Lillian has set up a lemonade stand outside her house and sells small cups and
large cups of lemonade. Each small cup holds 10 ounces of lemonade and each
large cup hold 24 ounces of lemonade. Lillian used 580 ounces of lemonade
and sold twice as many large cups as small cups. Write a system of equations
that could be used to determine the number of small cups sold and the number
of large cups sold. Define the variables that you use to write the system.

The system of equations that can be used to determine the number of small cups sold and the number  of large cups sold is:

10x + 24y = 580

y = 2x

Where:

x = number of small cups sold

y = number of large cups sold

The total ounces of lemonade sold is a function of the number of cups sold and the capacity of the cups. If there are two cups, the total ounces sold can be determined using this equation:

Total number of ounces sold = (number of small cups x capacity) + (number of large cups x capacity)

580 = 10x + 24y

If x is the number of small cups sold and Lilian sold twice as many large cups as small cups, this can be represented with this equation: y = 2x

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The number of small cups sold was 10 and the number  of large cups sold was 20

see the explanation

Step-by-step explanation:

Let

x ----> the number of small cups sold

y ---> the number  of large cups sold

we know that

Lillian used 580 ounces of lemonade

so

------> equation A

Lillian sold twice as many large cups as small cups

so

----> equation B

substitute equation B in equation A

solve for x

Find the value of y

therefore

The number of small cups sold was 10 and the number  of large cups sold was 20

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

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step-by-step explanation:

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