A soccer team purchased a set of team balls for $184.64. If each ball cost $11.54, how many balls were purchased?
O 13 balls
O 14 balls
O 15 balls
O 16 balls

The area of the given figure is 68.6

From the question, we are to determine the area of the given figure.

Area of the given figure = Area of the semicircle + Area of the rectangle + Area of the semicircle

Area of a semicircle = 1/2πr²

Where r is the radius

Area of a rectangle = Length × Width

From the given diagram,

The diameter of the semicircle is 4

Thus,

Radius, r = 4/2 =

r = 2

Length of the rectangle is 14

and the width of the rectangle is 4

Therefore,

Area of the figure = 1/2π(2)² + 14 × 4 + 1/2π(2)²

Area of the figure = 1/2π×4 + 14 × 4 + 1/2π×4

Area of the figure = 2π + 56+ 2π

Area of the figure = 4π + 56

Area of the figure = 68.566

Area of the figure ≈ 68.6

Hence, the area is 68.6

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Answer:

5/6

Step-by-step explanation:

he class ate 3/41 = <<3/41=3/4>>3/4 of one pan of plain brownies

They also ate 1/61 = <<1/61=1/6>>1/6 of another pan of plain brownies

The total amount of plain brownies they ate is 3/4 + 1/6 = <<3/4+1/6=5/6>>5/6

The class ate 5/61 = <<5/61=5/6>>5/6 of one pan of brownies with sprinkles

They also ate 1/101 = <<1/101=1/10>>1/10 of another pan of brownies with sprinkles

The total amount of brownies with sprinkles they ate is 5/6 + 1/10 = 5/6 + 1/10 = 41/60

The class ate more plain brownies because 5/6 > 41/60. Answer: {5/6}.

Applying the triangle midsegment theorem, the length of HJ is: 8 units.

The triangle midsegment theorem states that when a line connects the midpoints of two sides of a triangle, it is parallel to the third side and also has a length that is half of the length of the third side.

In the image attached below, segment LK is a midsegment of the triangle which is parallel to a third side, segment HJ.

Therefore:

LK = 1/2(HJ) [triangle midsegment theorem]

Substitute

4 = 1/2(HJ)

Multiply both sides by 2

4 × 2 = 1/2(HJ) × 2

8 = HJ

Length of HJ = 8 units.

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The polynomial y = (4 / 3) · x³ + (16 / 3) · x² + (4 / 3) · x - 8 is the cubic equation whose zeros are x₁ = -3, x₂ = - 2, x₃ = 1 and intercept is - 8.

Herein we must derive a cubic equation such that the zeros are x₁ = -3, x₂ = - 2, x₃ = 1 and its intercept is - 8. Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, where a, b, c, d are real coefficients.

If we know that (x₁, y₁) = (- 3, 0), (x₂, y₂) = (- 2, 0), (x₃, y₃) = (1, 0) and (x₄, y₄) = (0, - 8), then we solve the following system of linear equations to determine all real coeffcients by numerical methods:

- 27 · a + 9 · b - 3 · c + d = 0

- 8 · a + 4 · b - 2 · c + d = 0

a + b + c + d = 0

d = - 8

(a, b, c, d) = (4 / 3, 16 / 3, 4 / 3, - 8)

The cubic equation is y = (4 / 3) · x³ + (16 / 3) · x² + (4 / 3) · x - 8.

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Answer: 52

Step-by-step explanation:

    To find the range of a data set, we subtract the smallest value from the largest value.

54 - 2 = 52

The remaining material for sewing is 5/2 material.

Fractions are used to represent smaller pieces (or parts) of a whole.

Given that, Keith buys 3 yards of material to make a blanket. He trims off a total of 1/6 yard before he begins sewing.

1/6 of 3 = 3x1/6 = 1/2

The remaining material = 3-1/2

= 5/2

Hence, The remaining material for sewing is 5/2 material.

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Answer:

MAY BE IT'S HELP UHHH=^._.^

Answer:

The answer to the expression 3(6x-4y)-5 is 18x - 12y - 5. This is the result of following the order of operations and performing the necessary operations in the correct sequence.

Step-by-step explanation:

To solve this problem, you need to follow the order of operations, which is a set of rules that dictate the sequence in which operations should be performed in a mathematical expression to get the correct result. The order of operations is often abbreviated using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

According to the order of operations, the first step in solving this problem is to evaluate anything inside parentheses. In this case, there are no parentheses, so we can move on to the next step, which is to evaluate any exponents. Again, there are no exponents in this expression, so we can move on to the next step, which is to perform any multiplication or division.

In this case, there is a multiplication operation: 3 * (6x - 4y). So we need to evaluate this first. To do that, we need to multiply 3 by each of the terms inside the parentheses: 3 * 6x and 3 * -4y. This gives us 18x - 12y.

