3x +
9y = -27
x + y = -1

Answer:

8- 3x

Step-by-step explanation:

1- Calculate

The type of quadrilateral PQRS is a trapezium. A trapezium is a quadrilateral with one pair of parallel sides. In this case, the parallel sides are PQ and SR.

To find the value of x, we can use the distance formula. The distance formula states that the distance between two points is equal to the square root of the difference of their x-coordinates squared plus the difference of their y-coordinates squared.

In this case, we have the following:

PQ = √((x - 10)² + ((-9) - 3)²

We are given that PS = 15 units, so we can set the above equation equal to 15 and solve for x.

15 = √((x - 10)² + ((-9) - 3)²)

225 = (x - 10)² + 144

225 = x² - 20x + 100 + 144

(x - 15)(x - 5) = 0

Therefore, x = 15 or x = 5.

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Answer:

you dont have an image?

Answer:

A. {x,y}={-2,-3}

// Solve equation [2] for the variable  x

 [2]    x = 2y + 4

// Plug this in for variable  x  in equation [1]

  [1]    (2y+4) - y = 1

  [1]    y = -3

// Solve equation [1] for the variable  y

  [1]    y = - 3

// By now we know this much :

   x = 2y+4

   y = -3

// Use the  y  value to solve for  x

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

B.   [1]           3x=3y-6

 [2]           y=x+2

Equations Simplified or Rearranged :

  [1]    3x - 3y = -6

  [2]    -x + y = 2

Solve by Substitution :

// Solve equation [2] for the variable  y

 [2]    y = x + 2

// Plug this in for variable  y  in equation [1]

  [1]    3x - 3•(x +2) = -6

  [1]    0 = 0 =>  Infinitely many solutions

C.Step by Step Solution

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System of Linear Equations entered :

  [1]    4x - y = 2

  [2]    8x - 2y = 4

Solve by Substitution :

// Solve equation [1] for the variable  y

 [1]    y = 4x - 2

// Plug this in for variable  y  in equation [2]

  [2]    8x - 2•(4x-2) = 4

  [2]    0 = 0 =>  Infinitely many solutions

Answer:

Step-by-step explanation:

a) y = -1/4x    --------------(I)

x + 2y = 4 -----------------(II)

Substitute y = (-1/4)x in equation (I)

\(x + 2*\dfrac{-1}{4}x=4\\\\\\x -\dfrac{1}{2}x=4\\\\Multiply \ the \ entire \ equation \ by \ 2 \\\\2x -x = 8\\\\x=8\)

\(Substitute \ x = 8 \ in \ equation \ (I)\\\\y=\dfrac{-1}{4}*8\\\\\\y = -2\)

Answer: x = 8  ; y = -2

b) y = -x - 2 --------------(i)

   3x + 3y = 6   -----------(ii)

Divide equation (ii) by m

x + y = 2

  y = -x + 2  ----(iii)

From (i) and (iii), it shows that these lines have same slope. So, they are parallel lines

Answer: No solution

3) -8x + 2y =4

            2y = 8x + 4

Divide the entire equation by 2

             y = 4x + 2 -------------(i)

            y = 4x + 2 ----------------(ii)

From (i) and (ii), we come to know that these lines coincide.So, they have infinite solutions.

(a) V is a non measurable set, its Lebesgue measure is zero. Therefore, the Cartesian product R = V × V has a measure of zero as well

(b) S is not measurable in R²

(a) The S is a subset of a rectangle R such that m(R) = 0, we need to construct such a rectangle. Let's consider the interval V = [0, 1), which is a nonmeasurable set. We can define R as the Cartesian product of V with itself, i.e., R = V × V. Thus, R is a rectangle in R².

Now, let's show that S is a subset of R. For any point (x, y) in S, it can either belong to Q or CR².

If (x, y) is in Q, then x and y are rational numbers. Since V is a subset of [0, 1), which contains only irrational numbers, (x, y) cannot belong to V. Therefore, (x, y) must belong to CR².

If (x, y) is in CR², then x and y are irrational numbers. Since V contains only irrational numbers, (x, y) cannot belong to V. Therefore, (x, y) must belong to CR².

In both cases, (x, y) belongs to R = V × V. Hence, S is a subset of R.

To show that m(R) = 0, we need to show that the Lebesgue measure of R is zero. Since V is a non measurable set, its Lebesgue measure is zero. Therefore, the Cartesian product R = V × V has a measure of zero as well.

(b) No, S is not measurable in R². The reason is that V, being a non measurable set, does not have a well-defined Lebesgue measure. Consequently, any set containing V, such as S, will also be non measurable .

Measurability in R² requires all subsets to have a well-defined Lebesgue measure, which is not the case for S.

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The number of triangles that can be formed from a common vertex on the polygon shown is three triangles.

To form triangles on polygons, you can draw diagonals connecting the vertices of the polygon. A diagonal is a line segment that connects two non-adjacent vertices of a polygon. By drawing diagonals, you can create triangles within the polygon.

