanation:

Based on the fact that the widow got an exemption on homestead tax, the amount that the owner would pay in property taxes is $3,471.20.

The widow received a homestead tax exemption of $25,000 on the property.

The amount to be paid in property tax is:

= (8.8 + 9.3 + 6.5) / 1,000 x (185,000 - 25,000)

= 21.7/1,000 x 160,000

= $3,471.20

In conclusion, the property tax to be paid is $3,471.20.

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In linear equation , $8  the amount of money (cost) to play laser tag.

What are a definition and an example of a linear equation?

let x = number of games, let y = cost of  tag

then        Total cost = x•$3 + y

In this case, TC = 3•$2 + $2

TC = $8

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Colin paid the loan at a ten percent annual interest rate.

Simple interest is the form of interest calculation in which the principal amount remains the same for the entire duration for which the loan is taken.

It is also assumed that Colin will repay $35 per month for the next two years.

We must calculate a simple interest rate on Colin's borrowings.

As a result, Colin's total payment to his parents for two years is $35.

We are required to find simple interest rate on Colin's borrowings

Therefore, total amount paid by Colin to his parents= 35$ for 2 years

        =35*24=840

The amount paid by Colin is principal + interest

Thus, the simple interest amount= 840-700=140$

We know that the simple interest formula is principal*rate*time/100.

We know that the simple interest is 140, the principal is 700, the time is two years, and we need to find the rate of interest.

SI= P*R*T/100

140= 700*R*2/100

140/7*2=R

R=140/14=10

Therefore, The Rate of interest on which Colin paid the loan is 10 per cent per annum

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[tex]D=\frac{1}{5}kf \\ \\ 5D=kf \\ \\ \boxed{f=\frac{5D}{k}}[/tex]

Answer:

a

Step-bye-step explanation:

that's the correct answer

The number of black-and-white is 60 and the number of color copies is 8.

Let b = the number of black-and-white.

Let c = the number of color copies.

The equation will be:

b + c = 68

0.08b + 0.15c = 6

Multiply equation I by 0.08

Multiply equation ii by 1.

0.08c + 0.08c = 5.44

0.08b + 0.15c = 6

Subtract

0.07c = 0.56

c = 0.56/0.07

c = 8

Since b + c =68

b= 68 - 8 = 60

Therefore, the number of black-and-white is 60 and the number of color copies is 8.

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The Perimeter of rectangle 3cm 5cm is 16 cm.

In geometry, a rectangle is a plane figure of four sides having four angles of 90 degree. A rectangle has different length and breadth.

Some important formulas for rectangle :

Perimeter is define as the distance around all the edges of a shape. In case of rectangle perimeter is the distance of all 4 edges i.e. 2 lengths and 2 breadth .

Thus , perimeter of rectangle = ( 2 × length ) + (2 × breadth)

                                                 = 2 ( length + breadth )

In the given question,

length of rectangle =  3cm

breadth of rectangle = 5cm

therefore, perimeter of rectangle = 2(3+5) = 16cm

Hence, The Perimeter of rectangle is 16 cm.

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Thus standard daviation is x~N(4400,6500)

Let X denote the salaries for all the teachers in a particular alimentary school.

As per the generation X is commonly distinguished with a mean of u=44,000

standard daviation of €=$6500

The answer is x~N(44000,6500)

Since the 10 teachers are survived randomly from the district

The site of n=10

Variable€x present salary of all 10 teachers in a particular alimentary sel.

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Answer:

Area = 192.5 ft.²

Step-by-step explanation:

By splitting the shape in 2, we can find the area much simpler.

Starting with the parallelogram (on the left), the area formula is A = b × h.

b (base) = 11 ft.

h (height) = 7 ft.

A (area) = (11 ft.)(7 ft.)

A = 77 ft.² (save this for later)

Then, the trapezoid's (on the right) area formula is A = [(a + b) ÷ 2] × h.

a (first base) = 8 ft.

b (second base) = (20 - 7) = 13 ft.

h (height) = 11 ft.

A = [(8 ft. + 13 ft.) ÷ 2] × 11 ft.

A = [(21 ft.) ÷ 2] × 11 ft.

A = (10.5 ft.) × 11 ft.

A = 115.5 ft.²

Now, bringing back the first area, we can add them together to find the total:

A = 77 ft.² + 115.5 ft.²

A = 192.5 ft.²

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Daunte is incorrect. After 4 weeks, the price would be 68.5 percent off.

An exponential function is a mathematical function that has the form : f(x) = a^x

Where:

An exponential function indicates that the quantity is either increasing at a faster rate or reducing at a faster rate. This is true because an exponential increase or decrease is faster than a linear increase or decrease. In a linear increase or decrease, the function is either increasing or decreasing at a constant value.

