Cari knows that it is a 45 mile drive from her house to the airport. She also knows that it is a 45 mile drive from her house to her grandparents house in the woods. How many miles is it directly from the airport to her grandparents house in the woods? Show your work.

5. Vertex: (2, 2)

Dοmain: All real numbers

Axis οf symmetry: x = 2

Increasing οn: (-∞, 2)

Decreasing οn: (2, ∞)

A quadratic functiοn is a pοlynοmial functiοn οf degree 2, where the highest pοwer οf the variable is 2. It has a parabοlic graph and is cοmmοnly used tο mοdel real-wοrld phenοmena.

5. Vertex: (2, 2)

Dοmain: All real numbers

Axis οf symmetry: x = 2

Increasing οn: (-∞, 2)

Decreasing οn: (2, ∞)

7. Vertex: (2, 3)

Dοmain: All real numbers

Axis οf symmetry: x = 2

Increasing οn: (-∞, 2)

Decreasing οn: (2, ∞)

Range: y ≥ 3

6.Vertex: (-2, -4)

Vertical shift: -4 units

Hοrizοntal shift: -2 units

Width: Cοmpressed hοrizοntally by a factοr οf 1/3

Reflected: Nο

8. Vertex: (-2, -2)

Vertical shift: -2 units

Hοrizοntal shift: -2 units

Width: Stretched by a factοr οf 3 in the vertical

Reflected: Nο

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The brick weighs 3.4 kilograms.

Quantities are values that can be measured or counted. They are typically represented by numerical values and units of measurement.

Let's assume that the weight of each brick is the same. Let's also denote the weight of each brick by "w" (in kilograms).

On one side of the scale, we have 9 bricks and 5 kilograms. So the total weight on this side is:

Total weight = (9 x w) + 5

On the other side of the scale, we have 4 bricks and 22 kilograms. So the total weight on this side is:

Total weight = (4 x w) + 22

Since the bricks on the scale are in balance, the total weight on both sides must be equal. Therefore, we can set the two expressions for total weight equal to each other and solve for w:

(9 x w) + 5 = (4 x w) + 22

Expanding and simplifying the equation, we get:

5 x w = 17

Therefore, the weight of each brick is:

w = 17 / 5

w = 3.4 kilograms

So each brick weighs 3.4 kilograms.

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The solution to the system of equations is (1,1), which is the point where the two lines intersect on the coordinate axes.

An equation is a mathematical statement that shows the equality between two expressions. It contains one or more variables, which are usually represented by letters, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to model and solve various real-world problems in fields such as physics, engineering, and finance. The goal in solving an equation is to find the value of the variable that satisfies the equation. This can be done by applying mathematical operations to both sides of the equation in a systematic way until the variable is isolated on one side.

To solve the system of equations graphed on the coordinate axes, we need to find the point at which the two lines intersect. This point represents the solution to the system of equations.

First, we can set the two equations equal to each other, since they both equal y:

2x-1 = -x+2

Adding x to both sides, we get:

3x-1 = 2

Adding 1 to both sides, we get:

3x = 3

Dividing both sides by 3, we get:

x = 1

Now we can substitute x=1 into either equation to find y:

y = 2(1) - 1

y = 1

Therefore, the solution to the system of equations is (1,1), which is the point where the two lines intersect on the coordinate axes.

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Answer:

[tex]19h + 33t[/tex]
[tex]7h + 18t +12h + 15t[/tex]

Step-by-step explanation:

The two expressions above are equal and both represent the total spent on hoodies and t-shirts.

[tex]25(h+t) + 27(h + t)[/tex] is incorrect because this implies that the cost of t-shirts and hoodies are interchangeable. The choice in the bottom right is incorrect also because it is equivalent to the aforementioned expression.

The 95% confidence interval for tthe population mean, μ of all venture-capital investments in the fiber optics business sector is equals to the 4.472 ≤ μ ≤ 7.990 that is ( 4.472, 7.990).

We have a random sample of venture capital investments in the fiber optics business sector.

Sample size, n = 10

Standard deviations, σ = $2.84 million

Sum of data, ∑xᵢ = $62.32 million

Confidence interval, CI = 95% = 0.95

We have to determine the 95% confidence interval for the mean amount.

