The cost of holding a children’s birthday party at a roller rink is a function of n , the number of people in the party . The cost , c , can be represented with this set of rulesB . Which graph represents the function on the coordinate plane

Line Segment has 2 end points.

Building a line segment of a specified length involves the following stages.

First, draw a line.

Step 2: Pick any point on the line where point A is.

Step 3: Keep one end of the compass on the 0 cm mark at the specified length of the rule to extend it.

Step 4: Draw an arc on the line while maintaining the compass' pointed end on point A.

Make B the arc point.

In this way we can construct any line segment of given length using compass and scale.

Line Segment has 2 end points.

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All the options that result in (x + 4 ) (x 4 ) = 0 being true are the ultimate answer and x = − 4 , 4.

Here, x²-16=0

rewrite 16 as 4²

then, (x+4)(x-4)

Any factor on the left side of the equation that is equal to 0 will make the entire expression equal to 0.

x+4=0 and find x

Then x=-4

x-4=0 and find x

x=4.

Hence, All the options that result in (x + 4 ) (x 4 ) = 0 being true are the ultimate answer and x = − 4 , 4.

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Answer:

B. 1 & 1  

C. 5 & 3

D. 2 & 2

E. 4 & 0

Something interesting about these was me having to just use simple and smaller numbers to complete the equations.

Answer:

answers is in attached picture.

Step-by-step explanation:

The expression representing the height of the box is the difference between the length and width of the box, which is equal to x subtracting two, or x – 1.

The expression representing the height of the box can be determined by subtracting the width of the box from the length. The length of the box is x 6, and the width is x – 2. To calculate the height, we subtract the width from the length: x – (x – 2) = x – x + 2 = 2. Therefore, the expression representing the height of the box is x – 1. This indicates that the height of the box is equal to the length of the box minus one. This calculation can be applied to any rectangular prism to calculate the height.The volume of the box is represented by the function f(x) = x3 5x2 – 8x – 12. To calculate the volume, we can substitute the length and width into the function:

f(x) = (x – 6)(x – 2)(x – 1) = x3 – 8x2 + 11x – 12.

Therefore, the volume of the box is x3 – 8x2 + 11x – 12.

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The number of solutions that are to the system of equations is (a) one

From the question, we have the following parameters that can be used in our computation:

The graph

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the lines intersect at (3, 1)

Hence, the solution is (3, 1) ie. one solution

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Answer:

y = 3x + 5

Step-by-step explanation:

The slope-intercept form of a line is [tex]y = mx + b[/tex], where m is the slope, and b is the y-intercept.

To solve for m (the slope), use the formula: [tex]m = \frac{y__{2} - y__{1}}{x__{2} - x__{1}}[/tex], where [tex](x_{1} , y_{1} )[/tex] and [tex](x_{2}, y_{2})[/tex] are the points you are given.

. . . . . . . . m = (17 - 11) / (4-2)

. . . . . . . . m = 6/2

. . . . . . . ∴ m = 3

Substitute the slope, m, into the slope-intercept equation.

y = 3x + b

Now we have to solve for b, the y-intercept. To do so, substitute a point that was given to you into the equation.

I chose the point (4,17), but you can also do (2,11).

. . . . . . . . 17 = 3(4) + b

. . . . . . . . . . remember that the x-variable is being multiplied to the m

. . . . . . . .  -12 + 17 = 12 + b - 12

. . . . . . . .  ∴ 5 = b

Substitute the y-intercept, b, into the slope-intercept equation, and you're done!

[tex]y = 3x + 5[/tex]

The unit rate of bananas is $2.25 per pound.

What is the meaning of unit rate?

Unit Rate = Ratio between two separate quantities with different units. = a:b. = a/b. This formula can be used to determine the rate of any two given quantities, such as a and b.

Given that the cost of 2/3 pound of bananas is $1.50.

If the number of pound of bananas increase then the cost of bananas will be increase.

So the relation between amount of banana is directly proportion with the cost.

Therefore,

Amount of bananas/ cost of bananas = Amount of bananas/ cost of bananas

(2/3)/1.50 = 1/x

2/4.50 = 1/x

x = 4.50/2

x = 2.25

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The cost of 1 oz is $0.10625

From the question, we have the following parameters that can be used in our computation:

If there is $0.85 for 8 oz

This means that

The cost of 8 oz = $0.85

Assume there exist a proportional relationship between the cost and the size i.e. oz

The cost of 1 oz can be calculated using the following equation

The cost of 1 oz = $0.85/8

Evaluate the quotient

The cost of 1 oz = $0.10625

Hence, the cost of 1 oz is $0.10625

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The formula used to calculate the solving the volume of the rectangular prism is equal to ( length × width × height ).

