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Brums [2.3K]
3 years ago
10

Gavin and Caleb go to the movie theater and purchase refreshments for their friends. Gavin spends a total of $22.25 on 2 bags of

popcorn and 3 drinks. Caleb spends a total of $39.00 on 12 bags of popcorn and 4 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a drink, to the nearest cent.
Mathematics
2 answers:
gavmur [86]3 years ago
8 0

Answer:

Drinks = 6.75

Popcorn= 1

Step-by-step explanation:

Let the popcorn = P

Let the drink = D

2*P + 3*D = 22.25         multiply this equation by 6

12*P + 4D = 39.00

<u>12P + 18D = 133.5</u>          Subtract these two equations

- 14D = - 94.50               Divide by -14

-14D/-14 = -94.5/-14        Do the division

D = 6.75

=========================

12P  +  4D = 39            Substitute for D

12P + 4*6.75 = 39        Combine

12P + 27 = 39               Subtract 27 from both sides

12P + 27-27=39-27      Collect like terms

12P = 12                        Divide by 12

12P/12 = 12/12

P = 1                               Answer

gizmo_the_mogwai [7]3 years ago
5 0

Answer:

Step-by-step explanation:

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nikklg [1K]

Answer:

x = 13

Step-by-step explanation:

Sum or interior angles of a triangle is 180,

6x + 19 + 5x - 15 + 3x - 6 = 180

6x + 5x + 3x + 19 - 15 - 6 = 180

14x + 19 - 21 = 180

14x - 2 = 180

14x = 180 + 2

14x = 182

x = 182 / 14

x = 13

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3 years ago
Convert 5.764764764 … to a rational expression in the form of a over b, where b ≠ 0
zubka84 [21]
I just learned a short time ago how to convert a repeating decimal to a fraction.

-- Take the repeating part of the decimal.  In this one, it's '764' .

-- Make a fraction out of it by writing it over the same number of 9s.

       The fraction here is        764/999 .

-- Simplify it if possible and if you feel like it.

         764/999 can't be simplified.  (I think.)

So the rational expressions for this decimal are

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3 years ago
Let m = X^2 + 3.
Tpy6a [65]

The Equation in terms of m, m^2+7m+10=0

What is substituting in the equation ?

substituting means changing or replacing the values in the given equation.

Calculation:

Given equation is (x^2+3)^2+7x^2+21=-10

            and m= X^2 + 3.

make the given equation in the form X^2 + 3,

             now,

                     (x^2+3)^2+7x^2+21=-10

                     (x^2+3)^2+7(x^2+3)=-10

             where,

                      X^2 + 3= m

              after putting the value or replacing the values

             we get, m^2+7m=-10

                      m^2+7m+10=0

          the above equation is in the form of "m".

The Equation in terms of m, m^2+7m+10=0

Leran more about substitution here:

brainly.com/question/24094293

#SPJ1

4 0
1 year ago
Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6
Alla [95]

Given:

The expression is:

2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

m+n=-6

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

P(x)=2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

P(2)=P(-1)              ...(i)

Substituting x=-1 in the given polynomial.

P(-1)=2(-1)^3+m(-1)^2+n(-1)+c

P(-1)=-2+m-n+c

Substituting x=2 in the given polynomial.

P(2)=2(2)^3+m(2)^2+n(2)+c

P(2)=2(8)+m(4)+2n+c

P(2)=16+4m+2n+c

Now, substitute the values of P(2) and P(-1) in (i), we get

16+4m+2n+c=-2+m-n+c

16+4m+2n+c+2-m+n-c=0

18+3m+3n=0

3m+3n=-18

Divide both sides by 3.

\dfrac{3m+3n}{3}=\dfrac{-18}{3}

m+n=-6

Hence proved.

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3 years ago
A central angle measuring 150° intercepts an arc in a circle whose radius is 6. What is the area of the sector of the circle for
katovenus [111]

Answer: 15

Step-by-step explanation: its 15

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3 years ago
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