Now that we have performed all of the multiplication and division operations, we can move on to the final step, which is to perform any remaining addition or subtraction operations. In this case, there is only one subtraction operation: 18x - 12y - 5. So we need to subtract 5 from 18x - 12y to get our final answer: 18x - 12y - 5 = 18x - 12y - 5.

Therefore, the result of evaluating the expression 3(6x-4y)-5 is 18x - 12y - 5. I hope this helps! Let me know if you have any other questions.

The solution is

a) The slope/rate of change between the inputs in m = -1/2

b) Slope/rate of change between the domain values of 4 and 8 is m = -1/2

c) The slope/rate of change is constant

d) The function is a linear function

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be = A

Now , the value of A is

a)

when the inputs are 0 and 4 , the values of x = 0 and x = 4

So , the values of y = 5 and y = 3 respectively

Let the first point be P = P ( 0 , 5 )

Let the second point be Q = Q ( 4 , 3 )

Now , the slope of the line between the two points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 3 - 5 ) / ( 4 - 0 )

Slope m = -2/4

Slope m = -1/2

So , the slope of the line m = -1/2

b)

when the domain values are 4 and 8 , the values of x = 4 and x = 8

So , the values of y = 3 and y = 1 respectively

Let the first point be Q = Q ( 4 , 3 )

Let the second point be R = R ( 8 , 1 )

Now , the slope of the line between the two points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 1 - 3 ) / ( 8 - 4 )

Slope m = -2/4

Slope m = -1/2

So , the slope of the line m = -1/2

c)

The slope of the line m = -1/2 and it is constant

d)

The function is a linear function and the equation of line is given by

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 5 = -1/2 ( x - 0 )

On simplifying the equation , we get

y - 5 = -1/2 ( x )

Adding 5 on both sides of the equation , we get

y = ( -1/2 )x + 5

Therefore , the equation of line is y = ( -1/2 )x + 5 and it is linear

Hence , the equation of line is y = ( -1/2 )x + 5 and it is linear where the slope of the line is m = -1/2

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The solution is

A) The domain to plot the growth function is Domain = [ 0 , 8 ]

B) The y-intercept of the graph of the function f ( a ) is f ( 0 ) = 3 cm

C) The average rate of change of the function f ( a ) from m = 2 to m = 8 is given by T = 0.4022 cm per month

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Now , the value of A is given by

f ( a ) = 3 ( 1.09 )ᵃ

A)

To find the domain of the function f ( a )

The length of the fish was approximately 5.98 cm

So , substituting the value of f ( a ) as 5.98 cm , we get the value of m,

And , f ( a ) = 5.98 cm

So , 5.98 = 3 ( 1.09 )ᵃ

Solving for a , we get

Divide by 3 on both sides of the equation , we get

1.9933 = ( 1.09 )ᵃ

a = 8

So , the value of a is 8

So , the domain of the function is [ 0 , 8 ]

B)

The y-intercept of the graph is given by substituting the value of a = 0,

So , f ( a ) = 3 ( 1.09 )ᵃ

when a = 0 , we get

f ( 0 ) = 3 ( 1.09 )⁰

f ( 0 ) = 3 cm

Therefore,  the value of f ( 0 ) = 3 cm

C)

The average rate of change from m =2 to m = 8 is given by the equation ,

when m = 2 ,

f ( a ) = 3 ( 1.09 )ᵃ

f ( 2 ) = 3 ( 1.09 )²

f ( 2 ) = 3 x 1.1881²

f ( 2 ) = 3.5643

And , when a = 8

f ( a ) = 3 ( 1.09 )ᵃ

f ( 8 ) = 3 ( 1.09 )⁸

f ( 8 ) = 3 x 1.99256

f ( 8 ) = 5.97768

So , the average rate of change is the slope of the graph

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope = f ( 8 ) - f ( 2 ) / ( 8 - 2 )

Slope = ( 5.97768 - 3.5643 ) / 6

Slope = 2.4133879 / 6

Slope = 0.40223 cm per month

Therefore ,

The average rate of change of the function f ( a ) from a = 2 to a = 8 is given by T = 0.4022 cm per month

Hence ,

A) The domain to plot the growth function is Domain = [ 0 , 8 ]

B) The y-intercept of the graph of the function f ( m ) is f ( 0 ) = 3 cm

C) The average rate of change of the function f ( m ) from m = 2 to m = 8 is given by T = 0.4022 cm per month

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Answer:

D

Step-by-step explanation:

[tex]m\angle BCA+m\angle ACD=180^{\circ} \\ \\ 2x-5+3x+10=180 \\ \\ 5x+5=180 \\ \\ 5x=175 \\ \\ x=35 \\ \\ \\ m\angle ACD=3(35)+10=115^{\circ}[/tex]

Answer:

Step-by-step explanation:

[tex]\sqrt{2x+1} = -4 -1[/tex]

[tex]\sqrt{2x-1} = -5[/tex]

the number under a square root is always 0 or a positive number, so it can’t be equal to a negative number

The value of x and y are 3 and 11.

