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Yuliya22 [10]
3 years ago
12

A half dozen cupcakes cost $15. What constant of proportionality relates the number of cupcakes and total cost? Write an equatio

n that represents this relationship.
Mathematics
2 answers:
Norma-Jean [14]3 years ago
7 0
The constant of proportionality is 2.50
Gennadij [26K]3 years ago
7 0

Answer:

y=2.5x.

Step-by-step explanation:

Let x represent the number of cupcakes and y represent total cost.

We know that two proportional quantities are in form y=kx, where, k represents constant of proportionality.

1 dozen = 12

Half dozen = 6

Let us substitute y=15 and x=6 in above equation.

15=k*6

\frac{15}{6}=\frac{k*6}{6}

\frac{5}{2}=k

2.5=k

Therefore, the constant of proportionality is 2.5 and our required equation would be y=2.5x.

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Let g(x) = 2x and h(x)= x^2 -4. find (g o h)(0)
finlep [7]
The answer is -8

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

Explanation:

There are two ways to get this answer

Method 1 will have us plug x = 0 into h(x) to get
h(x) = x^2 - 4
h(0) = 0^2 - 4
h(0) = 0 - 4
h(0) = -4
Then this output is plugged into g(x) to get
g(x) = 2x
g(-4) = 2*(-4)
g(-4) = -8 which is the answer
This works because (g o h)(0) is the same as g(h(0)). Note how h(0) is replaced with -4
So effectively g(h(0)) = -8 which is the same as (g o h)(0) = -8

-----------------------

The second method involves a bit algebra first
Start with the outer function g(x). Then replace every x with h(x). On the right side, we will replace h(x) with x^2-4 because h(x) = x^2-4

g(x) = 2x
g(x) = 2( x )
g(h(x)) = 2( h(x) ) ... replace every x with h(x)
g(h(x)) = 2( x^2-4 ) ... replace h(x) on the right side with x^2-4
g(h(x)) = 2x^2-8
(g o h)(x) = 2x^2-8

Now plug in x = 0
(g o h)(x) = 2x^2-8
(g o h)(0) = 2(0)^2-8
(g o h)(0) = 2(0)-8
(g o h)(0) = 0-8
(g o h)(0) = -8

Regardless of which method you use, the answer is -8

5 0
3 years ago
What is the rational number equivalent to 3 point 12 with a bar over 12?
slamgirl [31]
\frac{12}{100}=0.12

To get the 0.12 to repeat, the trick is to subtract 1 from the denominator

\frac{12}{99}=0.12121212...

Then reduce the fraction.

\frac{12}{99}={4}{33}

now add the 3 to get

3.12121212.... = 3\frac{4}{33}
8 0
3 years ago
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Answer:

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Step-by-step explanation:

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Answer:

What??

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Answer:

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