From a hexagon, we can draw three diagonals from each vertex. So, from a common vertex, we can draw three diagonals and form three triangles. Since there are six vertices in a hexagon, we can choose any one of these vertices as the common vertex and form three triangles.

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Answer:

y=4x-5.

Step-by-step explanation:

slop-interception form of the required line is y=kx+b, where k - slop, b - intercept;

1) to find value of k:

if the required line is parallel to the given line, then slop of the given line = slop of the required line, it means k=4 and the required line is y=4x+b;

2) to find the value of 'b':

if to substitute the given coordinates into the equation of the given line, then:

15=4*5+b, b= -5.

3) finally, y=4x-5

Answer: John walks a total of 360 yards from school.

Step-by-step explanation:

Let's represent the total distance John walks from school as "x".

According to the problem, John has already walked 15% of the way, which can be written as:

0.15x

We also know that he has walked 54 yards so far, which means:

0.15x = 54

To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:

x = 54 ÷ 0.15

x = 360

Therefore, John walks a total of 360 yards from school.

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Answer

put 1 on top and exo on bottom

Step-by-step explanation:

The differential equation for the amount of salt a(t) in the tank at time t is da/dt = -100a/101.

The water input rate and solution output rate is 2 gal/ min. So the concentration of solution in tank is a/(200 + 2) at time t. So in next minute (t + 1), the amount of salt that leaves the tank is

(a/(200 + 2)) * 2 = a/101

So da/dt = a/ 101 - a = -100a/ 101

This equation models the rate of change of the amount of salt in the tank with respect to time, and it is a first-order linear ordinary differential equation because it is linear in the dependent variable a(t) and its derivative da/dt. The negative sign in front of the rate constant indicates that the amount of salt in the tank is decreasing over time due to the continuous outflow of the solution.

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The temperature is a function of time, as there is a single temperature for each instant of time.

A relation represents a function when each input value is mapped to a single output value.

For the set in this problem, we have that:

As there are no repeated inputs, the temperature is in fact a function of time.

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Answer:

3 3/5 or 18/5

Step-by-step explanation:

When we divide by fractions, we multiply by the reciprocal of the fraction.

So, 3 ÷ 5/6 is

3*6/5

=18/5

=3 3/5

Have a great day!

Answer:

18/5

3 3/5

3.6

Step-by-step explanation:

3 ÷ 5/÷6

3 × 6/5 → 18/5 (can be 18/5, 3 3/5 or 3.6)

Hope this helps! :)

The line integral of the vector field F over the line segment C is 97/12.

To calculate the line integral of the vector field F = <x^2, 2y, z^3> over the line segment C from (0, 0, 0) to (1, 2, 3), we can parameterize the line segment and then evaluate the integral. Let's denote the parameterization of C as r(t) = <x(t), y(t), z(t)>.

To parameterize the line segment, we can let x(t) = t, y(t) = 2t, and z(t) = 3t, where t ranges from 0 to 1. Plugging these values into the vector field F, we have F = <t^2, 4t, (3t)^3> = <t^2, 4t, 27t^3>.

Now, we can calculate the line integral of F over C using the formula:

∫F·dr = ∫<t^2, 4t, 27t^3> · <dx/dt, dy/dt, dz/dt> dt.

To find dx/dt, dy/dt, and dz/dt, we differentiate the parameterization equations:

dx/dt = 1, dy/dt = 2, dz/dt = 3.

Substituting these values, we get:

∫F·dr = ∫<t^2, 4t, 27t^3> · <1, 2, 3> dt.

Expanding the dot product:

∫F·dr = ∫(t^2 + 8t + 81t^3) dt.

Integrating each term separately:

∫F·dr = ∫t^2 dt + 8∫t dt + 81∫t^3 dt.

∫F·dr = (1/3)t^3 + 4t^2 + (81/4)t^4 + C,

where C is the constant of integration.

Now, we evaluate the definite integral from t = 0 to t = 1:

∫₀¹F·dr = [(1/3)(1^3) + 4(1^2) + (81/4)(1^4)] - [(1/3)(0^3) + 4(0^2) + (81/4)(0^4)].

∫₀¹F·dr = (1/3 + 4 + 81/4) - (0) = 97/12.

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Answer:

i think is c.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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It would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

Dennis' reasoning is incorrect.

To determine the rate of picking apples per minute, Dennis correctly divided the total number of apples (24) by the time it took (6 minutes), resulting in 4 apples per minute. However, his approach to calculating the number of apples that could be picked in 8 minutes is flawed.

Dennis multiplied the rate of picking apples per minute (4 apples) by the given time (8 minutes), assuming that the rate remains constant. This approach would be valid if the rate of picking apples per minute were constant, but in this scenario, it is not necessarily the case.

The rate of picking apples could vary depending on factors such as fatigue, efficiency, or other variables. Therefore, it is not accurate to assume that the rate of picking apples per minute remains the same over a longer duration of time.

To determine the number of apples that could be picked in 8 minutes, it would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

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The measure of the angles A and B are 55 and 70 respectively.

According to the triangle's "angle sum property," the sum of its interior angles is 180°. The total of the angles of a triangle, whether acute, obtuse, or right, is always 180°. The following is a representation of this: A + B + C Equals 180° in an ABC triangle.

By angle - sum property,

We know that the sum of the triangle is 180°

⇒  ∠A + ∠B + ∠C = 180

⇒   11x + 14x + 55 = 180

⇒   25x + 55 = 180

⇒   25x = 180 - 55

⇒   x = 125/25 = 5

x = 5

The measure of ∠A will be - 11x = 11× 5 = 55°

The measure of ∠B will be - 14x = 14×5 = 70°

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On solving the provided query we have Therefore, assuming that order equation counts, there are 20,736 different ways to arrange 12 different books on four shelves.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

Using the permutation formula with repetition, we can determine how many different ways there are to arrange 12 books on 4 shelves.

\(n^r\)

where r is the number of empty spaces to be filled (in this example, 4 shelves) and n is the number of options to select from (12 distinct books in this case).

\(12^4 = 20,736\)

Therefore, assuming that order counts, there are 20,736 different ways to arrange 12 different books on four shelves.

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Answer: i believe bill saved $21.44

Step-by-step explanation: 68.99-57=11.99

37.80-25%=28.35

37.80-28.35=9.45

9.45+11.99=21.44

Answer:

Step-by-step explanation:

Subtract 3x 3 x from both sides of the equation. Divide each term by 8 8 and simplify. Divide each term in 8y=2−3x 8 y = 2 - 3 x by 8 8

Answer:

x = 30

Step-by-step explanation:

As we know, the angles inside of a triangle added together all equal 180°, so you would combine 3x + 2x + x = 180°. And then from there you can solve.

3x + 2x + x = 180°

[Combine like terms] 6x = 180°

[Divide 6 from both sides of the equal sign] x = 30°

Hope this helps!!

Answer:

2x +3y= 5xy

-1(2x+y= 2xy+-1 = -3xy

Answer:

y= 9

x = -2

Step-by-step explanation:

Y= 9, X = -2 I use the simultaneous equation to solve it.

Assuming that the car is not moving, the force the car exerts against the driveway is equal in magnitude and opposite in direction to the force of gravity acting on the car. We can break down the force of gravity into two components: one perpendicular to the driveway and one parallel to the driveway.

The component of gravity perpendicular to the driveway is equal to the weight of the car times the cosine of the angle of inclination:

F_perp = mgcos(4°)

where m is the mass of the car, g is the acceleration due to gravity, and F_perp is the perpendicular component of the force of gravity.

The component of gravity parallel to the driveway is equal to the weight of the car times the sine of the angle of inclination:

F_parallel = mgsin(4°)

where F_parallel is the parallel component of the force of gravity.

Since the car is not moving, the force the car exerts against the driveway is equal in magnitude to the force required to keep the car from rolling down the driveway:

F_exerted = 480 lb

Thus, we have the equation:

F_exerted = F_parallel

Substituting the expressions for F_parallel and F_perp, we get:

mgsin(4°) = 480 lb

Solving for the mass of the car, we get:

m = 480 lb / (g*sin(4°))

Substituting the mass of the car into the expression for the perpendicular component of the force of gravity, we get:

F_perp = mgcos(4°) = (480 lb / (gsin(4°))) * gcos(4°)

Simplifying, we get:

F_perp = 480 lb / tan(4°)

Thus, the force the car exerts against the driveway is:

F_exerted = F_parallel = 480 lb

And the force of gravity perpendicular to the driveway is:

F_perp = 480 lb / tan(4°) ≈ 6,837 lb

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Domain is the input value, The x value)

The arrows on the graphed line mean the line continues in that direction,

There is arrows on both ends so the domain would be negative infinity to infinity.

The answer is B.

Answer:

c. A point reduces the interest rate by 1%.

Step-by-step explanation:

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

The 99% confidence interval for the population mean of seasonal pine saplings' heights is [266.98, 305.02] millimetres.

To calculate the confidence interval, we can use the formula:

sample mean ± (critical value) x (standard error)

The critical value for a 99% confidence level with 20 degrees of freedom (n-1) is 2.831. The standard error can be calculated as the population standard deviation divided by the square root of the sample size, which gives us 22 / sqrt(21) = 4.79.

Substituting these values into the formula, we get:

286 ± 2.831 x 4.79 = [266.98, 305.02]

Therefore, we can be 99% confident that the true population mean of seasonal pine saplings' heights falls within this interval.

In simpler terms, this means that if we were to take 100 random samples of 21 seasonal pine saplings and calculate the confidence interval for each sample using the same method, 99 of those intervals would contain the true population mean. This also means that there is a 1% chance that our interval does not contain the true population mean.

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26.4

Answer:

S8nce N is inthe center NL is one half of KM

Answer:

Here it is!

Step-by-step explanation:

I graphed it. The second one is just to show the points.

The points are (0,-6) and (-1/2,0)

Brainly pls!

Answer:

I think that the answer would be, 0.813

Step-by-step explanation:

5.8736

7.349

equals 0.812845

If you round it you get 0.813