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vampirchik [111]
1 year ago
7

By definition, (fog)(x) = f(g(x))So if g(2) = 3 and f(3) = 16, then (fog)(2) =

Mathematics
1 answer:
marusya05 [52]1 year ago
6 0

Answer:

(f\circ g)(2)=16

Step-by-step explanation:

By definition composite function would be:

(f\circ g)(x)=f(g(x))

Then, if g(2)=3 and f(3)=16, therefore for f(g(x)):

\begin{gathered} (f\circ g)(x)=f(g(2))=f(3) \\ \text{Hence,} \\ (f\circ g)(2)=16 \end{gathered}

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If y varies directly as x^2 and y=12 when x=2, find y when x=5
Shkiper50 [21]
y=ax^2\\\\y=12\ \ \ and\ \ \ x=2\ \ \ \Rightarrow\ \ \ 12=a\cdot 2^2\ \ \ \Rightarrow\ \ \ a= \frac{4}{12}= \frac{1}{3}  \\\\y=\frac{1}{3} x^2\\\\x=5\ \ \ \Rightarrow\ \ \ y=\frac{1}{3} \cdot5^2=\frac{25}{3} =8\frac{1}{3}
7 0
3 years ago
Of the students in your class, 12% are left-handed. What fraction of the students are left-handed? Are there more right-handed o
kvv77 [185]
The left-handed students
12% are left handed, percent means per hundred. Change percent into per 100.
12% = \dfrac{12}{100}

Then simplify the fraction by dividing the numerator and denominator by 4
\dfrac{12}{100}
= \dfrac{12:4}{100:4}
= \dfrac{3}{25}
This is the fraction showing the proportion of the left-handed students

The right-handed students
Determine the fraction showing the proportion of the right-handed students
1 - the left-handed
= 1 - \dfrac{3}{25}

Equalize the denominator to 25
\dfrac{25}{25} - \dfrac{3}{25}

Simplify
\dfrac{21}{25}
This is the proportion of the right-handed students

<span>Are there more right-handed or left-handed students?
There are more right-handed students than the left-handed students, because 21/25 is more than 3/25</span>
4 0
3 years ago
The map uses a scale of 1 in = 220 ft. On the map, how many inches<br> represent 1 mile?
ASHA 777 [7]

Answer:

24 inches

Step-by-step explanation:

There are 5280 feet in a mile
There are 220 feet in 1 in on the map

5280/220 = 24

6 0
2 years ago
If x+1 and x-1 are the factors of the polynomial ax^3 + x^2 - 2x +b,find the values of a and b
Nadusha1986 [10]

The polynomial remainder theorem says that dividing a polynomial p(x) by x-c leaves a remainder of p(c)=0 if x-c is a factor of p(x). In this case, check c=-1 and c=1.

a(-1)^3+(-1)^2-2(-1)+b=-a+b+3=0

a(1)^3+(1)^2-2(1)+b=a+b-1=0

From the first equation,

-a+b+3=0\implies a=b+3

and substituting into the second gives

(b+3)+b-1=0\implies2b+2=0\implies b=-1\implies a=2

3 0
3 years ago
Two of the lights at the local stadium are flickering. They both just flickered at the same time.
V125BC [204]

Answer:

76 seconds

Step-by-step explanation:

You need to find the first common multiple of both 7 and 8.  the LCM  is actually the numbers multiplies by each other, or 56.

4 0
2 years ago
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