Sample mean is defined as the sum of observations divided by number of observations. Mathematically, X-bar

= ∑xᵢ /n

= 62.32/10 = 6.232

Now, using the Z distribution table, the critical value at 0.05 significance level for two tailed test is = Z₀.₀₅/₂ = Z₀.₀₂₅

= 1.96

So, 95% confidence interval for the population mean is written as

CI₀.₉₅ = X-bar - Z(σ/√n ) ≤ μ ≤ X-bar + Z(σ/√n)

= 6.232 - 1.96(2.84/√10) ≤ μ ≤ 6.232 +

1.96(2.84/√10)

= 6.232 - 1.760 ≤ μ ≤ 6.232 + 1.760

= 4.472 ≤ μ ≤ 7.990

Hence, required interval is ( 4.472, 7.990).

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Area of the given trapezoid is 1.8m²

A trapezoid is a polygon having four sides, two of which are parallel and two of which are not. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively. The height or altitude of the trapezoid is defined as the distance between the bases.

The formula, which may be used to determine a trapezoid's area,

[tex]A= \frac{a+b}{2}h[/tex]

where, a and b are the lengths of the two bases and h is the height between two bases.

Given in the trapezoid figure, a= 2, b= 0.9, h is the base upper triangle.

We use the following trigonometric relationship to find the base of the upper triangle,

Apply sine rule in upper triangle with connecting line h.

Sin 45° =  [tex]\frac{h}{1.8}[/tex]

h = 1.8 × Sin 45°

h = 1.8 × 0.707

h = 1.273m

Then, the area of trapezoid:

[tex]A= \frac{a+b}{2}h= \frac{2+0.9}{2}*h[/tex]

[tex]A= \frac{2.9}{2}*1.273[/tex]

A = 1.845m²

Therefore, the area of the trapezoid to the nearest tenth is 1.8m²

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The probability of proper functioning of the sensors till the second scheduled inspection is `0.564`.

Given that the time length (in months) of uninterrupted functioning of soil moisture measuring sensors until failure follows a distribution, `1/7e−x/7`.The sensors are inspected at every 2 months.(a) Probability that the sensors need to be replaced at the first inspection= Probability that the sensors fail at the first inspection= Probability that the sensors fail before first inspection= Probability that the sensor functioned well up to the first inspection=  `F(2) = 1-e^(-2/7)` (Using the given exponential distribution)Therefore, the probability that the sensors need to be replaced at the first inspection is `0.226`. (Approximately, 0.23)(b) The probability of proper functioning of the sensors till the second scheduled inspection is the probability that the sensors do not fail in the first two months. That is, `P(t≥2)` = `1-P(t<2)`= `1-F(2)` = `1-(1-e^(-2/7))` = `0.564`.Therefore, the probability of proper functioning of the sensors till the second scheduled inspection is `0.564`.

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As per the unitary method, Aysha will spend Dh45.45 on souvenirs if she spends Dh100 on games, using the same ratios as on her last trip to the shopping festival.

Now, let's use the unitary method to solve the problem at hand. We know that Aysha wants to spend money using the same ratios as on her last trip to the shopping festival. So, let's find out the ratio of the amount she spent on games to the total amount she spent on all three items (snacks, games, and souvenirs) on her last trip:

Amount spent on games = Dh25

Total amount spent on all three items = Dh20 + Dh25 + Dh10 = Dh55

So, the ratio of the amount spent on games to the total amount spent on all three items is:

Dh25/Dh55

Now, we know that Aysha wants to spend Dh100 on games this time. Let's use the unitary method to find out how much she will spend on souvenirs, given the ratio we just found.

If Dh25 is spent on games, then the total amount spent on all three items will be:

(Dh25/Dh55) * Total amount spent

And we know that the total amount spent is Dh100 (the amount Aysha wants to spend on games). So, substituting this value, we get:

(Dh25/Dh55) x Dh100

Simplifying this expression, we get:

Dh45.45

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Answer:0.833333

Step-by-step explanation:

Answer:

0.08333

Step-by-step explanation:

pls mrk me brainliest

Answer:

Step-by-step explanation:

What side is opposite from angle B? AC

What side is adjacent to angle B but is not the hypotenuse? BC

What side is hypotenuse? AB

The solution to the system of equations is: x = -1 and y = -2.

