What is the rule for translations?

The 3 horizontal line refers the equivalent relation.

The term horizontal line in math defined as a straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system.

Here have to find the meaning of 3 horizontal line.

As per the definition of horizontal line, the three horizontal line also known as triple line defines the equivalent relation of the term.

Here the equivalent that is not the same as 'equals'

Where the double bar is more common and generally implies equality on the other hand the triple bar or equal sign with three lines means congruent or, more generally, an arbitrary equivalence relation.

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Answer: B

Step-by-step explanation:

Area = 4 x 5

         = 20 cm^2

Remember that area of parallelogram is the base x perpendicular height. is The perpendicular height is not 6cm but 5cm. (right angle labelled on diagram)

Answer: 20 cm²

Step-by-step explanation:

area parallelogram = base x height

=> 4 x 5 = 20

The number of machines to minimize the unit cost is 110 and minimum cost is 10,389 .

What is Quadratic Equation?

Quadratic equation can be defined as the equation which is in the form of ax^2 +bx +x = 0.

where a,b,c are constants.

Given ,

The standard form of a quadratic is given by:

ax^2 + bx + c

So for our function, we can say,

a = 0.1

b = -22

c = 11599

We can find the vertex (x-coordinate where minimum value occurs) by the formula -b/2a

So,

= -(-22) / 2*0.1

=22/0.2

= 110

Plugging this value into original function would give us the minimum (unit cost):

C(x) = 0.1 x ^2 - 22x +11599

C(x) = 0.1(110*110) - 22(110)+11599

C(x) = 110(11-22) + 11,599

C(x) = -11(110) + 11599

C(x) = -1210 + 11599

C(x) = 10,389

Hence , The number of machines to minimize the unit cost is 110 and minimum cost is 10,389 .

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Yes, 9 is a positive number because 9 is a natural number and also we use 9 in our daily life counting problems also.

Let's first attempt to understand what numbers are.

A number is an arithmetic value that is computed and used to represent a quantity. Numbers are represented in writing by symbols like "3," which are numerical symbols. A number system is a methodical way of employing digits or other symbols to represent numbers. The numerical system is a useful set of numbers that reflects the mathematical and algebraic structure of the number. provides a typical illustration.

Positive numbers Any number that represents something other than zero is considered to be positive. When referring to the amount of money in your bank account, a positive figure would undoubtedly make you feel good as well.

So 9 is a positive number.

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Answer:

P=3000$

T=2 years

R=1.6% per annum

Now,

interest=(3000×2×1.6)/100=96$

Amount=P+interest=3096$

Hence,Conan needs to pay back 3096$ and the interest is 96$

In linear equation, Ben is 9 years old currently.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Ben's mom = 22 years

Ben is 9 years old currently.

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Null hypothesis (H0): There’s no effect in the population. Alternative hypothesis (Ha or H1): There’s an effect in the population.

The null and alternative hypotheses are two opposing ideas that researchers use a statistical test to analyze evidence for and against: The null hypothesis (H0) states that there is no influence in the population. Alternative hypothesis (Ha or H1): There is a population effect.

Identify the null and alternative hypotheses.

As well as the sample size, specify.

Choose a suitable statistical test.

Gather information (note that the previous steps should be done prior to collecting data)

Based on the sample data, compute the test statistic.

Examine the null hypothesis, usually indicated by H0.

Always write the alternative hypothesis, which is usually marked by Ha or H1, with less than, greater than, or not equals symbols, i.e., (,>,or).

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The area of the shaded regions is 4π + 4, which can be obtained by subtracting 2π - 4 from 3π. This is an exact value, with no further simplification required.

Step 1: Calculate the area of the entire circle.

A = πr^2

A = π(5)^2

A = 25π

Step 2: Calculate the area of the unshaded region.

A = πr^2

A = π(2)^2

A = 4π

Step 3: Subtract the area of the unshaded region from the area of the entire circle.

A = 25π - 4π

A = 21π

Step 4: Calculate the area of the shaded region.

A = 21π - (2π - 4)

A = 21π - 2π + 4

A = 19π + 4

A = 4π + 4

The area of the shaded regions can be found by subtracting the area of the unshaded region from the area of the entire circle. To find the area of the entire circle, we use the formula A = πr^2, where r is the radius of the circle. Plugging in r = 5, we get A = 25π. To find the area of the unshaded region, we use the same formula, but now with r = 2. This gives us A = 4π. Subtracting the area of the unshaded region from the area of the entire circle gives us A = 21π. We then subtract 2π - 4 from 21π to get the area of the shaded region, which is 4π + 4. This is an exact value, with no further simplification required.

