Louis has 1 green counter, 2 white counters
and 2 yellow counters in a box.
Louis takes one counter at random from the
box, puts it back, and takes another
counter from the box.

The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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Answer:

15 nickels and 8 dimes

Step-by-step explanation:

Let N = number of nickels and D = number of dimes

N - D = 7   (the number of nickels exceeds the number of dimes by 7.)

or

N = D + 7

Total value of N nickels = 5N

Total value of D nickels = 10D

Combined total value => 5N + 10D = 155

Substitute for N in terms of D
==> 5(D + 7) + 10D = 155

5D + 35 + 10D = 155

15D + 35 = 155

15D = 155 - 35

15D = 120

D = 120/15

D = 8

N = D + 7 = 8 + 7 = 15

15 nickels and 8 dimes

The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.

For e.g. the range of the function F is {1983, 1987, 1992, 1996}.

On the other hand, the whole set B is known as the codomain of the function.

It is the set that contains all the outputs of the function.

So, the set of real numbers is a codomain for every real-valued function. The codomain of the function F is set B.

How to Find the Range of a Function

Consider a function y = f(x).

The spread of all the y values from minimum to maximum is the range of the function.

In the given expression of y, substitute all the values of x to check whether it is positive, negative or equal to other values.

Find the minimum and maximum values for y.

Then draw a graph for the same.

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Answer:

7500

Step-by-step explanation:

15/100×50000

750000/100

=7500

For math equation, To eliminate a variable, it must have the same coefficient. So if the coefficients of the variables are not the same then first equate the coefficients by multiplying or dividing them.

Determine the set of solutions to the following system of equations using the elimination method, if x and y are variables in the set of real numbers.

Completion:

1. x + y = 1 and x + 5y = 5

To eliminate the y variable, remember that the coefficients of y must be the same, so the equation x + y = 1 times 5 and the equation x + 5y = 5 times 1, then:

x + y = 1     │× 5 => 5x + 5y = 5

x + 5y = 5   │× 1 => x + 5y = 5

5x + 5y = 5

x + 5y = 5

--------------- –

4x + 0 = 0

x = 0

Same as step I, there is no need to equate the coefficients to eliminate variable x because the coefficients are the same, then:

x + y = 1

x + 5y = 5

--------------- –

0 + –4y = –4

y = 1

So, the solution set is {(0, 1)}.

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The measure of angle B is 50 degrees and angle C is 80 degrees.

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°.

In the given triangle, we can use the concept of triangle angle sum to find the unknown measures.

We know that the sum of the angles in a triangle is always 180 degrees.

Therefore, if we know two angles in a triangle, we can find the third angle by subtracting the sum of those angles from 180.

We are given that angle A is 50 degrees. We are also given that angles B and C are unknown. Therefore,

we can use the following equation to find the measure of angles B and C:

A + B + C = 180

50 + B + C = 180

B + C = 180 - 50

B + C = 130

So the sum of angles B and C is 130 degrees. Therefore, we can't find individual measures of angles B and C.

Alternatively, we can use the property of the angle pair which states that if two parallel lines are intersected by a transversal, the alternate interior angles are congruent.

If we know that angle A and angle B are congruent, we can find the measure of angle B as 50 degrees. As a result, angle C will be 180 - 50 - B = 130-50 = 80 degrees.

Hence, the measure of angle B is 50 degrees and angle C is 80 degrees.

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The angle e between vectors u and v to the nearest tenth of a degree is

≈ 3.14°.

An angle in plane geometry is a shape created by two rays or lines that have a shared termination. The name "angle" originates from the Latin word "angulus," which means "corner. "The common terminus of two rays is known as the vertex, and the two rays are known as sides of an angle.

When u and v's two vectors are at an angle, if, then cosθ = (u·v) / [llull llvll]

u·v = (5)(4) + (2)(-3)

       = 20 - 6

        = 14

llull = √[(5)2 + (2)2]

= √29    

llvll = √[(4)2+(-3)2]

= √25

So, cosθ = 14 / [√725]

            = 0.51

θ = cosθ-(0.51) ≈ 3.14°

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A linear inequality in two variables is an inequality that can be written in the form "ax + by < c" or "ax + by > c" or "ax + by = c", where a, b, and c are constants and x and y are variables. This inequality represents a boundary line and all the solutions of the inequality make up a region of the xy-plane.

For example, the inequality "2x + 3y < 6" represents the region of the xy-plane that is on one side of line 2x + 3y = 6. To graph this inequality, one can find the boundary line by setting the inequality equal to zero and then shading in the region that satisfies the inequality.

