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andrew11 [14]
3 years ago
13

For Emma's lemonade recipe, 9 lemons are required to make 18 cups of lemonade. At what rate are lemons being used in lemons per

cup of lemonade?
Mathematics
1 answer:
grigory [225]3 years ago
7 0

Answer:

1:2

A rate of 1 lemon per two cups of lemonade

Step-by-step explanation:

9 lemons for 18 cups can be seen as:

\frac{9}{18}

Simplify by dividing both numbers by 9:

\frac{9/9}{18/9} =\frac{1}{2}

So, one lemon is used for two cups of lemonade. Half a lemon for 1 cup of lemonade...

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Andrews [41]

Answer:

f(x) = \frac{24}{25} * \frac{5}{6}^x

Step-by-step explanation:

Given

(x_1,y_1) = (2,\frac{2}{3})

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Required

Write the equation of the function f(x) = ab^x

Express the function as:

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In (x_2,y_2) = (3,\frac{5}{9})

y = ab^x

\frac{5}{9} = a * b^3 --- (2)

Divide (2) by (1)

\frac{5}{9}/\frac{2}{3} = \frac{a*b^3}{a*b^2}

\frac{5}{9}/\frac{2}{3} = b

\frac{5}{9}*\frac{3}{2} = b

\frac{5}{3}*\frac{1}{2} = b

\frac{5}{6} = b

b = \frac{5}{6}

Substitute 5/6 for b in (1)

\frac{2}{3} = a * b^2

\frac{2}{3} = a * \frac{5}{6}^2

\frac{2}{3} = a * \frac{25}{36}

a = \frac{2}{3} * \frac{36}{25}

a = \frac{2}{1} * \frac{12}{25}

a = \frac{24}{25}

The function: f(x) = ab^x

f(x) = \frac{24}{25} * \frac{5}{6}^x

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

By pythagoras' theorem,

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