The price of the video games would reduce by 25% of the previous weeks' price. Thus, the function that would represent this is an exponential function.

The form of the exponential equation would be:

Price after 4 weeks = Initial price x (1 - percentage decrease)^number of years

Let's assume that the initial price is 100

100 x (1 - 0.25)^4

100 x (0.75)^4 = 31.64

The total percentage decrease in the price of the good: (current price initial price) - 1

(31.64 / 100) - 1 = 0.684 = 68.4%

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The real number that should be subtracted from - 5 to get 0 is -5 (option b).

A real number is a quantity that can be written as an infinite decimal expansion. A real number is made up of both rational numbers and irrational numbers.

Rational numbers are numbers that can be expressed as a fraction of two integers. An example is 5, -5.  Irrational numbers cannot be expressed as a fraction of two integers. An example is 22/7, 1/3.

In mathematics, the following rules exist:

-5 - (-5)

= -5 + 5

= 0

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Given the given task content, the answer to the sums are:

The subtraction of numbers is difference between two or more numbers

(a) -237 + 359

= 122

(b) 87 + (-163)

= 87 - 163

= -76

(c) - 35.7 + 22.9

= -12.8

(d) 8.79 + 6.41

= 15.20

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Answer:

translation

all the points are in the same orientation, and all the lengths are the same.

all that has changed are the coordinates.

Answer:

36.3 seconds per lap

Step-by-step explanation:

200m in 2.42  if each lap = 50m

50m = 36.3 seconds

Answer:

5y + 12x

Step-by-step explanation:

Let's simplify step-by-step.

5y+3x+9x

Combine Like Terms:

=5y+3x+9x

=(3x+9x)+(5y)

=12x+5y

Answer:

5y + 12x

Step-by-step explanation

Simplify step-by-step.

5y+3x+9x

Combine like terms:

=5y+3x+9x

=(3x+9x)+(5y)

=12x+5y

Answer:

6%

Step-by-step explanation:

First, let's break this down:

60% of arenas sold out

Out of those arenas that did NOT sell out

We want to know the joint relative frequency of area that were sold out AND NOT on the previous tour schedule, therefore all the information about areas that did NOT sell out is irrelevant.

Because 90% of the areas that were sold out had been on the previous tour, 10% had NOT been on the previous tour.

Therefore, considering all the arenas, 10% of 60% of the arenas were sold out and not on the previous tour.

Let x equal the total number of arenas:

[tex](.10)(.60)x=0.06x[/tex]

Convert to percent

6%

Therefore, the joint relative frequency of sold out arenas that were not on the previous tour is 6%.

Trent writes 10×6=60, then in multiplication equation 10 represents the number of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the total numbers of muffins.

Given,

Trent writes 10×6=60,

Here,

10 represents the number of muffin boxes

6 represents the numbers of muffins in each box

60 represents the total numbers of muffins

Hence, Trent writes 10×6=60, then in the multiplication equation 10 represents the number of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the total numbers of muffins.

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Answer:

see attached

Step-by-step explanation:

The vector difference u -v can be represented on a vector diagram by the sum u +(-v), where -v is a vector the same length as v, but in the opposite direction.

__

Answer: $15.75

Step-by-step explanation:

$78.75/5 hr=$15.75/hr

Answer:

He earns $15.75 an hour

Step-by-step explanation:

You have to divide $78.75 by 5 to get the unit rate(earnings for 1 hour).

The number of gallons that must be needed to antifreeze 50% solution is 105.

Given that 50% antifreeze solution must be mixed with 70 gallons of Strength 25% antifreeze to get a mixture that is 40% antifreeze.

The six-step method involves a few steps that need to perform. These are defining the problem, determining the root cause, finding the alternative solution to solve the problem, selecting the solution, implementing the solution, and finally evaluating the outcome.

Let's consider x be the number of gallons of a 50% antifreeze solution.

As we know we need to make an antifreeze solution by adding the given quantities.

Hence,

x×50%+70×25%=40%×(x+70)

x×0.5+70×0.25=0.4×(x+70)

Now, we will multiply the numbers, we get

0.5x+17.5=0.4(x+70)

Now, we will multiply both sides by 10, we get

0.5x×10+17.5×10=0.4(x+70)×10

5x+175=4(x+70)

5x+175=4x+280

Further, we will subtract 175 from both sides, we get

5x+175-175=4x+280-175

5x=4x+105

Furthermore we will subtract 4x from both sides, we get

5x-4x=4x+105-4x

x=105

Hence, 105 gallons of 50% antifreeze solution must be needed.

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