A linear equation in two variables is an equation that can be written in the form "ax + by = c", where a, b, and c are constants and x and y are variables. This equation represents a straight line in the xy-plane and all the solutions of the equation are the coordinates of the points on that line.

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The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)

The quotient of the rational expressions is

4(x+2) / 5(x-1) (x-1)

The quotient of the rational expressions shown below

Explanation in detail:

Two expressions are shown here.

Expression 1 : 2x/x-1

Expression II for 5x/2x+4.

The product of expressions I and II must be calculated.

(2x / x-1 ) ÷ (5x / 2x+4)

applying the upcoming regulation

a ÷ b = a× 1/b

(2x/x-1)×( 2x+4 / 5x)

(2x) (2x+4) / (x-1)(5x) (5x)

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

The solution to the previous question is 4(x+2) / 5(x-1).

The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)

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The cost of a book bought by Russell is found in in dollars is $7.

For the stated question-

Let the price of the each book be 'x'.

Let the price of movie  be 'y'.

Then,

11x + 12y = 245  ...eq 1

10x + 26y = 434  ...eq 2

Solving both eq 1 and 2 using calculator.

x = 7 and y = 14

Thus, the cost of a book bought by Russell is found in in dollars is $7.

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The scenario is best represented by a discrete or continuous domain is

a. discrete

b. continuous

c. discrete

d. continuous

e. discrete

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Based on the price of the hats and the new price after the discount, the percent discount is 15%.

What is the Percentage discount?

Discount refers to the condition of the price of a bond that is lower than the face value. The discount equals the difference between the price paid for and its par value.

Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.

To find the discount, use the formula:

= (Difference between price before discount and price after discount) / Initial price of hat x 100%

According to the given values,

Solving gives:

= (34.99 - 29.99) / 34.99 x 100%

= 15%

In conclusion, the approximate percent discount is 15%.

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The solution of the given linear equations is (x,y) = (1,-1).

The given linear equations are

8x + 3y = 5 - - - ( 1 )

3x - 2y = 5 - - - ( 2 )

As the RHS of both equations is equal, equating the LHS of both equations, we get,

8x + 3y = 3x - 2y

⇒ 8x - 3x = - 2y - 3y

⇒ 5x = - 5y

⇒ x = - 5y ÷ 5

⇒ x = - y

By substituting x = - y in equation ( 1 ), we get,

8x + 3y = 5 - - - ( 1 )

⇒ 8 ( - y ) + 3y = 5

⇒ - 8y + 3y = 5

⇒ - 5y = 5

⇒ y = - 5 ÷ 5

⇒ y = - 1

Now,

x = - y

⇒ x = - ( - 1 )

⇒ x = 1

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A horizontal straight line at the -7 point.

A straight line can be formed between two points also but both ends extend to infinity.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point.

A straight line does not have any curve in it. It can be horizontal, vertical, or slanted. If we draw an angle between any two points on a straight line, we will always get a 180-degree.

With no other values other than -7, the only value possible must be -7. Thus, we get a straight line.

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The vertex of the equation y = x² + 2x -3 is (-1, -4).

The term vertex in math is known as a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet.

Here we have the expression y = x² + 2x -3

As we all know that the given equation of parabola is written as,

=> y = ax² + bx + c

As we all know that the vertex of the parabola is given by (h, k).

Here we have calculated the value of the x coordinate of vertex as ,

=> h = -b/2a

And the value of y coordinate of vertex k by using the formula,

=> k  = y(h)

Through the given equation we have identified the value of a = 1, b = 2 and c = -3

Then the value of x coordinate is calculated as,

=> h = -2/(2 × 1)

Therefore, the value of h is -1

Then the value of y coordinate is calculated as,

=> k = y (-1)

Here we have to substitute -1 in the equation, then we get

=> k = (-1)2 + 2(-1) - 3

=> k = 1 - 5 = -4

Hence the coordinate of the vertex is (-1, -4).

Complete Question:

Where is the vertex of the parabola of the equation y = x² + 2x -3?

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A fraction share that Tiana share with her brother called half part. This because the part is split into two where the first part is called first half and other called as second half.

To name a piece of an object that split into several you have to:

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The two triangles in this problem are not similar, as they do not have congruent angle measures.

Similar triangles are triangle that share these following two features:

The angle measures for each triangle are given as follows:

As the triangles have different angle measures, they are not similar.

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Domain and range of a square root of a quadratic function is as [ 0, ∞ ) , and  [ 0 ,∞ ) respectively which is find by simplification.

Let us consider a square root quadratic function y = √x.