A system of equations is the set of two or more equations with the same variables.

An example is: 2x + 3y = 10 and 4x - 5y = -8

To solve the system of equations:

-4x + 3y = -2

y = x - 1

We can substitute the second equation into the first to eliminate y:

-4x + 3(x - 1) = -2

Simplifying and solving for x:

-4x + 3x - 3 = -2

-x = 1

x = -1

Now that we know x = -1, we can use the second equation to find y:

y = -1 - 1

y = -2

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To calculate the proportion of Dave's wages spent on rent, divide the amount of rent by his monthly earnings and multiply by 100 to obtain the percentage Rent as a percentage of earnings = (Rent / Earnings) x 100%.

When we substitute the provided values, we get: Rent as a percentage of wages = (840 / 2300) x 100% = 36.5% As a result, to the closest hundredth of a percent, Dave spends about 36.5% of his salary on rent. This indicates that rent accounts for around 36.5% of Dave's monthly income. This proportion might provide us with information about Dave's financial status. Financial experts often advise consumers to spend no more than 30% of their income on housing expenditures, including rent and utilities. In Dave's situation, his rent is somewhat higher than the recommended amount. This might signal that he is struggling to make ends meet or that he should look into more cheap housing possibilities. If David can easily pay his existing rent, this percentage may not be a reason for concern.

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The volume of soup in the can at first is 546 millilitres.

Angela drank 390 millilitres of soup from a can of the soup. 2 / 7 of the soup was left in the can after drinking the soup.

Therefore, the amount of soup in the can at first can be calculated as follows:

let

x = amount of soup initially in the can

Therefore, using equation let's find the volume of soup initially in the can.

2 / 7 x + 390 = x

390 = x - 2 / 7 x

390 =  7x - 2x / 7

390 = 5x / 7

cross multiply

5x = 390 × 7

5x = 2730

divide both sides by 5

x = 2730 / 5

x = 546

Therefore,

volume of soup in the can = 546 millilitres

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Answer:

3/2

Step-by-step explanation:

4 1/3 = 13/3

6 1/2 = 13/2

fraction x 13/3 = 13/2

=> fraction = 13/2 / 13/3 = 13/2 x 3/13 = 3/2

Answer:

Step-by-step explanation:

-14.76: Rational

-sqrt(64): 64 is a perfect square so it is rational

1.4444444… rational numbers repeat their decimal digits at one point or another, so this is rational

pi is irrational, so 19pi is irrational.

sqrt(2)*sqrt(2) is rational, but not 2sqrt(2). Irrational.

Glenn has 1/20 of the granola bar left.

How to find?

If Glenn has 2/5 of a granola bar and eats 7/8 of it, we need to find out how much is left.

First, we need to find out how much Glenn ate. To do this, we can multiply the fraction of the granola bar that Glenn had (2/5) by the fraction that he ate (7/8):

2/5 × 7/8 = (27)/(58) = 14/40

Simplifying this fraction, we get:

14/40 = 7/20

So, Glenn ate 7/20 of the granola bar.

To find out how much is left, we can subtract the fraction that he ate from the fraction that he had:

2/5 - 7/20

To subtract these fractions, we need to find a common denominator. The least common multiple of 5 and 20 is 20, so we can convert both fractions to have a denominator of 20:

2/5 = 8/20

7/20 = 7/20

Now we can subtract the fractions:

8/20 - 7/20 = 1/20

So, Glenn has 1/20 of the granola bar left.

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The National League variance is 0.00020 and the standard deviation is 0.0141 while the American League variance is 0.000191 and the standard deviation is 0.0138.

According to question, the team batting averages for Major League Baseball in a certain year are represented below. We have to find the variance and standard deviation for each league. Given below is the table of team batting averages in National League and American League.