As given in the question,

Given base of the prism is rectangular in shape ,

Area of the base with rectangular base is given by :

area of the rectangle = length × width

Volume of the rectangular prism = base area × height

⇒Volume of the rectangular prism = ( length × width ) × height

Therefore, the formula required to calculate the volume of the rectangular prism is given by ( length × width × height ).

The above question is incomplete , the complete question is:

What is the formula in solving volume of the rectangular prism?

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−10p + 4q is equivalent to −2(5p − 2q).

Given data :

−2(5p − 2q)

= -2 x 5p -(-2p) x 2q)

= = 10p + 4q

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The pair of equations y = -3 and y = 0 have No Solution .

The pair of equations is given as y = 0 and y = -3 .

In order to find number of solutions of the equations ,

we use the graphical method ,

the graph of the equation y = 0 is x axis .

and the graph of the equation y = -3 is a straight line that is parallel to the x axis , as shown in the figure below .

From the graph drawn below , we can see that the two lines are parallel and

We know that , when two lines are parallel they have No Solution .

Therefore , given pair equations have No Solution .

The given question is incomplete , the complete question is

How many solutions does a pair of equations y = -3 and y = 0 has ?

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Answer:

looooookkkkkk at the picture

Answer:

2x² - 20x - 32 = 0

Step-by-step explanation:

Trip upstream:

distance = 10 km

time = t

current = 4 km/h

speed of boat in still water = x

speed upstream: x - 4

speed = distance/time

distance = speed × time

10 = (x - 4) × t

10 = tx - 4t

t(x - 4) = 10

t = 10/(x - 4)

Trip downstream:

Distance = 10 km

time = 2 - t

current = 4 km/h

speed downstream = x + 4

speed = distance/time

distance = speed × time

10 = (x + 4) × (2 - t)

10 = 2x - tx + 8 - 4t

10 = 2x - 10x/(x - 4) + 8 - 40/(x - 4)

10(x - 4) = 2x(x - 4) - 10x + 8(x - 4) - 40

10x - 40 = 2x² - 8x - 10x + 8x - 32 - 40

2x² - 20x - 32 = 0

Since in [tex]y^{2} x^{2} 16[/tex] , there is no "=" sign in the given expression so we can conclude that given expression is not a function.

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You may think of expressions as being comparable to phrases.

Expression=[tex]y^{2} x^{2} 16[/tex]

Since there was not "=" sign in the given expression so output can't be achieved for any given inputs so we can conclude that the given expression is not a function.

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It is true that Sarah's maximum heart rate over this twenty-year period will have decreased by approximately 8%.

The percentage decrease is determined by ascertaining the reduction or difference in heart rate at the beginning and at forty.

This difference becomes the numerator of the division operation by the heart rate at the beginning and then multiplied by 100.

Sarah's heart rate at twenty years = 193 beats per minute

Sarah's heart rate at forty years = 178 beats per minute

Difference (Decrease) in heart rate = 15 beats per minute (193 - 178)

Percentage decrease = 7.77% (15/193 x 100)

= 8%

Thus, we can conclude that Sarah's heart rate has decreased by about 8%.

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Properties of equilateral triangles are:

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The ratios of win to lose are 13 : 8, 13/8 and 1.625%

From the question, we have the following parameters that can be used in our computation:

Win = 50 more than lose

Win = 130

This means that

Win = 50 + Lose

So, we have

50 + Lose = 130

Evaluate

Lose = 80

The ratio is then represented as

Ratio = win to lose

This gives

Ratio = 130 : 80

So, we have

Ratio = 13 : 8

Express as fraction

Ratio = 13/8

Lastly, we have

Ratio = 1.625%

Hence, the ratio is 1.625%

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Answer:  3.6y^2

Step-by-step explanation:

To calculate this, you simply multiply the two numbers together: 1.2y * 3y = 3.6y^2.

Answer:

[tex] \sf \: c) \: 3.6 {y}^{2} [/tex]

Step-by-step explanation:

Now we have to,

→ find the product of 1.2y and 3y.

Forming the problem,

→ 1.2y × 3y

Then the product will be,

→ 1.2y × 3y

→ (1.2 × 3)(y × y)

→ (1.2 × 3)y²

→ (3.6)y²

→ 3.6y²

Hence, the answer is 3.6y².

Considering the definition of parallel line, the equation of the line d is y= 3x -7.

A linear equation o line can be expressed in the form y = mx + b

where

Parallel lines are two lines that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts.

In this case, the line is y=3x-4

where:

Since two lines are parallel if they have the same slope, the parallel line has a slope of 3.

The line passes through the point (2, -1). Replacing in the expression for a line:

-1= 3× 2 + b

-1= 6 + b

-1 -6= b

- 7= b

Finally, the equation of parallel line is y= 3x -7.

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Exponential equation has tow major types

exponential decay

exponential growth

Exponent-based equations in which the exponent or a portion of the exponent is a variable are known as exponential equations.

