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3 years ago

Given that f(x)= x2+3 and g(x)= x+4/3 solve for (f(g(x)) when x =2

1 answer:

7 0

$\bf \begin{cases}
f(x)=x^2+3\\\\
g(x)=x+\cfrac{4}{3}
\end{cases}
\\\\\\
\boxed{x=2}\qquad g(2)=(2)+\cfrac{4}{3}\implies \boxed{g(2)=\cfrac{10}{3}}
\\\\\\
f(~~g(x)~~)=[g(x)]^2+3\implies f(~~g(2)~~)=[g(2)]^2+3
\\\\\\
f(~~g(2)~~)=\left[ \boxed{\frac{10}{3}} \right]^2+3\implies f(~~g(2)~~)=\cfrac{10^2}{3^2}+3
\\\\\\
f(~~g(2)~~)=\cfrac{100}{9}+3\implies f(~~g(2)~~)=\cfrac{100+27}{9}
\\\\\\
f(~~g(2)~~)=\cfrac{127}{9}$

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Answer:

The correct estimate of the amount generated to the local economy is $3,333,333. $\bar3$

Step-by-step explanation:

The amount the expected to be generated for the local economy = $3.3 million

The amount of salaries that will generate $3.3 million = $1 million

The percentage of the amount of the salaries and the subsequent earnings expected to be spent on the local community = 70%

Therefore, we have;

For a first amount of 1 million into the economy, the next amount to into the economy is 70/100 × 1 million = 700,000, then we have 70/100 × 700,000 and so on, which is a geometric sequence, with first term, a = $1 million, the common ratio, r = 70/100 = 0.7, the number of terms = Infinity = ∞

The sum of a geometric sequence to infinity is given as follows;

$\sum\limits_{k = 0}^{\infty }a \cdot r^k = S_{\infty} = \dfrac{a}{1 - r}$

Substituting the known values gives;

$\sum\limits_{k = 0}^{\infty }1,000,000 \times 0.7 ^k = \dfrac{1,000,000}{1 - 0.7}= 3,333,333.\bar 3$

Therefore, the correct estimate of the amount generated to the local economy by the $1 million salaries that will be paid = $3,333,333. $\bar3$ .

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3 years ago

Todea what did one pencil say to another mathematics algebra order of operations answer

Serjik [45]

Part 1

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Part 2

$7-8\div4(3^2-1)=7-8\div4(9-1) \\ \\ =7-8\div4(8)=7-8\div32=7- \frac{1}{2} \\ \\ =6 \frac{1}{2} = \frac{13}{2}$

Part 3

$2-2(2-5)^2+3^2=2-2(-3)^2+9 \\ \\ =2-2(9)+9=2-18+9=-7$

Part 4

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Part 6

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$-5+1\cdot3-(7-2^3)=-5+3-(7-8) \\ \\ =-2-(-1)=-2+1=-1$

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Part 12

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3 years ago

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asambeis [7]

First subtract the two numbers:

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Now divide this to the original:

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Multiply by 100:

0.6 * 100 = 60%

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3 years ago

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Answer:
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3 years ago