National League   American League
 .240                .237
 .242                .244
 .240                .251
 .247                .233
 .256                .243
 .249                .248
 .256                .238
 .240                .241
 .243                .250
 .237                .238

We know that,

variance = (1/N)* Σ(xi - µ)²
Standard deviation = √variance

National League:
The mean of National League, µ = (0.240 + 0.242 + 0.240 + 0.247 + 0.256 + 0.249 + 0.256 + 0.240 + 0.243 + 0.237)/10 = 2.443/10 = 0.2443.
Substitute the values in the formula, variance = (1/10)* Σ(xi - µ)² = (1/10)* [ (0.240 - 0.2443)² + (0.242 - 0.2443)² + (0.240 - 0.2443)² + (0.247 - 0.2443)² + (0.256 - 0.2443)² + (0.249 - 0.2443)² + (0.256 - 0.2443)² + (0.240 - 0.2443)² + (0.243 - 0.2443)² + (0.237 - 0.2443)² ]= 0.00019749
Standard deviation = √variance = √0.00019749 = 0.01405
The National League variance is 0.00020 and the standard deviation is 0.0141

American League:
The mean of American League, µ = (0.237 + 0.244 + 0.251 + 0.233 + 0.243 + 0.248 + 0.238 + 0.241 + 0.250 + 0.238)/10 = 2.423/10 = 0.2423
Substitute the values in the formula, variance = (1/10)* Σ(xi - µ)² = (1/10)* [ (0.237 - 0.2423)² + (0.244 - 0.2423)² + (0.251 - 0.2423)² + (0.233 - 0.2423)² + (0.243 - 0.2423)² + (0.248 - 0.2423)² + (0.238 - 0.2423)² + (0.241 - 0.2423)² + (0.250 - 0.2423)² + (0.238 - 0.2423)² ]= 0.00019119
Standard deviation = √variance = √0.00019119 = 0.01383

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The units for base area calculations are squared units and the units for volume calculations are cubed units. This is because the area and volume calculations require different equations and different units of measurement.

The units on your base area calculations should be squared units, such as square meters, square centimeters, square inches, or square feet. This is because the area of a two dimensional shape is the amount of space occupied by the shape and is calculated by taking the length of the base and multiplying it by the width of the base. For example, if a rectangle has a length of 5 meters and a width of 3 meters, the area of the rectangle would be 5 x 3 = 15 square meters.

The units on your volume calculations should be cubed units, such as cubic meters, cubic centimeters, cubic inches, or cubic feet. This is because the volume of a three dimensional shape is the amount of space occupied by the shape and is calculated by taking the area of the base and multiplying it by the height of the shape. For example, if a cube has an area of 15 square meters and a height of 4 meters, the volume of the cube would be 15 x 4 = 60 cubic meters.

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If the price of the mobile with 13% VAT is Rs 28,476, the discount percent is 10%.

The discount is the difference between the marked price and the selling price.

Discounts are depicted in percentages to show the rates at which the discounts are given.

The selling price of the mobile set with 13% VAT = Rs. 28,476

The selling price of the mobile set without VAT = Rs. 25,200 (Rs. 28,476/1.13)

The difference (discount) between the marked price and the selling price = Rs. 2,800

The marked price = Rs. 28,000 (Rs. 25,200 + Rs. 2,800)

The discount percent given = 10% (Rs. 2,800/Rs. 28,000 x 100)

Thus, we can conclude that the discount percent is 10%.

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We can find the slope between the first two points (-2, 2) and (0, 1):

m = (1 - 2) / (0 - (-2))

m = -1 / 2

Now that we have the slope (m), we can use the point-slope form of the equation of a line to find the y-intercept (b). Using the point (0, 1):

y - y1 = m(x - x1)

y - 1 = (-1/2)(x - 0)

y = (-1/2)x + 1

Therefore, the equation of the line in slope-intercept form that passes through the given points is:

y = (-1/2)x + 1

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We can use the rule for h(x) to calculate the output values of the function for each given input value of x, which allows us to complete the function table mathematically.

In mathematics, a function is a rule or mapping that assigns a unique output value for every input value in a specified set

To complete the function table mathematically, we need to use the given rule for the function h(x) = 5x - 1 and substitute the given values of x to find the corresponding values of h(x).

