The Rao family won a raffle of $1,000 to spend at Dixie Amusement Park. They want to use it for a group tour and for meals. A tour can have at most 8 people in the group, and if there are children on the tour there must be at least one adult. The tour cost $250 plus $100 for each adult and $50 for each child. The meal plan for the park is $15 per person.

A) Write a system of inequalities to model this scenario, and graph the system.
B) What is the maximum number of people who could be in the group, and how much would it cost? Justify your answer
C) Suppose that only adults are going to go on the tour. How many can there be? Explain your answer.​

Answer:

-7, 14

Step-by-step explanation:

We start by writing this in the form $x^2 + bx + c = 0$, so we subtract 98 from both sides of the equation.

This gives us $x^2 - 7x - 98 = 0$. We proceed by factoring $x^2 - 7x - 98$, so we seek numbers that multiply to $-98$ and add to $-7$. We find that $7$ and $-14$ work.

Thus, our equation becomes $(x + 7)(x - 14) = 0$. We can now apply the fact that if the product of two real numbers is zero, then at least one of the real numbers must be 0.

Solving $x + 7 = 0$ and $x - 14 = 0$, we find that the solutions are $\boxed{x  =-7~\text{and}~x = 14}$.

The value of the equation is given by x = 14 or x = -7

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

x² - 7x = 98   be equation (1)

Subtracting 98 on both sides of the equation , we get

x² - 7x - 98 = 0

Now , on simplifying the equation , we get

x² - 14x + 7x - 98 = 0

Taking x as the common factor of the equation , we get

x ( x - 14 ) + 7 ( x - 14 ) = 0

On further simplification , we get

( x + 7 ) ( x - 14 ) = 0

Now , the two solutions to the equation is

( x + 7 ) = 0

Subtracting 7 on both sides of the equation , we get

x = -7

( x - 14 ) = 0

Adding  14 on both sides of the equation , we get

x = 14

Therefore , the value of A is 14 or - 7

Hence , the equation x² - 7x - 98 = 0 has the solutions of 14 and -7

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Answer:

The quotient is 2.352

Step-by-step explanation:

The term quotient is simply the result of division

Thus; if we divide 54.096 by 23, we get 2.352

Answer:

x=-4

Step-by-step explanation:i think this is is i hope it helps

Answer:

$60

Step-by-step explanation:

75÷5=15, meaning he earns $15 per dog so if we do 15×4 we end up with 60 dollars

Answer:

I think it's C or D

Step-by-step explanation:

All decimals are rational numbers and so are repeating ones

Answer:

Each repeating decimal number satisfies a linear equation with integer coefficients, and its unique solution is a rational number.

Step-by-step explanation:

Answer:

You need to know the least common denominator (LCD) of 40 and 29 if you want to add or subtract two fractions with 40 and 29 as denominators. The least common denominator, also called lowest common denominator (LCD), of 40 and 29 is 1160 .

Step-by-step explanation: hope this helps

Answer:

[tex]X = 22[/tex]

Step-by-step explanation:

Given

Represent Emma with E and Nikki with N

From the question, we have that:

[tex]E = 1 + 2N[/tex]

and

[tex]E = 15[/tex]

Required

Determine the X number of goals

Substitute 15 for E in [tex]E = 1 + 2N[/tex]

[tex]15 = 1 + 2N[/tex]

Subtract 1 from both sides

[tex]15 -1 = 1 - 1 + 2N[/tex]

[tex]14 = 2N[/tex]

Divide both sides by 2

[tex]\frac{14}{2} = \frac{2N}{2}[/tex]

[tex]\frac{14}{2} = N[/tex]

[tex]7 = N[/tex]

[tex]N=7[/tex]

This implies that Nikki scored 7 goals in total

The X number of goals is then calculated as:

[tex]X = N + E[/tex]

[tex]X = 7 + 15[/tex]

[tex]X = 22[/tex]

Answer:

Do you need all 6 of them?

Answer and Step-by-step explanation:

w = -1

x = 6

y = 3

z = -2

32. Plug -2 for z and 6 for x.

(9(-2)) / 6

-18 / 6

3

33.

[tex]6^{2} - 3^{2}[/tex]

36 - 9

27

34.

[tex]3^{2} - (-2)^{2}[/tex]

9 - 4

5

35.

[tex]\frac{2(6)+3}{-2 + -1} \\\\\frac{12+3}{-3}\\\\\frac{15}{3} \\\\5[/tex]

36.

[tex]\frac{3(6)-(-2)}{-(-1)} \\\\\frac{18 + 2)}{1)} \\\\\frac{20}{1} \\\\20[/tex]

37.

[tex]\frac{6 + -1}{3 - (-2)} \\\\\frac{5}{5}\\\\1[/tex]

#teamtrees #WAP (Water And Plant) #SPEW (Society for the Promotion of Elfish Welfare)

Answer:

Gifted European Mathematicians (G.E.M.) project

Step-by-step explanation:

hope it is correct

Answer:

Step-by-step explanation:

n - 4 < 5

n < 9

Answer:

15 and 10

Step-by-step explanation:

I hope this helps :)

Answer:

Yes they are the same

Step-by-step explanation:

(3x2)^2=36. 3^2X2^2 =36

Answer:

it has to be in the negative numbers

Step-by-step explanation:

reason is that if you add positive numbers to a negative then the number goes down but back up to 0

Answer:

-20

Step-by-step explanation:

I think that is right I might be trippin tho I think I'm tripping but  also think it's right not 100% sure tho

Answer:

C

Step-by-step explanation:

hope this helps!!! have a nice day

Answer:

15

Step-by-step explanation:

2 times 4 is 8 minus 2 equals 6- Nia's Score

2 times 6 is 12 plus 3 equals 15- Mark's Score

Answer:

15

Step-by-step explanation:

2 X 6 is 12 + 3 = 15 (Mark's Score)

Answer:

1

Step-by-step explanation:

Answer:(-1,1) - (4,4)

Step-by-step explanation:

ez

Answer:

w=−12

Step-by-step explanation:

1

6

w+

5

8

=

−11

8

Step 2: Subtract 5/8 from both sides.

1

6

w+

5

8

−

5

8

=

−11

8

−

5

8

1

6

w=−2

Step 3: Multiply both sides by 6.

6*(

1

6

w)=(6)*(−2)

w=−12

Answer:

16870

Step-by-step explanation:

Answer: um 16870 I guess

Step-by-step explanation: I hope I help and can you plz give me a brainliest

Answer:

£12

Step-by-step explanation:

To find the original amount, divide 6.60 by 0.55:

6.60/0.55

= 12

So, Sophie had £12 to begin with

Answer:

Step-by-step explanation:

x+y=7

x=7-y

So x=7-y

Put this in 5(7-y)+45y=195

35-5y+45y=195

35+40y=195

40y=195-35

40y=160

y=160/40

y=4

So I know you just want the answer now.. so it’s just (3,4) your welcome

Answer:

1/2 the length of the third side

Step-by-step explanation:

Answer:

I know that the equation has infinity many solution

12x+8=12x+8

That would be the final answer

Answer:

b; vertically compressed by a factor of 2

Step-by-step explanation:

Here, we want to select from the options, the transformation that was not done on the parent function;

a) shifted up seven units

This was done

as we can see, we have + 7 from the initial 0 point

b) vertically compressed by a factor of 2

This is wrong

What we had is 1/2 multiplied by x

If there is any compressor done, it is to a factor of 1/2 and not 2

This, is thus our answer

Answer:

Following are the solution to this question:

Step-by-step explanation:

x was its full computer product revenue from March to December.  In january and february, the revenue towards products and services before x quantities for computer product revenues will happen between March to December is $2,500.  

Whenever x quantity is sold, then 0.05x quantity was sold for supplies and equipment.  

The sum of accessories to sell should be calculated, indeed, year-round.  

It helps us to split into two parts  

y = accessory sales in January and February + accessories sales in March and December  

Use item 2  

y = $2,500 + March to December accessories sale  

Now use sections 1 and 3  

y = $2,500 + 0.05x

The above equation rewriting gives  

y = 0.05x + $2,500 (a)  

This formula is compared with a standard y = mx+c interrupt slope  

We got a pitch of 0.05 and a pitch of $2,500.

Answer:

b

can i have brainliest