What is the congruent triangle?

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

Given that,

△LMN = △PQR

Thus ∠L = ∠P, ∠M = ∠Q, and ∠N = ∠R.

Also,  ∠L = 40°, ∠M = 90°, ∠P = (17x − y)°, ∠R = (2x + 4y)°.

The sum of interior angles of a triangle is 180°.

∠L + ∠M + ∠N = 180°

40° + 90° + ∠N = 180°

∠N = 50°.

Therefore,

17x − y = 40   .....(i)

2x + 4y = 50  .....(ii)

Multiply equation (i) with 4 and add with equation (ii)

68x - 4y = 160

2x + 4y = 50

_________

70x     = 210

x = 210/70

x = 3

Putting x = 3 in equation (ii)

6 + 4y = 50

4y = 44

y = 11

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Answer:

The missing term in the output of the function [tex]g(f(x))[/tex] is -18.

[tex]g(f(x))=10x^2-18[/tex]

Step-by-step explanation:

In mathematics, function composition is a term that encompasses a relationship between two functions wherein the output of one function is used as the input for another function. This relationship combines two functions to form a single function, known as a composite function. For future reference, function composition may also be denoted by a small circle, see below:

[tex](g\circ f)(x)=g(f(x))[/tex]

In the given problem, we must evaluate the composite function [tex]g(f(x))[/tex] / [tex](g\circ f)(x)[/tex] to identify the unknown term.

With composite functions, we begin evaluating from the inside. To evaluate [tex]g(f(x))[/tex], we must substitute the output of the function [tex]f(x)[/tex] (given as the expression [tex]2x^2-5[/tex]) as the input ([tex]x[/tex]) for the function [tex]g(x)[/tex]:

[tex]g(f(x))=g(2x^2-5)[/tex]

Now, using [tex]f(x)[/tex] as the input ([tex]x[/tex]) for the function [tex]g(x)[/tex] (given as the expression [tex]5x+7[/tex]), we can substitute [tex]2x^2-5[/tex] into the output for the function [tex]g(x)[/tex]:

[tex]g(f(x))= 5(2x^2-5)+7[/tex]

From here, we can go ahead and distribute the 5:

[tex]g(f(x))=10x^2-25+7[/tex]

Combine like terms:

[tex]g(f(x))=10x^2-18[/tex]

With the composite function evaluated, we can identify our missing term as [tex]-18[/tex].

Answer:

x = 2

<1 = 28

Step-by-step explanation:

The two angles equal each other.

4x + 20 = 5x + 18  Subtract 4x from both sides

20 = x + 18  Subtract 18 from both sides

2 = x

4x + 20

4(2) + 20

8 + 20

28

Answer:

57 years old

Step-by-step explanation:

Bob=31

Mark= 31 x 2 - 5

31 x 2= 62

62- 5 = 57

Mark is 57 years old

Answer:

Mark is 18

Step-by-step explanation:

The triangle has three side x,y and √(x²+y²), the slope of x is zero, the slope of y is undefined, the slope of √(x²+y²) is tanα. The coordinate of the midpoint of x is x/2,0 and y is 0, y/2

suppose the triangle is right-angled and the sum of other two angles are also 90 degrees. we know that the side opposite to the right angle is called hypotenuse. let the other two side is denoted by x and y. Now, x is the base of triangle, and the rest of the side is y. The angle between hypotenuse and base is denoted by α . As per Pythagorean theorem, hypotenuse = √(x²+y²).

slope can be calculated by tanα or using the formula (y₂-y₁)/(x₂-x₁)

according to trigonometric ratio, tanα = opposite side/base = x/y

 tanα is the slope of hypotenuse.

the side length x is along the horizontal axis, so its y coordinate is zero and slope is also zero.

the side length y is along the vertical axis whose x coordinate is zero that means slope is undefined.

As per the formula (y₂-y₁)/(x₂-x₁) used to calculate slope, whenever x coordinate is zero the result is written as undefined.

hence, the triangle is right-angled, and the biggest side has a slope only.

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Answer:A

Step-by-step explanation:

The possible lengths of the side x + 30 are given as follows:

199.5 - x ≤ x + 30 ≤ 399 - x.

The perimeter of a rectangle of base b and height h is given by the equation presented as follows:

P = 2(b + h).

The dimensions in the triangle in this problem are given as follows:

The budget allows for at least 399 feet of fencing, hence:

2(x + x + 30) ≥ 399

x + x + 30 ≥ 199.5.

x + 30 ≥ 199.5 - x.

The budget allows for no more than 798 feet to be used, hence:

2(x + x + 30) ≤ 798

x + x + 30 ≤ 399

x + 30 ≤ 399 - x.

Then the range of values that can be assumed by the side with dimensions x + 30 is given as follows:

199.5 - x ≤ x + 30 ≤ 399 - x.

The park has a rectangular format, with dimensions x and x + 30.

It asks for the possible lengths of the side with dimensions x + 30.

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Answer:

Step-by-step explanation:

2, i would eat there sometimes!

Answer:

3. I would eat there rarely.

Step-by-step explanation:

Please give brainliest!!!

In a triangle, The value of ''h'' will be;

⇒ h = 2.7 m

What is mean by proportion?

A proportion is a fraction of a total amount, in which two ratios are set equal to each other.

Given that;

The triangle is right triangle.

The values are,

AB = 6 m

BD = 12 m

BC = 0.9 m

DE = h m

Now,

Since, The triangle is right triangle.

Hence, By using definition of proportional we get;

⇒ AB / BC = AD / ED

Substitute all the values, we get;

⇒ 6/0.9 = (6 + 12) / h

⇒ 6 / 0.9 = 18 / h

⇒ h = 18 × 0.9 / 6

⇒ h = 2.7 m

Thus, The value of h = 2.7 m

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Step-by-step explanation:

because it is an isoceles triangle (both legs are equally long), E and F are the side angles in the baseline.

and because both leg sides are equally long, also both side angles must be equally large

therefore,

angle E = angle F = 55°.

Answer:

Given that,

We know that

Work = Force × distance

So, the force = work ÷ distance

= 28 ÷ 4

Therefore we can conclude that the force that he used is 7 newtons.

Answer:

-3

Step-by-step explanation:

A (0,2)

B (2,-4)

slope = (-4-2)/(2-0)

-6/2

-3

a parallel line has the same slope

The integral of f (z) around the positively oriented circle |z|

[tex]\int\limits^_ {} \,[/tex]f(z) dz = -8πi/3

In mathematics, an integral lends numerical values to functions to represent notions like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.

With the exception of the point where z = z, where f(z) is analytic within and on C, let C be the smooth, simple closed curve except at z =z , then ,

[tex]\int\limits^_ {} \,[/tex] f(z) dz = 2πi [ res f(z)] z = [tex]z_{1}[/tex]

here f(z) is singular at z = -1,

res  [tex]f(z)_{z = -1}[/tex] = [tex]\lim_{z\to \-1} z+1 f(z)_[/tex]

[tex]\lim_{z\to \-1}[/tex] [tex]z^{3}[/tex](1-3z)/(1+2[tex]z^{4}[/tex])

when z = -1 then f(z) = -4/3

Therefore [tex]\int\limits^_ {} \,[/tex]f(z) dz = 2πi (-4/3)

[tex]\int\limits^_ {} \,[/tex]f(z) dz = -8πi/3.

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Answer: The equation for simple interest is:

Future interest = Principal*(interest rate*number of years). Remember to write the interest rate of 1.25% as 0.0125 (rather than directly as 1.25)

812.50 = x(0.0125*20)

812.5 = x(0.25)

x = $3250

This means that Samson deposited $3250 when he opened the account.

Step-by-step explanation:

Answer:

------------------------------

The volume will remain constant if both input and output cross - sections are equal:

Among any group of d+1 integers there are two with exactly the same remainder when divided by d.

Positive integers are those bigger than 0 that don't contain any fractional portions. On the number line, these figures are located to the right of 0.

Since it is neither positive nor negative, 0 is not a positive integer. Positive integers are defined as numbers greater than 0 in mathematics.

The possible remainders after dividing an integer by d are 0, 1, 2,..., d-1.

The number of remainders that can be obtained is d, or |0, 1, 2,..., d-1|=d0,1,2,...,d-1=d.

According to the Pigeonhole Theory:

objects are the number of integers in d+1.

"holes" = "remainders" + "d"

[d+1/d]=2

According to the Pigeonhole Principle, there are always two d+1 integers in every group that have precisely the same residual after being divided by d.

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There are always two d+1 numbers in any group that have the exact same residual after division.

An integer, pronounced "IN-tuh-jer," is an entire number which can be positive, minus, even zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, among 3,043. 1.43, 1 3/4, 3.14, and other values which aren't integers seem to be some examples.

The potential remainders after dividing an integer by d are 0, 1, 2,..., d-1.

The possible number of remainders is d, or I{0,1,2,.......d-1}I = d

By the Pigeonhole Principle:

Objects = umber of integers = d+1

Holes = number of remainders = d

[tex]\frac{d+1}{d} = 2[/tex]

According to the Pigeonhole Principle, there are always two d+1 numbers in every group that have precisely the same residual after being divided by d.

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Answer:

4%

Step-by-step explanation:

2/50= 4/100
4/100= 0.04 or 4%