Find the image of the given point
under the given translation.

The values of Q(C1), Q(C2), and Q(C3) are 4, 4, and π, respectively.

The concept of the integral is a fundamental part of calculus and it is used to calculate the area under a curve or the volume of a 3-dimensional object. In this context, we will be exploring the integral of a two-dimensional set in the R^2 plane.

For every two-dimensional set C contained in R^2 for which the integral exists, the function Q(C) is defined as the double integral of the function (x^2 + y^2) over the set C. The double integral is a mathematical tool for finding the total volume under a surface.

Let's consider the three sets C1, C2, and C3 and find Q(C1), Q(C2), and Q(C3).

C1={(x,y) : −1 ≤ x ≤ 1, −1 ≤ y ≤ 1}

Q(C1) = ∬C1 (x^2 + y^2) dxdy = ∫^1_{-1}∫^1_{-1} (x^2 + y^2) dxdy = ∫^1_{-1} [(x^2 + y^2)/2]^1_{-1} dx = 4.

C2 ={(x,y):−1≤x≤1,−1≤y≤1}

Q(C2) = Q(C1) = 4.

C3 = {(x,y):x^2 + y^2 ≤1}

Q(C3) = ∬C3 (x^2 + y^2) dxdy = π.

In conclusion, the values of Q(C1), Q(C2), and Q(C3) are 4, 4, and π, respectively.

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Answer:

The ratio of circumference of circle and diameter of circle is π

B is correct

Step-by-step explanation:

The radius of a circle is 6.

We need to find the ratio of circumference of circle and diameter

Circumference of circle = 2πr

                                  C = 12π

Diameter of circle = 2r

                       D = 12

Substitute 12 as D

Now we find the ratio of circumference and diameter    

Hence, The ratio of circumference of circle and diameter of circle is π

When we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

To subtract 3 from 22, we can perform the subtraction operation as follows:

22

3

19

We align the numbers vertically and subtract each corresponding place value from right to left. In this case, subtracting 3 from 2 requires borrowing or regrouping. However, since 2 is greater than 3, we can directly subtract 3 from 2 and write the difference, which is 1, in the one's place.

Therefore, the simplified answer is 19.

The subtraction process involves taking away or removing a certain quantity from another. In this case, we subtracted 3 from 22, resulting in a difference of 19. The process of simplifying the answer is simply expressing the result in its most concise and reduced form.

By subtracting 3 from 22, we removed 3 units from the original value of 22, leaving us with 19. This can be visualized as taking away three objects from a group of 22 objects, resulting in a remaining count of 19.

In summary, when we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

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The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.

The allocation of weights to the relevant variables that produce the calculation's equilibrium is referred to as a consequence.

A connection between two or more factors results in a linear model when displayed on a graph. The variable will have a degree of one.

The linear equations are given below.

y = -3x + 9        ...1

3y = -9x + 9     ...2

Divide the equation 2 by 3, then the equation will become.

y = -3x + 3

The slope of the lines is the same but the lines are separated by a distance.

The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.

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The required equation of the line is 2x + 5y + 5 = 0

What is an equation?

Equations are used to describe geometric shapes in Cartesian geometry. Because the equations under consideration, such as implicit equations or parametric equations, contain an unlimited number of solutions, the goal has shifted: instead of directly stating the solutions or counting them, which is impossible, one utilizes equations to investigate the features of figures. This is the fundamental concept of algebraic geometry, a significant branch of mathematics. Algebra is concerned with two types of equations: polynomial equations and the particular case of linear equations. Polynomial equations have the form P(x) = 0, where P is a polynomial, while linear equations have the form ax + b = 0, where a and b are parameters, when there is only one variable. Algorithms are used to solve equations from either family.

Given equation of the line is 2x + 5y = 10

or, 5y = -2x + 10

or, y = -2x/5 + 2

slope of the equation, m = -2/5

Since the lines are parallel, so the required equation of the line is

y-1 = (-2/5)(x+5)

or, 5(y-1) = -2(x+5)

or, 5y-5 = -2x-10

or, 2x + 5y + 5 = 0

Hence, the required equation of the line is 2x + 5y + 5 = 0

i.e. 2x + 5y = -5

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Answer:

C=-3t+30

Step-by-step explanation:

Using proportions, the lengths of the unknown sides are given as follows:

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the triangles are similar, hence the lengths of it's sides follow the proportion given next:

\(\frac{2x}{4} = \frac{5}{x - 3}\)

Applying cross multiplication:

2x(x - 3) = 20

2x² - 6x - 20 = 0

x² - 3x - 10 = 0

(x - 5)(x + 2) = 0.