For example, when x = -5, we can find the corresponding value of h(x) as follows:

h(-5) = 5(-5) - 1

= -26

Similarly, we can substitute x = -4, 1, 2, and 3 into the rule for h(x) to find the corresponding values of h(x) for each input value of x. This gives us the completed function table:

x        h(x)

-5      -26

-4      -21

1        4

2       9

3       14

Therefore, we can use the rule for h(x) to calculate the output values of the function for each given input value of x, which allows us to complete the function table mathematically.

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The answer of the question based on the inequality the answer is  Andy can rent up to 20 DVDs in a month and spend no more than $25.

An inequality equation is mathematical statement that compares the two values or expressions using inequality symbol such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).

The total cost, C, for renting n DVDs in a month is given by:

C = 10 + 0.75n

The question tells us that Andy wants to spend no more than $25 per month on DVD rentals. Therefore, we can write an inequality:

C ≤ 25

Substituting the expression for C from above, we get:

10 + 0.75n ≤ 25

Simplifying the inequality, we can subtract 10 from both sides:

0.75n ≤ 15

Finally, we can divide both sides by 0.75:

n ≤ 20

Therefore, the inequality that represents how many DVDs Andy can rent in one month that satisfies the condition of spending no more than $25 per month is:

n ≤ 20

So, Andy can rent up to 20 DVDs in a month and spend no more than $25.

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a. To find the z score for a given confidence level, you can use the `qnorm()` function in R. The `qnorm()` function takes a probability as an argument and returns the corresponding z score. To find the z score for a 95% confidence level, you can use `qnorm(1-.025)`:

```R
z <- qnorm(1-.025)
```

This will give you the z score for a 95% confidence level, which is approximately 1.96.

b. To create a vector `x` with 50 numbers from a normal distribution with mean 30 and standard deviation 2, you can use the `rnorm()` function:

```R
x <- rnorm(50, mean = 30, sd = 2)
```

To calculate the confidence interval for this data, you can use the formula:

```R
CI <- mean(x) + c(-1, 1) * z * sd(x) / sqrt(length(x))
```

This will give you the lower and upper bounds of the 95% confidence interval. You can check whether the interval covers the true mean of 30 by seeing if 30 is between the lower and upper bounds:

```R
lower <- CI[1]
upper <- CI[2]
if (lower <= 30 && upper >= 30) {
 print("The interval covers the true mean.")
} else {
 print("The interval does not cover the true mean.")
}
```

c. To repeat the above experiment 200 times and calculate the percentage of intervals that cover the true mean, you can use a for loop:

```R
count <- 0
for (i in 1:200) {
 x <- rnorm(50, mean = 30, sd = 2)
 CI <- mean(x) + c(-1, 1) * z * sd(x) / sqrt(length(x))
 lower <- CI[1]
 upper <- CI[2]
 if (lower <= 30 && upper >= 30) {
   count <- count + 1
 }
}
percentage <- count / 200
```

This will give you the percentage of intervals that cover the true mean.

d. To write a function that takes a confidence level as an input and returns the percentage of intervals that cover the true mean, you can use the following code:

```R
calculate_percentage <- function(CL) {
 z <- qnorm(1-(1-CL)/2)
 count <- 0
 for (i in 1:200) {
   x <- rnorm(50, mean = 30, sd = 2)
   CI <- mean(x) + c(-1, 1) * z * sd(x) / sqrt(length(x))
   lower <- CI[1]
   upper <- CI[2]
   if (lower <= 30 && upper >= 30) {
     count <- count + 1
   }
 }
 percentage <- count / 200
 return(percentage)
}
```

You can then use this function to create a 5 by 2 matrix with one column showing the theoretical CL and the other showing the empirical coverage probability:

```R
CL <- c(.8, .85, .9, .95, .99)
percentage <- sapply(CL, calculate_percentage)
matrix <- cbind(CL, percentage)
```

This will give you a matrix with the theoretical CL in the first column and the empirical coverage probability in the second column.

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The combination of weights listed above would balance a mass of 45 grams on the balance scale.

A instrument used to determine an object's mass is a balancing scale. It is made out of a beam suspended from a fixed point, with two pans or trays hanging from either end. The beam is balanced when the mass of the objects on one tray equals the mass of the objects on the other tray. The principle of moments, according to which, when the beam is in equilibrium, the moment of force on one side of the balance is equal to the moment of force on the other, governs how a balancing scale functions.

Given that, Rosa can balance a mass of 45 grams using the given combinations.

Thus, total weight on the two sides are:

Left side: 32g + 6g + 6g + 1g = 45g

Right side: 8g + 8g + 2g + 2g = 20g

Hence, the combination of weights listed above would balance a mass of 45 grams on the balance scale.

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Answer:

6.8 I think

Step-by-step explanation:

The x-intercepts for the equation y=0 is -1 and 14 respectively

Intercepts in mathematics are points where a graph crosses the x and/or y axes, or n x-intercept is where the graph crosses (or touches) the x-axis; a y-intercept is where the graph crosses (or touches) the y-axis

The given equation is 2(x+1)(x-14)

Opening the bracket to have

x²-14x+x-14 = 0

Solving the quadratic equation to have

2[x²-13x+14] =0

2x-26x+28 = 0

Dividing by 2 to have

x²-13x-14 =0

(x²-14x)+(x -14) =0

x(x-14) + 1(x-14)

x+1 = 0 and x-14 = 0

there values of x are

x= -1 and x = 14

The intercept of the equation is at x=-1 and x=14

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Answer:

-10

Step-by-step explanation:

BODMAS

Brackets

Of

Division

Multiplication

Addition

Subtraction

●When simplifying an equation follow the above order.

•Since division comes before subtraction, first divide -24 by -8 to get 3

•Then subtract 13 from 3 to give you -10.

Answer:

5'6 and 5'0

Step-by-step explanation:

Put the graph in order of dots

4'11- 1

5'1- 1

5'3- 1

5'6- 1

5'0- 2

5'2- 2

5'5- 2

5'4- 5

The middle values are 5'6 and 5'0, so that should be the answer.

1) The surface area of the figure is of 72 square units.

2) Removing the top two cubes, the surface area of the figure would be of 60 square units.

The surface area of a cube of side length a is given by the equation presented as follows:

S = 6a².

For this problem, we have that the parameters are given as follows:

Hence the surface area of the figure is given as follows:

S = 12 x 6 x 1

S = 72 square units.

Removing the top two cubes, the surface area of the figure would be given as follows:

S = (12 - 2) x 6 x 1

S = 60 square units.

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Addressing issue hand, we state that Therefore, the linear equation solution to the system of equations is: x = 0.5, y = 0.1667, z = -0.5 and x = 0.500, y = 0.167, z = -0.500

In algebra, a linear equation refers to one with its form y=mx+b. B is the gradient, and m is the esta. The preceding clause is commonly referred to as a "linear function with two variables" so even though y and x are variables. Bivariate linear equations are linear equations with two variables. There are several linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation seems to have the structure y=mx+b, where m is the slope and b is the y-intercept, it is said to be linear. When a measurement seems to have the formula y=mx+b, both with m identifying its slope and b denoting the y-intercept, it is said to be linear.

values of x, y, and z, we can use the system of equations

3x - 2y + z = 1

2x + y - z = 0

x + 2y + 3z = -1

We can use Gaussian elimination or any other suitable method to solve the system. Here's one way to do it:

3x - 2y + z = 1          (eq. 1)

2x + y - z = 0           (eq. 2)

x + 2y + 3z = -1         (eq. 3)

       3x - 2y + z = 1          (eq. 1)

       0.6667x + 1.3333y - 1.3333z = -0.6667    (eq. 2')

       -0.3333y + 2.3333z = -1.3333    (eq. 3')

       3.3333x - 0.3333z = 0.1667    (eq. 1')

       0.6667x + 1.3333y - 1.3333z = -0.6667    (eq. 2')

       2.1667z = -1.0833    (eq. 3')

       z = -0.5

       y = 0.1667

       x = 0.5

Therefore, the solution to the system of equations is:

x = 0.5, y = 0.1667, z = -0.5

x = 0.500, y = 0.167, z = -0.500

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