This is a type of function that are of 3 main parts

the starting or initial value

base function

the exponents

Atypical example includes:  f(x) = 300(1.16)^x

the starting = 300

the base = 1.16

the exponents = x

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so forth.

The base is what determines exponential growth or decay

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'4 more than a number' implies that there exists a number which is 4 units greater than the original number, using the concept of addition.

Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").

Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.

Now, let us understand the meaning.

Let the original number be x.

'4 more than a number' implies x + 4.

This means that the new number, x + 4, is greater than the original number, x, by 4 units. We also have to keep in mind, [tex]x + 4 > x[/tex].

Hence, the final meaning is 4 units greater than the original number.

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When we multiply 4 with 4 we get 16 again

when we multiply (-4) with (-4) we get 16. so 16 has 2 square root.

There are always two solutions to the square root of a number: a positive response and a negative answer. Because the square of a negative and positive integer is the same, there are two possible solutions.

Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root is a value that, when multiplied by itself, returns the original value.

The values that result from multiplying an integer by itself are known as square numbers. Among the attributes are:

When we multiply 4 with 4 we get 16 again

when we multiply (-4) with (-4) we get 16. so 16 has 2 square root.

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58 is the number which would be much more than 23 is 9*9.

Here,

It is asked that how much more we need to add in 23 to get the value 9*9.

Here, 9*9 means we simply have to multiply 9 with 9 and we will get 81.

so, we know that

     9*9 = 81

Now, we have to find how much we need to substract in 81 to get the value as 23

     81-23 =58

when we deduct 23 from 81 then we get 58.

hence, 58 is the answer.

In this situation we just replace the much more word with subtraction to get the answer.

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Answer:

To find (g o f)(3), we need to first apply f to 3, which gives us f(3) = 3 * 3 - 2 = 7. Then we need to apply g to the result of f(3), which gives us g(7) = 7^2 = 49. Therefore, (g o f)(3) = 49, so the answer is c.

Step-by-step explanation:

It isometric to rotate, reflect, and translate. This indicates that the character size is unaffected by these modifications. If a form's size and shape have not altered, it is congruent.

A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.

If 3 sides are equal

then By SSS, its congruent

AB = DE = 12

BC = EF = 11

AC= DF = 10

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Answer:

8 minutes = 3 songs

Step-by-step explanation:

Time taken for 1 song is,

→ 72/27

→ 2.6667

→ ≈ 2.7 minutes

Then songs played in 8 minutes,

→ Total time ÷ Time for 1 song

→ 8 ÷ 2.7

→ 2.96296

→ ≈ 3 songs

Hence, the answer is 3 songs.

The graph of quadratic inequality when plotted represents the parabola.

The quadratic inequality will have a range of solutions, unlike the quadratic equation.

The quadratic inequality could be solved using factorization method for example

The quadratic inequality x²+6x+5 ≤0 can be solved by factorizing but instead of two solutions, there are a range of solutions.

For given equation we need to calculate value of x such that the graph is less than zero.

Hence solution to this inequality can be written as

−5≤x≤−1.

And the graph of given quadratic inequality represents the parabola.

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By simplifying [tex]\sqrt{75a^{8}b^{5} }[/tex], we get 5[tex]a^{4} b^{2}[/tex][tex]\sqrt{3b}[/tex].

What is square root?

A number can be obtained by multiplying the square root of that integer by itself. The word "square root" is represented by the symbol "sqrt"—square root of, end square root. The opposite of squaring an integer is finding its square root.

How to find square root?

[tex]\sqrt{75a^{8}b^{5} } =\sqrt{25*3*a^{4}*a^{4}* b^{2} *b^{2}*b }[/tex]

             =[tex]\sqrt{5*5*3*a^{2}*a^{2}*a^{2}*a^{2}*b^{2}*b^{2}*b }[/tex]

             =5×a×a×a×a×b×b[tex]\sqrt{3*b}[/tex]

             =5[tex]a^{4}b^{2}[/tex][tex]\sqrt{3b}[/tex]

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The roots of the quadratic equation x² + 2√3 x + 3 = 0 have only one root and it is -√3

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² + 2√3 x + 3 = 0   be equation (1)

On factorizing the equation , we get

The roots of the quadratic equations are calculated by

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

Substituting the values in the equation , we get

x = [ -2√3 ± √ ( ( 2√3 )² - 4 ( 3 ) ) ] / 2

On simplifying the equation , we get

x = [ -2√3 ± √ ( 12 - 12 ) ] / 2

The discriminant is zero we get just one real solution

So ,

x = [ -2√3 ± √0 ] / 2

x = ( -2√3 ) / 2

x = -√3

Therefore , the value of x is -√3

Hence , the root of the quadratic equation is -√3

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