Then the positive solution is:

x - 5 = 0 -> x = 5.

And the lenghts are:

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Answer:

y = -1/2x + 19/2

Step-by-step explanation:

Hi there!

We are given the points (9,5) and (7,6)

We want to write an equation of the line that contains these two points, in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, let's find the slope of the line

The formula for the slope (m) calculated from 2 points is \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points

We have everything we need to find the slope, but let's label the values of the points to avoid any confusion.

\(x_1=9\\y_1=5\\x_2=7\\y_2=6\)

Now substitute these values into the formula to find the slope

m= \(\frac{y_2-y_1}{x_2-x_1}\)

m=\(\frac{6-5}{7-9}\)

Subtract

m=\(\frac{1}{-2}\)

m=-1/2

The slope of the line is -1/2

We can substitute this as m into the formula for slope-intercept form:

y = -1/2x + b

Now we need to find b

As the equation passes through (9, 5) and (7, 6), we can use either one to solve for b

Taking (7, 6) for example:
Substitute 7 as x and 6 as y into the equation

6 = -1/2(7) + b

Multiply

6 = -7/2 + b

Add 7/2 to both sides

19/2 = b

substitute 19/2 as b:

y = -1/2x + 19/2

Hope this helps!

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Answer:

Option C is the answer to this question

Answer: 2.5

Step-by-step explanation: 40 divided by 4 = 10  1.4 x 10 = 2.5

Answer:

2.5

Step-by-step explanation:

1/4 is equal to 0.25, So if it's 0.25 for 4 servings, the ratio is 0.25:4. You can the divide 40 by 4 and get 10. You can now take that ten and multiply it by 0.25 to get 2.5 or 2 and 1/2

Solutions refers to the answer to the problem, Real Solutions are realistic and practical whereas ideal solutions are the best cases for the solutions.

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

Ideal Solutions - Best cases, Usually not possible.

Real Solutions - Practical and possible to attain.

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Answer:

If you're asking for the new price, just find 5% of $75.

$75 * 0.05 = $3.75

1.) c. 1,232

There are 16 ounces in 1 pint. So to solve how many ounces are in 77 pints, you should multiply 16 ounces by 77 pints.

2.) d. 10

There are 8 ounces in 1 cup. Since you have 80 ounces, you should divide that by 8 ounces (aka 1 cup).

3.) b. 2

There are 16 ounces in 1 pound. Since you have 32 ounces you should divide it by 16.

In the future, you would need to find out the conversion of measurements and then multiply/divide to solve. Make sure you keep track of your units when solving! Good luck!

Answer:

16 square inches

Step-by-step explanation:

First, find the area of the square.

Area of a square = width x length = 2 x 2 = 4 in²

All the triangles are the same, so we need to find the area of one of the triangles and multiply it by 4.

Area of a triangle = 1/2 x base x height = 1/2 x 2 x 3 = 3 in²

So the total area of all 4 triangles = 4 x 3 = 12 in²

Therefore the total surface area = 4 + 12 = 16 in²

Answer:

(- ∞,1]

Step-by-step explanation:

Answer:

The correct answer should be D. 19.2!!!

Step-by-step explanation:

hope this helps :))

Based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

To solve the problem using the determinant method (Cramer's rule), we need to set up a system of equations based on the given information and then solve for the unknowns, which represent the number of 0.5 litre bottles and 0.7 litre bottles.

Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y.

From the given information, we can set up the following equations:

Equation 1: 0.5x + 0.7y = 16.5 (total volume of moonshine)

Equation 2: 8x + 10y = 246 (total earnings from selling moonshine)

We now have a system of linear equations. To solve it using Cramer's rule, we'll find the determinants of various matrices.

Let's calculate the determinants:

D = determinant of the coefficient matrix

Dx = determinant of the matrix obtained by replacing the x column with the constants

Dy = determinant of the matrix obtained by replacing the y column with the constants

Using Cramer's rule, we can find the values of x and y:

x = Dx / D

y = Dy / D

Now, let's calculate the determinants:

D = (0.5)(10) - (0.7)(8) = -1.6

Dx = (16.5)(10) - (0.7)(246) = 150

Dy = (0.5)(246) - (16.5)(8) = -18

Finally, we can calculate the values of x and y:

x = Dx / D = 150 / (-1.6) = -93.75

y = Dy / D = -18 / (-1.6) = 11.25

However, it doesn't make sense to have negative quantities of bottles. So, we can round the values of x and y to the nearest whole number:

x ≈ -94 (rounded to -94)

y ≈ 11 (rounded to 11)

Therefore, based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

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Question

Matti is making moonshine in the woods behind his house. He’s selling the moonshine in two different sized bottles: 0.5 litres and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for a 0.7 litre bottle 10€. The last patch of moonshine was 16.5 litres, all of which Matti sold. By doing that, he earned 246 euros. How many 0.5 litre bottles and how many 0.7 litre bottles were there? Solve the problem by using the determinant method (a.k.a. Cramer’s rule).

