The owner of a baseball stadium found that he sells an average of 586 tickets to each game when he charges an average of $59 per ticket. In addition, he found that with every $6 increase in ticket price, the average number of tickets sold decreases by an average of 4.

Which of the following functions describes the baseball stadium's profit in terms of x, the number of $6 increases over $59?

A.
P(x) = $34,574 + $3,280x - $24x2

B.
P(x) = $34,574 + $3,516x

C.
P(x) = $59 + $3,280x

D.
P(x) = $59 - $3,752x - $24x2

Answer:

a = 1 and b = 2

Step-by-step explanation:

Using the Quotient Rule>

d/dx[(sin x)/(2+cos x) ]

=   [(2 + cos x) * cosx -  sin x * - sin x)]  /  (2 + cos x)^2

= 2cos x + cos^2x + sin ^2 x) /  (2 + cos x)^2

But cos^2x + sin^2x = 1 so we have:

(1 +  2 cos x)  /   (2 + cos x)^2

- so a = 1 and b = 2.

Answer:

x=-7

x=7

Step-by-step explanation:

we have

[tex]2x^{2}-98=0[/tex]

Solve for x

Adds 98 both sides

[tex]2x^{2}-98+98=0+98[/tex]

[tex]2x^{2}=98[/tex]

Divide by 2 both sides

[tex]2x^{2}/2=98/2[/tex]

[tex]x^{2}=49[/tex]

take square root both sides

[tex]x=\pm7[/tex]

therefore

The solutions are

x=-7

x=7

Answer:

m∠EAD =  29°

m∠CAB =  119°

Step-by-step explanation:

m∠EAD = 180 - 61 - 90 = 29°

m∠CAB = 180 - 61 = 119°

Answer:

y = -x

Step-by-step explanation:

Explained in picture:

SORRY IF INCORRECT!!!!!

Answer:

Step-by-step explanation:

y - 6 = b

y =  b + 6

Answer:

6+b=y

Step-by-step explanation:

If you plug in real values (y=8 and b=2) you can see that at first, you had y-6=b. Basically, 8-6=2. In order to find eight, you would need to reverse the equation to 6+2. The answer is 6+b=y.

Answer:

B seems right

Step-by-step explanation:

Answer:

[tex]d < 20\ donuts[/tex]

The graph of the solution set in the attached figure

Step-by-step explanation:

 Let

d ----> the possible number of donuts Monica brought

we know that

The number of donuts d multiplied by $0.50 plus the cost of a box of coffee for $5 must be less than $15

so

The inequality that represent this situation is

[tex]0.50d+5 < 15[/tex]

Solve for d

subtract 5 both sides

[tex]0.50d < 15-5[/tex]

[tex]0.50d < 10[/tex]            

Divide by 0.50 both sides

[tex]d < 10/0.50[/tex]      

[tex]d < 20\ donuts[/tex]

The solution is all whole numbers greater than zero and less than 20 ( I say greater than zero because the problem states that Monica brought some donuts)

The solution set is the interval {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19}

Answer:

three angles measuring 109º, 25º, and 145º cannot create a triangle

three angles measuring 40º, 70º, and 65º cannot create a triangle

Step-by-step explanation:

Verify each dimensions

Part 1) three angles measuring 109º, 25º, and 145º

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

In this problem we have

[tex]109^o+25^o+145^o=279^o[/tex]

[tex]279^o> 180^o[/tex]

therefore

three angles measuring 109º, 25º, and 145º cannot create a triangle

Part 2) three sides measuring 9 m, 15 m, and 9 m

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Applying the triangle inequality theorem

1) 9+15 > 9 ---> is ok

2) 9+9 > 15 ---> is ok

therefore

three sides measuring 9 m, 15 m, and 9 m can create a triangle

Part 3) three angles measuring 40º, 70º, and 65º

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

In this problem we have

[tex]40^o+70^o+65^o=175^o[/tex]

[tex]175^o< 180^o[/tex]

therefore

three angles measuring 40º, 70º, and 65º cannot create a triangle

Part 4) three sides measuring 6 cm, 8 cm, and 10 cm

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Applying the triangle inequality theorem

1) 6+8 > 10 ---> is ok

2) 8+10 > 6 ---> is ok

3) 6+10 > 8 ---> is ok

therefore

three sides measuring 6 cm, 8 cm, and 10 cm can create a triangle

Answer:

its c i promise

Step-by-step explanation:

Answer:

0.43 liters = 430 milliliters

Step-by-step explanation:

There are 1000 milliliters in each liter so all you have to do is multiply 0.43 by 1000. :)

Answer:

0.43 liters = 430 milliliters

0.43 liters = 430 milliliters

Step-by-step explanation:

There are 1000 milliliters in each liter so all you have to do is multiply 0.43 by 1000. :)

Answer:

x=-1539/445, y=1724/445. (-1539/445, 1724/445).

Step-by-step explanation:

y=9x+35

y=-8/9x+4/5

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

9x+35=-8/9x+4/5

9x-(-8/9x)=4/5-35

9x+8/9x=4/5-175/5

81/9x+8/9x=-171/5

89/9x=-171/5

x=(-171/5)/(89/9)

x=(-171/5)(9/89)

x=-1539/445

y=9(-1539/445)+35

y=1724/445

Answer:

y=15x-6x^2

Step-by-step explanation:

3x+y/2x=15/2

y/2x=15/2-3x

y=2x(15/2-3x)

y=15x-6x^2

Answer:

-3/4

Step-by-step explanation:

The least common denominator is 8.

So you make -3/4 into -6/8 by multiplying 2 in the numerator and denominator.

Now just compare them -6/8 compared to -7/8

-6/8 is bigger since it is closer to 0 (since we are dealing with negative numbers.)

Have a great day!

Answer: 5 Kilometers Per Hour

Answer:

1/12 km per minute

Step-by-step explanation:

1 hour=60 minutes

5/60=1/12

Answer:

x=30

Step-by-step explanation:

ratio: 8:10 as 24:x

8/10=24/x

10x * 8/10= 10x * 24/x

x * 8 = 10 * 24

8x = 240

8x/8 = 240/8

8x/8 = 30

x = 30

Answer: [tex]6y^2i\sqrt{6}[/tex]

Step-by-step explanation:

For this exercise it is important to remember the following property:

[tex]\sqrt[n]{a^n}=a^{({\frac{n}{n})}}=a[/tex]

Then, given the expression:

[tex]\sqrt{-216y^4}[/tex]

You can follow these steps in order to simplify it:

1. Descompose 216 into its prime factors:

[tex]216=2*2*2*3*3*3[/tex]

2. The Product of powers property states that:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

Then:

 [tex]216=2^2*2*3^2*3[/tex]

3. Now you can substitute:

[tex]=\sqrt{-2^2*2*3^2*3*y^4}[/tex]

4. Finally, substituting [tex]\sqrt{-1}=i[/tex] and simplifying, you get:

[tex]=2*3*y^2i\sqrt{2*3}=6y^2i\sqrt{6}[/tex]

Answer:

Area [tex]=62.5\sqrt{6}[/tex] square units

[tex]AB=5\sqrt{15}[/tex] units

[tex]BC=5\sqrt{10}[/tex] units

Step-by-step explanation:

In a right triangle the altitude drawn to the hypotenuse is the geometric mean of the segments at which this altitude divides the hypotenuse.

So,

[tex]BD^2=15\cdot 10\\ \\BD^2=150\\ \\BD=\sqrt{150}=5\sqrt{6}\ units[/tex]

a. The area of the triangle ABC is

[tex]A_{ABC}=\dfrac{1}{2}\cdot BD\cdot AC=\dfrac{1}{2}\cdot 5\sqrt{6}\cdot (15+10)=\dfrac{125\sqrt{6}}{2}=62.5\sqrt{6}\ un^2.[/tex]

b. The legs of the right triangle are geometric means of the segment adjacent to this leg and the hypotenuse, so

[tex]AB^2=AD\cdot AC=15\cdot 25\Rightarrow AB=5\sqrt{15}\ units\\ \\BC^2=CD\cdot AC=10\cdot 25\Rightarrow BC=5\sqrt{10}\ units[/tex]

Final answer:

To find the number of defective computer chips the company would expect out of the 36,000 chips they make each year, we can set up a proportion: 22 defective chips / 600 chips = x defective chips / 36,000 chips. Dividing both sides by 600, we find that x = 1,320. Therefore, we would expect approximately 1,320 of the 36,000 computer chips the company makes each year to be defective.

Explanation:

To find the number of defective computer chips the company would expect out of the 36,000 chips they make each year, we can set up a proportion:

22 defective chips / 600 chips = x defective chips / 36,000 chips

Cross-multiplying, we get 600x = 22 * 36,000

Dividing both sides by 600, we find that x = 22 * 36,000 / 600 = 1,320

Therefore, we would expect approximately 1,320 of the 36,000 computer chips the company makes each year to be defective.

Answer:

The correct answer is C. 5⁶

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Number of hens in a bird enclosure = (5³)² * 5⁰

2. What is the total number of hens in the enclosure?

Let's recall a couple of properties of the exponents:

1. When you raise any number to a zero power you'll always get 1, with the exception of zero itself.

x⁰ = 1, x ≠ 0

2. The power of a power property says that to calculate a power of a power you just have to multiply the exponents, this way:

(x⁴)⁵ = x ⁴°⁵ = x²⁰

Now, applying those two properties, we have:

(5³)² * 5⁰ = 5³°² * 1 = 5⁶

The correct answer is C. 5⁶

Answer:

c

Step-by-step explanation:

The cost of one peppermint cookie is $0.60 and cost of one cinnamon sugar cookie is $0.30

Step-by-step explanation:

Let,

Cost of 1 peppermint cookie = x

Cost of 1 cinnamon cookie = y

According to given statement;

120x+30y=81     Eqn 1

70x+60y=60     Eqn 2

Multiplying Eqn 1 by 2

[tex]2(120x+30y=81)\\240x+60y=162\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](240x+60y)-(70x+60y)=162-60\\240x+60y-70x-60y=102\\170x=102\\[/tex]

Dividing both sides by 170

[tex]\frac{170x}{170}=\frac{102}{170}\\x=0.60[/tex]

Putting x=0.60 in Eqn 2

[tex]70(0.60)+60y=60\\42+60y=60\\60y=60-42\\60y=18[/tex]

Dividing both sides by 60

[tex]\frac{60y}{60}=\frac{18}{60}\\y=0.30[/tex]

The cost of one peppermint cookie is $0.60 and cost of one cinnamon sugar cookie is $0.30

Keywords: linear equation, elimination method

Learn more about elimination method at:

#LearnwithBrainly

Answer:

At 9pm Greta and Marge have collected the same amount  of money.

Step-by-step explanation:

Consider the provided information.

Let x represents the number of hours Greta and Marge are both collecting.

It is given that  Greta had already collected $45.00 till 11 am.

Greta = 45 + 15x

Marge collects money at a rate of $20 per hour.

Marge = 20x

Greta and Marge have collected the same amount  of money.

Thus,​

45 + 15x = 20x

45 = 5x

9 = x

Hence, once Marge starts collecting, it would take 9 hours to collect same amount of money.

9 hours after 11am is 8pm. It is given that there is a break time of 1 hour

Hence, at 9pm Greta and Marge have collected the same amount  of money.

Answer:

35 - 45x

Step-by-step explanation:

-7(-5) + -7(8x) + 11x => 35 - 56x + 11x => 35 - 45x

Answer:

multiplicative identity

Step-by-step explanation:

Anything that is divisible by 0 or 1  is called multiplicative identity.

Hey there!

To find the slope of the two points that you were given, use the slope formula:

[tex]\frac{y2-y1}{x2-x1}[/tex]

y2 is the y value of the second point pair, y1 is the y value of the first point pair, x2 is the x value of the second point pair, and x1 is the x value of the first point pair.

Now, plug in your values:

y2= 9

y1= 6

x2= 6

x1= 3

[tex]\frac{9-6}{6-3}[/tex] = [tex]\frac{3}{3}[/tex] = 1

Therefore, the slope of the two points is 1.

10 small boxes and 11 large boxes were shipped.

Step-by-step explanation:

Given,

Total boxes shipped = 21

Total volume of shipped boxes = 342 cubic feet

Volume of each small box = 10 cubic feet

Volume of each large box = 22 cubic feet

Let,

Number of small boxes = x

Number of large boxes = y

According to given statement;

x+y=21     Eqn 1

10x+22y=342    Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=21)\\10x+10y=210\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](10x+22y)-(10x+10y)=342-210\\10x+22y-10x-10y=132\\12y=132[/tex]

Dividing both sides by 12

[tex]\frac{12y}{12}=\frac{132}{12}\\y=11[/tex]

Putting y=11 in Eqn 1

[tex]x+11=21\\x=21-11\\x=10[/tex]

10 small boxes and 11 large boxes were shipped.

Keywords: linear equation, subtraction

Learn more about linear equations at:

#LearnwithBrainly

Answer: [tex]6.9\ minutes[/tex]

Step-by-step explanation:

Let "x" represents the 16% of 43 minutes.

Once you analize the information given in the exercise, you can identify that 43 minutes is the 100%.

Then, with this data, you can set up the following proportion:

[tex]\frac{100}{43}=\frac{16}{x}[/tex]

Now you must solve for "x". The steps are:

- Multiply both sides of the equation by "x"

 [tex](x)(\frac{100}{43})=(\frac{16}{x})(x)\\\\\frac{100x}{43}=16[/tex]

- Multiply both sides by 43:

[tex](43)(\frac{100x}{43})=(16)(43)\\\\100x=688[/tex]

- Divide both sides by 100:

[tex]\frac{100x}{100}=\frac{688}{100}\\\\x=6.88[/tex]

- Rounding to the tenths place:

[tex]x\approx6.9[/tex]

Answer:

y<x+1      y>x-2

Step-by-step explanation:

upper line: (0,1) (-1,0)

y=x+1

Lower line: (0,-2) (2,0)

y=x-2

I did not see any solid boundry on the line

Shaded: y<x+1      y>x-2

Answer:

[tex]y <x+1[/tex]

[tex]y>x-2[/tex]

Step-by-step explanation:

According to the graph, the system is formed by two inequalities. Let's find out the equation to each line in first place.

Notice that the upper line passes through points (-1,0) and (0,1). First, we find its slope

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{1-0}{0-(-1)}=\frac{1}{1}=1[/tex]

Then, we use the point-slope formula to find the equation

[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-(-1)\\y=x+1[/tex]

Now, the dashed line indiactes that the inequalities must have sings < or >.

Notice that point (0,0) is part of its solution, that means the inequality is

[tex]y <x+1[/tex]

We do the same process to find the other inequality.

The line passes through points (0,-2) and (2,0).

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{0-(-2)}{2-0}=\frac{2}{2}=1[/tex]

Then,

[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-2)\\y=x-2[/tex]

Notice that point (0,0) is part of its solution, so the inequality is

[tex]y>x-2[/tex]

Therefore, the system of inequalities is

[tex]y <x+1[/tex]

[tex]y>x-2[/tex]

Answer:

90% of the questions she answered correctly

Step-by-step explanation:

%age = 81/90 * 100= 90 % correctness

Answer:

2d(d³-9d-30)

Step-by-step explanation:

2d⁴ - 6d - 18d² - 54d

= 2d⁴- 18d²-60d

=2d(d³-9d-30)