Domain of a square root quadratic function is :

All input values of x are domain of a function.

y = √x

⇒ x = y²

⇒ x ≥ 0

All the input values representing the domain are x > 0.

This implies domain is [0 , ∞ ).

And range of a square root quadratic function is:

All output values of y are range of a function.

y = √x

As we know x = y²

√y² = y > 0 .

Range is [ 0, ∞ ).

Therefore, domain and range of square root of a quadratic function is calculated by simplifying the function.

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ok

0 is the smallest value or X is the smallest value

An x-y (or bivariate) plot is any graph or plot with two axes. The "x-axis" is typically the horizontal axis, whereas the "y-axis" is typically the vertical axis.

Your plot's axes should be identified, and the scale should be chosen (if the graph is not already labeled). Plot the first two pairs of numbers first (the top row of numbers).

Finding the number a on the horizontal, or x-, axis and tracing up or down from there while maintaining a parallel path to the vertical, or y-, axis, will allow you to draw the point at (a, b) on the Cartesian plane.

The position of the point is this area (a, b). The intersection of the two axes defines the plane's center. It is referred to as the beginning or point (0,0).

Each axis is further subdivided into equal units starting at the origin: rising, positive numbers on the x-axis and up the y-axis; falling, negative numbers on the x-axis and down the y-axis.

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Answer:

Step-by-step explanation:

-4,+ infinity symbol which I can’t find

16x - 4y = 12

4x - y = 3

4x = 3+y

x= 3+y/4

for y = 1

x= 3+1/4 = 1

y = 2

x=3+2/4 = 5/4 = 1.25

y = 3

x = 3+3/4 = 6/4 = 1.5

Answer:

cindy is 51

Step-by-step explanation:

70 divided by 2 is 45

45+ 6 is 51

The area will be 1/4 of the original.

The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.

The area of all shapes is determined by their dimensions and attributes. Different shapes have various areas. The perimeter of a shape is defined as the total distance around the shape.

Given that,

[scale factor]=1/2

[dilated area of circle]=[original area of circle]*[scale factor]²

so

[dilated area of circle]=[original area of circle]*[1/2]²

[dilated area of circle]=[original area of circle]*[1/4]

Thus, The area will be 1/4 of the original.

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Five rays from common endpoints or vertex form 10 distinct angles.

Angles are constructed when two lines intersect at a point. The measurement of the 'opening' between these two rays is called an 'angle'. The symbol represents it ∠. Angles are usually measured in degrees and radians, which is a measurement of circularity or rotation.

In geometry, an angle is constructed when two rays are joined at their endpoints. These rays are named the sides or arms of the angle.

The arms and the vertex are two primary parts of an angle.

The two rays which converge at a common point to create the angle are called the arms of the angle.

Vertex is a common endpoint that is shared by the two sides.

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The solution of the system by using elementary row operations on the equations or on the augmented matrix following systemic elimination procedure is x1 = −8 and x2 = 3.

The complexity of the algebra required to solve a linear system rises as the number of equations and unknowns grows. By streamlining the nomenclature and standardizing processes, the necessary computations may be made easier to handle.

The procedures listed below should be followed in order to solve a system of linear equations using the row operations:

1. As a matrix equation, write the equations as AX = B.

2. Create an augmented matrix by converting the matrix equation to the following form: [A | B] (the word "augmented" refers to the vertical line we create to remind us where the equals sign belongs).

3. Reduce the augmented matrix using row operations to arrive at the answer.

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Lance and Alberto cycled along the same 75 km route. Speed of Alberto is 30 km/ hr

Since, Lance takes 3 hours to complete 75km, his speed will be

v= [tex]\frac{75}{3}[/tex]

v= 25 km/hr

The amount of time taken by Lance to complete 10 km is

t= 10/25

t =0.4 hr

t= 0,4×60 min

t=24 min.

Since Alberto started 4 min late and  time taken by Alberto to complete 10 km is

t= 24-4

t=20 min.

Hence, speed of Alberto is v=10/0.33

v=30 km/hr.

A measure of how quickly something is moving is speed. The distance an object travels in a single time unit is its speed. The speed formula is: Distance times speed. Meters per second (m/s), kilometres per hour (km/h), and miles per hour (mph) are the most common units of speed.

Speed is calculated by dividing distance by time. You must be familiar with the distance and time units in order to determine the units of speed. The units will be measured in meters per second (m/s) because distance is measured in meters (m) and time is measured in seconds (s).

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To see the steps of linear and non linear system of equation.

Now, According to the question:

Steps to solve non linear equation are:

To solve a system of linear equations using substitution:

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It is option D (f-¹ (x) = x-3/5