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If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.

The following formula determines how many combinations of n objects can be taken r at a time: (n,r) = C(n,r)! .

She was a master of both wit and martial arts. The art and science of education blend beautifully. He saw slam poetry as the ideal synthesis of thought, writing, and theater. The desired mix is produced by the computer system (the perfect combination of arabica and robusta).

Five documentaries make up the total.

7 comedies total are available.

Four mysteries are present.

5 horror movies are there.

A total of 14 films, excluding comedies, are available.

If he wants to rent all 7 comedies, there are a total of 9 different combinations that he can do.

1 * (14*13)/2 = 91

If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.

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Answer:

The value of x is 12.

i think it is correct.

The number of blueberry muffins the baker makes on Tuesday is given by the equation A = 24 blueberry muffins

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of blueberry muffins the baker makes be A

Now , the equation will be

The total number of muffins the baker makes on Tuesday = 60 muffins

The percentage of blueberry muffins = 40 %

So ,

The number of blueberry muffins the baker makes A = total number of muffins the baker makes on Tuesday x percentage of blueberry muffins

Substituting the values in the equation , we get

The number of blueberry muffins the baker makes A = 60 x ( 40/100 )

On simplifying the equation , we get

The number of blueberry muffins the baker makes A = 60 x 0.4

The number of blueberry muffins the baker makes A = 24 blueberry muffins

Therefore , the value of A is 24

Hence , the number of muffins is 24

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If the radius is quadrupled, then the area of the new area to the old area will be 4:1

You should be aware that the quadrupled of a circle is four times the area of the old one.

In this case the area of the circle is denoted by

Area = πr²

Where r= radius=6 cm

The area of the old circle is 22/7 * 6 * 6

Area of the circle is = 113.1cm²

To this effect, the area of the new circle is 4(area of the old one)

Area = 4*22/7 * 6 * 6

Area = 3167/7

Area is = 452.6

This implies that 4(113.2) =452.6

In conclusion, you will discover that four times the area of the new circle is the old circle

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The Equation for the value y is a. y = 21 + 0.25x (where x represents the number of weeks)

b. The value of the stock after 20 weeks would be 21 + (0.25 * 20) = $26.

This equation represents the linear relationship between the value of the stock (y) and the number of weeks (x). The value of the stock is initially $21, and it increases by $0.25 every week. This is represented by the coefficient of x (0.25) in the equation. By plugging in x=20 into the equation, we can find that after 20 weeks, the value of the stock would be $26. This is assuming that the rate of increase remains constant over time.

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A particle takes 5 × 10^7 sec of time to travel a distance of 9.0 × 10^12 meters at a rate of 1.8 × 10^5 meters.

What is speed?

Speed indicates how quickly something or someone is moving. If one knows how far something has travelled and how long it took to get there, then one can calculate its average speed.

The particle travels at a rate of 1.8 × 10^5 m.

The particle travels a distance of 9.0 × 10^12 m.

Let the time taken for the particle to travel be x.

The formula for calculating the distance traveled by the particle is -

distance = rate × time

time = distance/rate

Plugging in the values in the equation -

x = 9.0 × 10^12/1.8 × 10^5

x = 9.0/1.8 × (10^12-5)

x = 5 × 10^7 sec

Therefore, the time taken by the particle to travel is 5 × 10^7 sec.

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Assuming segments that appear to be tangent are tangent, sqrt(277) = x has an estimated value of 16.64331698.

The Pythagorean Theorem, often referred as the Mathematics, is the fundamental Euclidean geometry relationship among the three sides of a right triangle. The area of a squares with the equilateral triangles side is the sum of the surfaces of square with the other two sides, according to this rule. The Pythagorean Theorem says that the square that spans a right triangle's hypotenuse opposite the perfect angle equals the sum of the squares that span its sides. It is sometimes written as the generic algebra notation a2 + b2 = c2.

given

14 is tangent to the circle and 9 is a radius, making this a right triangle.

In order to resolve this issue, we can employ the Pythagorean theorem.

a^2 +b^2 =c^2

9^2+14^2 =x^2

81+196 = x^2

277 = x^2

Taking the square root of each side

sqrt(277) = sqrt(x^2)

sqrt(277) =x

Assuming segments that appear to be tangent are tangent, sqrt(277) = x has an estimated value of 16.64331698.

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Answer: $95.76

Step-by-step explanation:

If the 15 is referencing 15%.

15% of 638.40 can be found by making 15% a decimal by moving the decimal to the left twice.

.15 X 638.40= 95.76

N is the integer between {3,4,5}.so we can find all possible values of n is 2 and 8.

An integer is a whole number that can be positive, negative or zero. Examples of integers are -5, 1, 5, 8, 97, and 3,043.The integers are generated from the set of counting numbers and the operation.

Subtract the same number from both sides. Multiply both sides by the same positive number. Divide both sides by the same positive number. Multiply both sides by the same negative number and reverse the sign.

Now we solve

3n+4 <19

3n+4-4<19-4

3n<15

n<5

so n is less than and equal to 5 it will be {3, 4, 5].

10n/[tex]n^{2}[/tex]+16  >1

10n> [tex]n^{2}[/tex] +16

0> [tex]n^{2}[/tex]-10n +16

0>[tex]n^{2}[/tex] -8n -2n +16

0> n(n-8)-2(n-8)

0> (n-8) (n-2)

So         n-2<0          n-8<0

             n<2              n<8

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Answer:

72.38

Step-by-step explanation:

When converting from mm to cm divide the length value by 10

The graphic solution for each system of equations is given as follows:

20. (5/3, 28/3).

21. (0.205, 3.846).

22. (-1/2, -5/2).

23. (-4.615, 7.462).

The graphic solution of a system of equations is given by the point of intersection of all the equation that compose the system.

For this problem, the systems are composed by functions of the first degree, hence they are linear functions.

For each system, the graph is traced, and then the point of intersection is identified on the graph given at the end of the answer.

Each system is traced on a different color, as follows:

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The formula to find the side of a geometric shape depends on the shape itself. Few details like area or perimeter of a shape or surface area or volume of a solid with few other parameters should be known.

Few examples :

For a square, the formula to find the side (s) is:

s = √(A)

where A is the area of the square.

For a rectangle, the formula to find the length (l) and width (w) are:

l = A/w and w = A/l

where A is the area of the rectangle.

For a triangle, the formula to find the base (b) and height (h) are:

A = (b*h)/2

where A is the area of the triangle.

For a cube, the formula to find the side (s) is:

V = s^3

where V is the volume of the cube.

Keep in mind that these are a few examples of formulas that can be used to find the side of a geometric shape. Depending on the specific problem, different formulas may be required.

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The value of the expression [tex]343^{-4/3}[/tex] is 1/2401.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]343^{-4/3}[/tex]

This can be written as,

1/[tex]343^{4/3}[/tex]

343 = 7³

= 1/[tex]7^{3\times4/3}[/tex]

= 1/[tex]7^4[/tex]

[tex]7^4[/tex] = 7 x 7 x 7 x 7 = 49 x 49 = 2401

= 1/2401

Thus,

The value of the expression is 1/2401.

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The amount that Cheryl left with is $ 1.9 or 1 dollar and 90 cents.

1. READ and reread the problem first

2. DRAW an image to illustrate the information. Ask your self Can I infer anything from this information during this step? What could I doodle? Which model will best convey the information? What inferences may I draw from the illustration?

3. WRITE the drawings as a basis for your conclusions. This can be expressed as a mathematical expression, an equation, or a statement.

Given that

Cheryl bought a sandwich for 5 1/2 dollars and a drink for $2. 60  

Here 5 1/2 = 11/2 = 5.5 dollars

Then the total cost of the sandwich and drink = $ 5.5 + $ 2.60 = $ 8.1  

Given that Cheryl gave $ 10

The amount that Cheryl left with = $ 10 - $ 8.1 = $ 1.9

Here is $ 1.9 = 1 dollar and 90 cents

Therefore,

The amount that Cheryl left with is $ 1.9 or 1 dollar and 90 cents.

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The flux of F across S will be [tex]\frac{3\Pi}{2}[/tex]

A vector of magnitude 1 that is at some point perpendicular to a two-dimensional curve is referred to as the unit normal vector. Normally, you search for a function that returns not just one vector but all potential unit normal vectors of a given curve.

A vector that is perpendicular to a surface at a certain location is known as the normal vector, also referred to as the "normal" to a surface. The inward-pointing normal (pointing toward the interior of the surface) and outward-pointing normal are often distinguished when normals are taken into consideration on closed surfaces.

[tex]$Z_x=-2 x: \quad Z_y=-2 y$[/tex]

[tex]$N=\langle 2 x, 2 y, 1\rangle \quad: f=\langle x, y, z\rangle$[/tex]

[tex]f. $N=2 x^2+2 y^2+z=2 x^2+2 y^2+1-x^2-y^2$[/tex]

=1+x^2+y^2

[tex]x^2+y^2=1\\ \Rightarrow \quad x=r \cos \theta\\ \Rightarrow \quad y=r \sin \theta \\ \Rightarrow x^2+y^2=r^2 \\ 0 < r < 1: \quad 0 < \theta < 2 \pi[/tex]

[tex]$R \cdot v=\int_0^{2 \pi} \int_0^1\left(1+r^2\right)(r) dr d \theta$[/tex]

[tex]$=2 \pi \int_0^1 r+r^3 d r$[/tex]

[tex]$2 \pi\left[\frac{r^2}{2}+\frac{r^4}{4}\right]_0^1$[/tex]

[tex]$=(2 \pi)\left(\frac{1}{2}+\frac{1}{4}\right)$[/tex]

[tex]$=\frac{(2 \pi)(3)}{42}=\frac{3 \pi}{2}$[/tex]

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If George is trying to fence the garden with less fences possible between the two options given in the question, the first option of measurements i.e 20 feet long and 15 feet wide would take less fencing.

It is the entire distance encircled on all sides by the rectangle.One of the key equations for the rectangle might be regarded to be its perimeter.

The formula for calculating the perimeter of a rectangle is :

P = 2*l + 2 *b where , l and b are the length and breadth of the rectangle.

For the first option, where the garden is 20 feet long and 15 feet wide, the perimeter would be 20+20+15+15 = 70 feet.

For the second option, where the garden is 30 feet long and 10 feet wide, the perimeter would be 30+30+10+10 = 80 feet.

Therefore, the first option where the garden is 20 feet long and 15 feet wide would use less fencing, 70ft in this case, as the perimeter is lower than the other option which is 80 ft.

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The velocity of an ant moving along the x-axis whose position is given by x(t) = 2cos(π/2 t^2) is v(t) = -πtsin(π/2 t^2) and acceleration is a(t) = -π²t²cos(π/2 t^2) - πtsin(π/2 t^2). The ant moves in right direction in the time interval [-1, 0) and changes direction at t = 0.

(a) To find the velocity of the ant at any given time t, we need to take the derivative of the position function x(t) with respect to t. The derivative of x(t) = 2cos(π/2 t^2) is:

v(t) = -πtsin(π/2 t^2)

So the velocity of the ant at time t is given by -2πsin(π/2 t^2)

(b) To find the acceleration at any given time t, we need to take the derivative of the velocity function v(t) with respect to t. The derivative of v(t) = -πtsin(π/2 t^2) is:

a(t) = -π²t²cos(π/2 t^2) - πtsin(π/2 t^2)

So the acceleration of the ant at time t is given by  -π²t²cos(π/2 t^2) - πtsin(π/2 t^2).

(c) To determine the values of t for which the ant is moving to the right, we need to look at the sign of the velocity function v(t) = -πtsin(π/2 t^2). Since the sine function oscillates between -1 and 1, this function will be positive when sin(π/2 t^2) is negative, and negative when sin(π/2 t^2) is positive. Moving rights means positive value of x.

Therefore, the ant is moving to the right when sin(π/2 t^2) < 0. That is

(π/2)t^2 < sin⁻¹(0)

sin⁻¹(0) = nπ, where n = ..., -2, -1, 0, 1, 2, ...

t is in interval [-1, 1] so π/2t^2 is in interval [0, π/2]

sin⁻¹(0) = 0

(π/2)t^2 < 0

Therefore t < 0

That is possible values of t is [-1, 0)

(d) To determine the values of t for which the ant changes direction, we need to look at the sign of the acceleration function a(t) = -π²t²cos(π/2 t^2) - πtsin(π/2 t^2).

When ant change direction a(t) = 0.

-π²t²cos(π/2 t^2) - πtsin(π/2 t^2) = 0

πtcos(π/2 t^2) + sin(π/2 t^2) = 0

sin(π/2 t^2) = -πtcos(π/2 t^2)

tan(π/2 t^2) = -πt

On solving possible values of t in the interval [-1, 1] is 0.

So, the ant changes direction when t = 0.

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