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Crazy boy [7]
3 years ago
6

Can someone simplify 9^-2.5?

Mathematics
1 answer:
tresset_1 [31]3 years ago
3 0

Answer: 1/243

Step-by-step explanation: To simplify the problem shown, our first step is to convert the decimal in the exponent, -2.5, to a fraction.

-2.5 is the same thing as -2 and 1/2 so we have 9^-2 and 1/2 and -2 and 1/2 is the same thing as -5/2 so we have 9^-5/2.

The rest of my work is attached in the image provided.

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Find (f • g) when f(x) = x^2 + 5x + 6 and g(x) = 1/x+3
Nikitich [7]

Answer:

option D

Step-by-step explanation:

f(x) = x^2 + 5x + 6

g(x)= \frac{1}{x+3}

(fog)(x) = f(g(x))

Plug in g(x) in f(x)

We plug in 1/x+3 in the place of x  in f(x)

f(g(x))= f(\frac{1}{x+3})= (\frac{1}{x+3})^2 + 5(\frac{1}{x+3}) + 6

To simplify it we take LCD

LCD is (x+3)(x+3)

\frac{1}{(x+3)(x+3)}+5\frac{1*(x+3)}{(x+3)(x+3)}+\frac{6(x+3)(x+3)}{(x+3)(x+3)}

\frac{1}{x^2+6x+9}+\frac{(5x+15)}{x^2+6x+9}+\frac{6x^2+36x+54}{x^2+6x+9}

All the denominators are same so we combine the numerators

\frac{1+5x+15+6x^2+36x+54}{x^2+6x+9}

\frac{6x^2+41x+70}{x^2+6x+9}

Option D is correct

8 0
2 years ago
Read 2 more answers
Write down the solution set for x<3 in the set of natural numbers.
Gre4nikov [31]

Answer:

domain:{ [3, ∞], int}

Step-by-step explanation:

this is every possible number that is an integer, so domain:{ [3, ∞], int}

note that the format may be different

4 0
3 years ago
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A radio station plays a total of 272 pop, rock, and hip-hop songs during a day. The number of pop songs is 3 times the number of
Norma-Jean [14]
Let the daily played number of pop songs be P, the number of rock songs be R and the number of hip-hop songs be H.

i) 
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means that : P+R+H=272

ii) 
"The number of pop songs is 3 times the number of rock songs. "

so, P=3R

iii)
"The number of hip-hop songs is 32 more than the number of rock songs."

means: H=32+R

iv)

since both P and H can be written in terms of R, we have:

P+R+H=272

(3R)+R+(32+R)=272

3R+R+32+R=272

5R+32=272

5R=272-32=240

R=240/5=48


vi) 

thus: P=3R=3*48=144,    H=32+R= 32+48=80

Answer: 

48 Rock, 144 Pop and 80 Hip-hop

5 0
2 years ago
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liq [111]

Answer:

m=-44

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3 0
3 years ago
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What number produces a rational number when added to 1/5
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You should download Mathpro
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