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Doss [256]
3 years ago
15

Kennedy and Olivia go to the movie theater and purchase refreshments for their friends.

Mathematics
1 answer:
Anvisha [2.4K]3 years ago
3 0

Answer:

6x + y = 38.75

x + 2y = 17

price of drink is $5.75

Step-by-step explanation:

Let the price  of popcorn be x

Let the price  of drink be y.

price  of  12 bags of popcorn will be 12x

price  of  2 drinks  will be 2y

it is given that "Kennedy spends a total of $77.50 on 12 bags of popcorn and 2 drinks."

thus

12x + 2y = 77.50

dividing LHS and RHS by 2 we have

12x/2 + 2y/2 = 77.50/2

=> 6x + y = 38.75 _________(1)

__________________________________________________

price  of  3 bags of popcorn will be 3x

price  of  6 drinks  will be 6y

it is given that "Olivia spends a total of $51.00 on 3 bags of popcorn and 6 drinks."

thus

3x + 6y = 51.00

dividing LHS and RHS by 3 we have

3x/3 + 6y/3 = 51/3

=> x + 2y = 17   _____________(2)

__________________________________________________

Thus we have two equation

6x + y = 38.75 _________(1)

x + 2y = 17

=> x = 17 - 2y

putting this value of x in equation 1 we have

6( 17 - 2y) + y = 38.75

=> 102 - 12y + y = 38.75

=> 102 - 11y = 38.75

=> -11y = 38.75 -102

=> -11y = -63.25

=> y = -63.25/-11 = 5.75

as we have x = 17 - 2y

using 5.75 in place of y

x = 17 - 2(5.75 )

=> x = 17 - 11.5

=> x = 5.5

Thus, system of equations are

6x + y = 38.75

x + 2y = 17

price of drink is $5.75

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laila [671]

Answer:

At 25 = 6.8612mm

At 50 years = 5.422mm

Step-by-step explanation:

Equation,

d = 2.115Logₑa + 13.669

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a = number of years

Note : Logₑa = In a (check logarithmic rule)

d = 2.115Ina + 13.669

1. At 25 years,

d = -2.115In25 + 13.669

d = -2.115 × 3.2188 + 13.669

d = -6.807762 + 13.669

d = 6.8612mm

At 25 years, the pupil shrinks by 6.86mm

2. At 50 years,

d = -2.1158In50 + 13.669

d = -2.1158 * 3.912 + 13.669

d = -8.2770 + 13.699

d = 5.422mm

At 50 years, the pupil shirks by 5.422mm

To save this question, I had to plug in the values into the equation.

Solving for Logₑa might be difficult, so instead I used Inx which is the same thing. Afterwards, i substituted in the values and solve the equation for each years.

8 0
3 years ago
Factor −1/3 out of −1/3x−8.
Gnom [1K]

For this case we have the following expression:

- \frac {1} {3} x-8

We take common factor - \frac {1} {3}, for this we must take into account that:

- * + = -\\\frac {24} {3} = 8

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- \frac {1} {3} (x + 24)

ANswer:

The factored expression is:

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8 0
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Ari borrowed $2000 and paid it back over 3 years. The simple interest rate was 2% annually. How much interest did ari pay over t
sukhopar [10]
If the interst rate is 2% per year and she paid it back after 3 years , it means she paid an extra 6% of $2000 just in interests.

Now we just need to find how much 6% is and add to 2000.

to discover the value of 6% of 2000 we can divide it by 100 ( to find 1%) and then multiply it by 6 ( to find 6%) :

2000 ÷ 100 = 20
1% = 20
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Now add 120 to 2000 to find out how much she paid in total:
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Awnser : She paid the total of $2120 over 3 years

I hope you understood my brief explanation. And please consider marking this awnser as Branliest. Thank you ! :)
6 0
3 years ago
if a area of a triangle is 64 and if the base is twice as big of the height what are the base and height
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The formula for area of a triangle is A = bh/2, where b is the base length and h is the height of the triangle. For this triangle, the base is twice as big as the height; the base and height are represented as follows.

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A = bh/2
64 = 2h(h)/2
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b = 2h
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