Answer:

only one solulton and its 7

Step-by-step explanation:

x=7/2,y=7

Answer:

B

Step-by-step explanation:

A = 1/2π  * r²

A/(1/2π) = r² (Divide by 1/2π)

r = √(2A/π) (Take the square root of both sides then simplify)

Answer:

B. r=\(\sqrt{\frac{2A}\pi}}\)

Step-by-step explanation:

First multiply both sides by 2. This gives us 2A=\(\pi\)r². Now, divide both sides by \(\pi\). Now we have \(\frac{2A}{\pi}\)=r². Now, square root both sides. The final answer is r=\(\sqrt{\frac{2A}{\pi}}\)

Answer:

both are reciprocals

Step-by-step explanation:

15.

\(\frac{5}{8}\cdot \frac{16}{20}\\\\=\frac{5}{8}\cdot\frac{8}{5}=1\)

so they are reciprocals

17.

\(\frac{2}{3}\cdot\frac{12}{18}\\\\=\frac{2}{3}\cdot \frac{3}{2}=1\)

so they are reciprocals

1.62 is the volume (in cm3) of 2 troy ounces of pure gold .

What is full answer for density?

We determine the volume, V, corresponding to the given amount of gold. We do this by dividing the given mass, m, by the density, d, such that

               V = m/d

  m = 31.03 g

   d = 19.3 g/ml

We proceed with the solution

  V = m/d

     = 31.03/19.3

      ≈ 1.62 ml

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Answer:

y = 6/5x + 2

Step-by-step explanation:

First let's fix this equation

5x + 6y = 36 (subtract 5x on both sides)

6y = -5x + 36 (divide by 6 on both sides)

y = -5/6x + 6

NOW

The perpendicular slope of this equation is 6/5

Now we have to plug in (-5,-4) to get the y-intercept

-4 = 6/5(-5) + b  (distribute 6/5 to -5)  (b represents the y-intercept)

-4 = -6 + b (add 6 on both sides)

2 = b

So your equation is...

y = 6/5x + 2

HOPE THIS HELPED!!!!!

Answer:

\(x= 1 +5\sqrt 2,~~ x=1-5\sqrt 2\)

Step-by-step explanation:

\(~~~~~~(x-1)^2 = 50\\\\\implies x -1 = \pm\sqrt{50}\\\\\implies x = \pm\sqrt{25 \times 2} +1\\\\\implies x= 1 \pm 5\sqrt 2\)

Answer:

B. $0.27

Step-by-step explanation:

300 centimeters is 3 meters

So, no we just multiply the number of meters by the price (0.09)

0.09 X 3 = 0.27

So, the answer is B, $0.27

300 cm of streamers

0.09 per m

1 m= 100 cm

the price in dollars of 300 centimeters of streamers.

\(300cm = 3m\)

\(price = 3 \times 0.09\)

\( = 0.27\)

therefore, the price of 300 cm of streamers is $0.27.

answer= option B

Answer: 79.2!!!!!!!!!

Step-by-step explanation:

If you are here from delta math this is the answer

Answer:

Equation: x + 16 + 13 + x = 21 ; x = -4

Step-by-step explanation:

x + 16 + 13 + x = 21 (Given)

2x + 29 = 21 (Added like terms)

2x = -8 (Subtracted 29 on both sides)

x = -4 (Divided 2 on both sides)

Answer:

Step-by-step explanation:

80 tems or 8 hundreds

\(For\)

\(10\ times\ as\ many\ as\ 8\ tens\ is\)

   \(80\ tens\ or\ 8\ hundreds\)

              \(\left\{8\ tens\ x\bullet10=80\ \left.\ ten\right\}\right.\)

                                     \(=\ 8\ \left.\ hundreds\right\}\)

I hope this helps you

:)

Answer:

3.14 cm

Step-by-step explanation:

From the question,

Applying

s = πdФ/360................... Equation 1

Where s = length of arc AB, d = diameter of the circle, Ф = angle at the center of the circle, π = pie

From the question,

Given: d = 8 cm, Ф = π/4 rad = 45°

Constant: π = 22/7

Substitute these values into equation 1

s = (22/7)(8)(45)/360

s = 3.14 cm.

Hence the lenght of arc AB = 3.14 cm

Answer:

13.1

Step-by-step explanation: