The admission fee at a county fair is $2 for children and $4 dollars for adults. Suppose that on the last day, 1600 people enter the fair and $5000 is collected. Choose the two equations that can be solved as a system of equations to determine how many children and how many adults attended the fair.

1.) a-c=1600
2.) 4a+2c=5000
3.) 4a-2c=5000
4.) a+c=1600

Your answer would be B. (-1,5).

In order for the order pairs to be a function. All of the x coordinates must be different from each other, they can't be the same. There can't be any repeats of the x coordinates. But for the y coordinates, it's okay for them to be the same. The reason why you would eliminate (-1,5) is because there are 2 -1 x coordinates, and that would not make the ordered pairs a function. When you remove them, none of the x coordinates are the same anymore, so it would now be a function.

Hope this helps out :)

Answer:

Step-by-step explanation:

Which of these ordered pairs could you remove to make this relation a function? {(-2,1), (-1, -5), (-1,5), (0, -7), (2, 1)}

B. (-1, 5)

Answer:

[tex]C=9.4\pi[/tex] meters

Step-by-step explanation:

Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex].

We start by substituting 4.7m for r in the second circumference formula.

[tex]C=2\pi r\\C=2\pi (4.7)\\C=9.4\pi [/tex]. We input this value of r into the area formula.

Answer:

its C.

Step-by-step explanation:

Answer:

V = 1570.796327  cm^3

Step-by-step explanation:

V= pi *r^2h

diameter = 2 * radius

10 = 2r

r = 5

substitute in what we know

V = pi *( 5^2) * 20

V = pi * 25 * 20

V = pi *500

V = 1570.796327  cm^3

Answer:

Step-by-step explanation:

Surface Area of circle on top of cylinder:

= πr²

= π(d÷2)²

= π(10÷2)²

= π(5)²

= 25π

Volume of Cylinder:

= 25π × h

= 25π × 20

= 500π

= 1570.8 cm³ (to 1 decimal place)

Dani is correct. The equation can be written as y = 3x+50, which is a linear equation in the form y = mx+b. We have m = 3 as the slope and b = 50 as the y intercept

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

x is the number of square feet, y is the total cost in dollars

3*x or 3x repesents multiplying the cost per square foot ($3) by the number of square feet (x). For example, if you have 10 sq ft, then so far the cost would be 3*x = 3*10 = 30 dollars.

This result is then added to 50 to get the total cost. We say that 3x is the variable cost, as it changes or varies depending on how large x gets. Additionally, the 50 is the fixed cost because this cost stays the same no matter what x is

total cost = variable cost + fixed cost

y = 3x + 50

Answer:

The answer would be (6-2) +d

Step-by-step explanation:

That is the answer because first you subtract 6 from 2. You dont have a choice. Simplified it would be 4+d. Please give me brainliest

Answer:

The answer is 25 units

Step-by-step explanation:

Answer:

g(10) = -37

Step-by-step explanation:

g(x)= -4x+3

g(1) means evaluate when x=10

g(10) = -4*10 +3

g(10) = -4*10 +3

g(10) = -40+3

g(10) = -37

x + (x + 2) = 50

Combine like terms.

2x + 2 = 50

Subtract 2 from both sides.

2x = 48

Divide both sides by 2.

x = 24

Now that we have the value of x, we can find the value of the 2nd integer by adding 1 to the value of x.

24 + 1 = 25

Answer:

3x-21

Step-by-step explanation:

We want to distribute the 3

3(x-7)

3*x -3*7

3x-21

Hi there!

Answer:

3x-21

Step-by-step explanation:

Distributive property: a(b+c)=ab+ac

A=3, B=x, C=7

First, you expand.

3x-3*7

3*x=3x

3*7=21

3x-21

Final answer is 3x-21

Hope this helps!

Have a nice day! :)

:D

-Charlie

Thank you! :)

:D

the main difference between a square and a rectangle is that a square has all sides of equal length, while a rectangle has opposite sides of equal length and adjacent sides of different lengths.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

• Heptagon

• Octagon

• Nonagon

Given, a polygon is a square, then all 4 angles are right. If all 4 angles of a polygon are right, then it is a rectangle.

A square is a special case of a rectangle where all four sides are of equal length. So, a square is a rectangle with all right angles and all sides of equal length.

On the other hand, a rectangle is a four-sided polygon with all four interior angles equal to 90 degrees.

However, in a rectangle, the opposite sides are parallel, and the adjacent sides are of different lengths.

In summary, the main difference between a square and a rectangle is that a square has all sides of equal length, while a rectangle has opposite sides of equal length and adjacent sides of different lengths.

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Complete question:

If a polygon is a square, then all 4 angles are right. If all 4 angles of a polygon are right, then it is a rectangle. what is the difference between a square and a rectangle?

Answer:

Using the formula to calculate the area of a square, the side of the patio can be 11.4 ft.

Step-by-step explanation:

Square patio

Area: A=130 square feet= 130 ft^2

Side of the square: s=?

The formula to calculate the area of a square is:

A = s^2

Replacing A by 130 ft^2

130 ft^2 = s^2

Solving for s: Square root both sides of the equation above:

sqrt(130 ft^2) = sqrt(s^2)

11.40175425 ft = s

s = 11.40175425

Rounding to the nearest tenth:

s = 11.4 ft

To find the side length of a square given the area, take the square root of the area. So, the sides of Vince's patio will be approximately 11.4 feet long.

A square root is a mathematical operation that determines the value that, when multiplied by itself, equals a given number. It is denoted by the radical symbol (√). For example, the square root of 25 is 5, as 5 * 5 equals 25. Square roots are essential in various fields, including geometry, physics, and engineering, where they help calculate dimensions, solve equations, and analyze data. Square roots can be both real (positive or negative) and complex, depending on the input number.

To solve this problem, you need to understand that a square has four equal sides. The area of a square is calculated by squaring the length of one of its sides. So if we know the area, we can find the side length by taking the square root of the area.

Since Vince's area is 130 square feet, we calculate the square root of 130 which is approximately 11.4. Therefore, Vince can make each side of his patio 11.4 feet long, rounded to the nearest tenth.

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The Mathematics problem involves adding areas in different units and converting them appropriately. After conversion and addition, the correct answer from the options provided is 1 acre, 7 square feet, and 119 square inches: (a) 1a 7 sqft 119 sqin.

The subject of this question is Mathematics, specifically dealing with area measurements in different units and their conversions. The student needs to solve an addition problem that involves square yards, square feet, and square inches. To solve this problem, we must first understand that there are 9 square feet in one square yard, and we use this knowledge to convert all measurements to the same unit before summing them up.

To answer the student's question, we must add the areas given in the problem:

First, we convert square yards to square feet using the conversion 1 sq yd = 9 sq ft:

4,839 sq yd = 4,839 × 9 sq ft = 43,551 sq ft

Now we add the square feet:

43,551 sq ft + 8 sq ft + 7 sq ft = 43,566 sq ft

Lastly, we add the square inches:

139 sq in + 124 sq in = 263 sq in

Since there are 144 square inches in one square foot, we must convert the excess square inches into square feet and square inches:

263 sq in = 1 sq ft (144 sq in) + 119 sq in

Adding the converted square inches to the total square feet:

43,566 sq ft + 1 sq ft = 43,567 sq ft 119 sq in

Next, we convert the total square feet to acres, understanding that 1 acre = 4,840 sq yd or approximately = 43,560 sq ft.

43,567 sq ft ÷ 43,560 sq ft per acre ≈ 1 acre 7 sq ft 119 sq in

Thus, the correct answer is (a) 1a 7 sqft 119 sqin.

Complete question is here:

Solve the following problem 4,839 sq yd 8 sq ft 139 sq in + 7 sq ft 124 sq in Select one of four

a)1a 7 sqft 119 sqin

b)4a 10 sqft 145 sqin

c)3a B sqft 130 sqin

d)2a 9 sqft 150 sqin

The question asks for the addition of different area units, which requires unit conversion. Square yards are converted to square feet and then to square inches, ensuring all areas are in the same units before adding them together.

The question involves adding areas measured in different units (square yards, square feet, and square inches) and converting between these units. To perform the calculation correctly, we need to convert all areas to the same unit. One square yard is equivalent to 9 square feet, and one square foot is equivalent to 144 square inches. Thus, to add the areas given in the question, we should first convert the 8 sq. ft. 139 sq. in. to sq. in. by multiplying 8 by 144 and then adding 139. After that, we would need to convert this total area into square yards if required. For the second part, we convert 7 sq. ft. 124 sq. in. to square inches similarly. Once both areas are in square inches, they can be added together. Additionally, it's important to remember that there is no direct conversion between square inches and square yards, so a two-step conversion is needed via square feet.

Answer:

-71/15

Step-by-step explanation:

Order of operations rules require that we do any work enclosed in parentheses first.  Thus, we must evaluate -13÷3/5.  Multiplication and division can be done in either order, but for the sake of consistency, move from left to right:

-13÷3 comes out to -13/3.  Divide this result by 5, obtaining -13/15.

Then the original expression, −29−(−13÷3/5), becomes -29-(-13/15), or

-29 + 13/15.

Since -29 is negative and + 13/15 is positive, we must add 13/15 to -29:

-29

+13/15

----------

This is easily done if we rewrite -29 as -28 - 15/15.

Then we have:

-28 - 15/15 +13/15, which simplifies to -28 - 2/15, or -28 2/15.

As a single fraction, that would be -71/15.

Among the given equations, only 'y = 6/13x' shows a proportional relationship because the ratio between x and y remains constant. The other two equations-'y = x + 2.3' and '7 - y = 2x' are not showing proportional relationships because the ratio between the variables doesn't remain constant.

A proportional relationship is one where the ratio between two variables remains constant. This relationship can be represented by the equation y = kx, where k is the constant of proportionality.

a) The equation y = x + 2.3 is not a proportional relationship because it involves an added constant. If x is zero, y is not zero, thus it's not proportional.

b) The equation y = 6/13x is a proportional relationship, because there is a direct proportion between x and y. If x is multiplied by a certain factor, y will be multiplied by the same factor, thus maintaining the ratio.

c) The equation 7 - y = 2x rearranges to y = 7 - 2x, which is not a proportional relationship. Again, if x is zero, y is not zero, thus it's not proportional.

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Answer:

x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac} }{2a}[/tex]

Step-by-step explanation:

We have

7x²=9+x

Subtracting x from both sides, we get

7x²-x=9+x-x

Cancelling out +x and -x from the right side, we get

7x²-x=9

Subtracting 9 from both sides, we get

7x²-x-9=9-9

Cancelling out 9 and -9 from the right side, we have

7x²-x-9 = 0

The above equation is in the form ax²+bx+c=0 where upon comparing we get a= 7 , b = -1 and c= -9

We can solve for x using the below quadratic formula:-

x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac} }{2a}[/tex]

Upon solving we'll get two values for x, one positive an the other negative.

Answer:

A: 15.23 ft, B: 7.75 ft

Step-by-step explanation:

A:

√(14² + 6²)

√(196 + 36)

√232 = 15.23

B:

√(16² - 14²)

√(256 - 196)

√60 = 7.75

NOTES:

Since Q is a right angle then PQ and QR are the legs and PR is the hypotenuse.  Use the Pythagorean Theorem to solve.

********************************************************************************

Part A Answer: PR = 15.23

Step-by-step explanation:

PQ² + QR² = PR²

6² + 14² = PR²

36 + 196 = PR²

    232    = PR²

     15.23 = PR

************************************************************************************

Part B Answer: PR = 7.75

Step-by-step explanation:

PQ² + QR² = PR²

PQ² + 14² = 16²

PQ² + 196 = 256

PQ² = 60

PQ = 7.75

Answer:

(x - 2)² = 0

Step-by-step explanation:

given x² - 4x + 9 = 5 ( subtract 5 from both sides )

x² - 4x + 4 = 0

This is a perfect square of the form

(x - a)² = x² - 2a + a²

compare coefficients of the x-term

- 2a = - 4 ⇒ a = 2

⇒ (x - 2)² = 0 ← is the required form

Answer:

14 pieces

Step-by-step explanation:

We will divide 6 m into 3/7 m pieces

6 ÷ 3/7

Use copy dot flip

6 * 7/3 =

42/3

14

She will have 14 pieces

Answer:

Ram will get 10 chocolates

Step-by-step explanation:

It the chocolates are shared in the ratio of 1 to 3 then the total is 4

Ram : I

1:3  

1+ 3 = total

1+ 3 =4

Our total is 40, but the ratio stays the same, we just add the variable x to the 1 and the 3

1x+ 3x =40

Combine like terms.

4x = 40

Divide each side by 4

4x/4 = 40/4

x =10

So ram will get 1 * 10 = 10 and you will get 3 * 10 = 30

Answer:

(-4, 6), (0, 2), (4, -2)

Step-by-step explanation:

x + y = 2?

(-4, 6),   -4+6 = 2    True  this is a solution

(0, 2),    0+2  = 2    True  this is a solution

(4, 2);    4+2 = 6    False  this is not a solution

This is not a solution set since we have a pair that is not a solution

(-4, -6),   -4+-6 = 10  False  this is not a solution.  We do not have to check the rest since this cannot be a solution set

(0, 2),

(4, 2);

This is not a solution set since we have a pair that is not a solution

(-4, 6),  -4 + 6 = 2  True  this is a solution

(0, 2), 0 + 2 =2   True  this is a solution

(4, -2)  4-2 =2   True  this is a solution

This is a solution set since all the points are a solution

Answer:

(-4,6), (0,2), (4,-2)

Step-by-step explanation:

If you substitute the ordered pairs in the equation and all three of the ordered pairs in the list equals to 2 that is the list that represents the solution

By adding Janelle's spending to what she came home with and dividing by the hours worked, we find that she earned $8 per hour babysitting.

To find out how much Janelle made per hour babysitting, we need to add the money she spent at Walmart to the money she came home with.

This gives us the total amount she earned.

Since she spent $12 at Walmart and came home with $36, we add these two amounts together to get $48.

Janelle babysat for 6 hours, so to find out her hourly wage, we divide the total amount she earned ($48) by the number of hours she worked (6 hours).

= $48 / 6 hours = $8 per hour

Thus, Janelle earned $8 per hour for her babysitting.

Answer:

1A/3 OR 1/3A

Step-by-step explanation:

The cost of one doughnut is $0.75 and the cost of one cookie is $0.60.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Alexandra buys two doughnuts and three treats at a donut shop and is charged $3.30. Brianna buys five doughnuts and two treats at a similar shop for $4.95. Every one of the doughnuts and treats has a similar cost.

Assume 'x' is the cost of doughnuts and 'y' is the cost of one cookie. Then the equations are given as,

2x + 3y = 3.30         ...1

5x + 2y = 4.95        ...2

Multiply equation 1 by 5 and equation 2 by 2, then we have

10x + 15y = 16.50     ...3

10x + 4y = 9.90       ...4

Subtraction equation 2 from equation 1, then we have

15y - 4y = 16.50 - 9.90

11y = 6.60

y = $0.60

Then the value of 'x' is given as,

2x + 3(0.60) = 3.30

2x + 1.80 = 3.30

2x = $1.50

x = $0.75

The expense of one donut is $0.75 and the expense of one treat is $0.60.

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Answer:

9(m+H) = a

Step-by-step explanation:

m=a/9-H

The first step is to add H to each side.

m+H = a/9 -H+H

m+H = a/9

Now multiply both side by 9

9(m+H) = a/9*9

9(m+H) = a

3x+y=6

x+y=2

rewrite x + y = 2 as y = 2-x

Replace Y in the first equation with the re-written equation:

3x + 2-x = 6

Solve for x:

3x + 2-x = 6

subtract x:

2x +2 = 6

Subtract 2 from each side:

2x = 4

Divide both sides by 2:

x = 2

Now you have x, replace x with 2 in the second equation and solve for y:

x + y = 2

2 + y = 2

Subtract y 2 from each side:

y = 0

The answer is: X = 2, Y = 0

Answer:

The correct answers would be

vertex A' (-8,4)

vertex B' (-12,12)

vertex C' (-4,12)

Step-by-step explanation:

I'm not 100% sure but I took this test a couple days ago and didn't do terribly:).

Answer:

She has 11/20 yds left

Step-by-step explanation:

We take what she had and subtract what she gave away

9/10 - 7/20

We need to get a common denominator of 20

9/10 *2/2 - 7/20

18/20 - 7/20

11/20

She has 11/20 yds left

Answer:

x<44

Step-by-step explanation:

Answer:

x<-28

Step-by-step explanation:

Answer:

[tex]\displaystyle \frac{dy}{dx} = 3(x + 8)^{3x} \bigg[ \ln (x+ 8) + \frac{x}{x + 8} \bigg][/tex]

General Formulas and Concepts:
Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                          [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                        [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Derivative Rule [Basic Power Rule]:

Derivative Rule [Product Rule]:                                                                            [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Chain Rule]:                                                                               [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle f(x) = (x + 8)^{3x}[/tex]

Step 2: Differentiate

∴ we have found the derivative of the given function.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation