Your school's drama club charges $10 per person for admission to a play. The club borrowed $400 to pay for costumes and props. After paying back the loan, the club has a profit of $100. Write an equation. Let x represent the number of people who attended the play.

Answer:

[tex]\huge\boxed{\sf a = -12 , b = 8}[/tex]

Step-by-step explanation:

Given polynomial is:

[tex]f(x) = ax^3+ b^2 + 3x + 4[/tex]

[tex]\rule[225]{225}{2}[/tex]

First factor is (x-1)

Let x - 1 = 0  => x = 1

Putting this in the above polynomial

[tex]f(1) = a(1)^3 + b(1)^2 + 3(1) + 4[/tex]

Given that it's remainder is 3

[tex]3 = a + b + 3 + 4[/tex]

[tex]3 = a + b + 7[/tex]

Subtracting 7 to both sides

[tex]-4 = a + b\\OR \\[/tex]

[tex]\rule[225]{225}{2}[/tex]

Second Factor is 2x + 1

Let 2x + 1 = 0 => x = - 1 / 2

Putting in the above polynomial

[tex]f(-\frac{1}{2} ) = a (-\frac{1}{2} )^3 + b (-\frac{1}{2} )^2 + 3 (-\frac{1}{2} ) + 4[/tex]

The remainder is 6

[tex]6 = -\frac{a}{8} + \frac{b}{4} - \frac{3}{2} + 4\\6 - 4 = -\frac{a}{8} + \frac{b}{4} - \frac{3}{2}\\2 = \frac{-a + 2b -12 }{8} \\-a + 2b - 12 = 16\\-a + 2b = 16 + 12\\[/tex]

[tex]\rule[225]{225}{2}[/tex]

Adding both equations

a + b -  a + 2b = -4 + 28

3b = 24

Dividing both sides by 3

b = 8

[tex]\rule[225]{225}{2}[/tex]

Putting b = 8 in Equation (1)

a + 8 = -4

a = - 4 - 8

a = -12

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

side side angle is the best answer

Answer:

Look below:

Step-by-step explanation:

adding is when u see 6 + 10. the plus sign ( the cross ) means to add. Subtract is using the minus sign: 6 - 10.

Answer:

You will know when to add or subtract because of keywords and symbols.

Step-by-step explanation:

Most addition and subtraction problems have keywords that tell you what operation to use. For example, so keywords that tell you that you have to add are altogether, sum, together, and a few other words. Some examples of subtraction problems are less than, and a bunch of other words.

Hope This Helps :)

Answer:

70%

Step-by-step explanation:

So, first, our set of choices is 10. This means that there are 10 choices.

We want a number that is greater than 5 or even. Thus, let's mark down all of our choices.

Numbers greater than 5 are:

6, 7, 8, 9, and 10.

Even numbers are:

2, 4, 6, 8, 10.

However, we already counted 6, 8, and 10 previously, so we'll ignore that.

All in all, the following numbers will satisfy our requirements:

2, 4, 6, 7, 8, 9, and 10.

This is 7 out of 10 numbers.

Therefore, our probability is:

[tex]7/10=70\%[/tex]

Answer:

109545

Step-by-step explanation:

              Formula

multiply the time value by 3600

Hope this helps

plz mark brainlest

Answer:

c = (t - 2 + 7t) / 2

Step-by-step explanation:

We can isolate c, getting 2c = t - 2 + 7t.

Then, we can divide both sides by 2, getting c = (t - 2 + 7t) / 2.

Answer:

Step-by-step explanation:

2x + 8 = 8

Subtract 8 from both sides.

2x = 0

Divide both sides by 2.

x = 0

The required number, eight more than twice a number is eight, is 0.

Given that,
To find the number which is eight more than twice a number is eight.

The technique in computation to use and analyze the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

In mathematics, it vends on a number of procedures according to the declarations. There are four primary arithmetic operators, addition, subtraction, multiplication, and division,

Let the number be x,
The eight more than twice a number is eight. So,
8 = 2x + 8
2x = 0
x = 0

Thus, the required number, eight more than twice a number is eight, is 0.

Learn more about simplification here:

brainly.com/question/12501526

#SPJ2

Answer:

[tex]\%Off-Campus = 45.5\%[/tex]

Step-by-step explanation:

Given

----------------------Dorms ---- Off-Campus ---- Total

Freshman -------- 88  ------  ---------12   ------- 100

Sophomore  ------62  ---------------38  --------- 100

Junior --------------43 -----------------  57  ---------- 100

Senior -------------25  -----------------75  ------------ 100

Total ---------------218 -------------182  --------------400

Required

Determine the percentage of off-campus students

From the above table, we have that:

[tex]Off-Campus = 182[/tex]

[tex]Total\ Surveyed = 400[/tex]

The percentage is then calculated as follows;

[tex]\%Off-Campus = \frac{Off-Campus}{Total-Surveyed} * 100\%[/tex]

[tex]\%Off-Campus = \frac{182}{400} * 100\%[/tex]

[tex]\%Off-Campus = 0.455 * 100\%[/tex]

[tex]\%Off-Campus = 45.5\%[/tex]

Hence, option C answers the question

Answer:

oh 45%

Step-by-step explanation:

Answer:

n+(-7)= choose a letter to replace it with the sum

Step-by-step explanation:

[tex](\frac{1}{2} ) {}^{ - 5} [/tex]

[tex] \frac{1 {}^{ - 5} }{ {2}^{ - 5} } [/tex]

[tex] \frac{1}{ \frac{1}{32} } [/tex]

[tex] \frac{1}{1} \times \frac{32}{1} [/tex]

[tex]32[/tex]

Answer: 3/10

Step-by-step explanation:

2/5 x 3/4

2x3=6

5x4=20

6/20

________

Simplify

6/2=3

20/2=10

3/10 Final Answer

Turn the percentage into a decimal.

95% / 100 = 0.95

Multiply.

200 * 0.95 = 190

Subtract.

200 - 190 = $10

Therefore, the dress costs $10 on sale.

Best of Luck!

Answer: The answer is 190.

Answer:

v10

Step-by-step explanation:

Answer:

5 days

Step-by-step explanation:

Set up linear equation; food= 240-12(day) f=240-12d

f(1)=240-12(1)=240-12=228

f(2)=240-12(2)=240-24=216

Now set food to equal 180, solve for days:

180=240-12d

-240  -240

-60=-12d

/-12  /-12

5=d

To check: f(5)=240-12(5)=240-60=180

Answer: 5

Step-by-step explanation:

5765.903

going backwards-in front of the decimal -5 ( ones place) 6 (tens place) 7 ( hundreds) 5 (thousands) .

.9 ( tenths) 0 (hundredths) 3 (thousandths)

Answer:

3(3) + 0.75(2) = (3 + 0.75)x

Step-by-step explanation:

The cost per pound of the mixture is the total cost divided by the total weight.

3 lb granola at $3 per lb has a cost of 3(3)

0.75 lb of raisins at $2 per lb has a cost of 0.75(2)

The total cost is 3(3) + 0.75(2)

The mixture has an unknown cost per lb, so we call it x.

When you multiply the cost per lb of the mix by the total weight, you get the total cost.

Total weight of mix: 3 + 0.75

Cost per lb of mix: x

Total cost of mix: (3 + 0.75)x

Above, we know the total cost is 3(3) + 0.75(2)

We set these two amounts equal to get our equation.

3(3) + 0.75(2) = (3 + 0.75)x

Answer: 3(3) + 0.75(2) = (3 + 0.75)x

Answer:

Step-by-step explanation:

First multiply 3x9 and you get 27 and then add 7 to 27

3x9 27

27+7 34

Answer:

34 is the answer

Step-by-step explanation:

Answer:

1,386

Step-by-step explanation:

guessed it in my head

Answer:

Step-by-step explanation:

Let the amount of trail mix in each bag be x pounds. If Mario has [tex]2\frac{1}{4}[/tex] pounds of trail mix and puts equal amounts of the trail mix into 6 bags for a hike with his friends, the amount of trail mix in each bag can be derives using the expression;

[tex]2\frac{1}{4} = 6 * x[/tex]

solving for x

[tex]\dfrac{9}{4} = 6x\\\\2.25 = 6x\\\\divide\ both \ sides \ by \ 6\\\\\dfrac{2.25}{6} = \dfrac{6x}{6} \\\\x = 0.375\\[/tex]

Hence 0.375 pounds of trail mix will be in each bag

Let y = 4x + 9

4x = y - 9

x = (y-9) / 4

f(x) = (x-9) / 4

Answer:

14 gallons

Step-by-step explanation:

357/25.5 = 14

14 gallons

hopefully this helps you :)

pls mark brainlest ;)

Thank you :)

Answer:

14 gallons

Step-by-step explanation:

took the test

Answer:

12 only.

Step-by-step explanation:

When the question is asking for f(0), it is asking for the value of y when x = 0.

We see that there is only 1 intersection at x = 0, and the y value would equal 12.

Therefore, our answer is 12 only.

Answer:

The answer is a.12 only its where the x coordinate stays 0 and the y coordinate decreases or increases

Step-by-step explanation:

Answer: (Median)

Sorry, I'm a bit late but I got 100% on my test!

Hope this helps!

Answer:

Mary- $18

Jane- $30

Step-by-step explanation:

Add the numbers in the ratio together to get 8, and multiply 8 by the variable of x. Divide the total amount of money that both girls earned by 8. You will get x=6. Multiply 6 by 3 to get the amount of money Mary earned, which is 18, and multiply 6 by 5 to get the amount of money Jane earned, which is 30.

x(3+5) = $48

3x + 5x = $48

8x = $48

8x/8 = $48/8

x = $6

3($6):5($6) = $18:$30

Answer:

Mary = $18

Jane = $30

Step-by-step explanation:

The first thing you need to do is find out how much each part is.  To do that you need to add each side of the ratio together (3 + 5 = 8).  THen you set up an equation showing the 8 parts * x = 48 and solve for x.

8x = 48

x = 6 <--  Value of each part

Now you multiply the 6 by the number on each side of the ratio,

Mary = 3 * 6 = 18

Jane = 5 * 6 = 30

The above is your answer.

Answer:

2

Step-by-step explanation:

1+1=2