(04.05, 04.06 MC)

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

5 0

Answer:

siblings. Each cupcake costs $2, and each piece of fudge costs $1.

This system of inequalities models the scenario:

2x + y = <8

x + y > 4

Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)

Part B: Is the point (8, 10) included in the solution area for the system? Justify your answer mathematically. (3 points)

Part

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3. Find f[h(a+4)], given the functions below. *

mote1985 [20]

Answer:

C 5a^2 +70a +240

Step-by-step explanation:

We have given these following functions:

$f(x) = 5x, g(x) = -2x + 1, h(x) = x^2 + 6x + 8$

h(a+4)

This function is:

$h(a+4) = (a+4)^2 + 6(a + 4) + 8$

$h(a+4) = a^2 + 8a + 16 + 6a + 24 + 8$

$h(a+4) = a^2 + 14a + 48$

f[h(a+4)]

$f(x) = 5x$

Thus

$f(h(a+4)) = f(a^2+14a+48) = 5(a^2 + 14a + 48) = 5a^2 + 70a + 240$

The correct answer is given by option C.

8 0

3 years ago

Gina puts $ 4500 into an account earning 7.5% interest compounded continuously. How long will it take for the amount in the acco

Elza [17]

$~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5150\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=years \end{cases}$

$5150=4500e^{0.075\cdot t} \implies \cfrac{5150}{4500}=e^{0.075t}\implies \cfrac{103}{90}=e^{0.075t} \\\\\\ \log_e\left( \cfrac{103}{90} \right)=\log_e(e^{0.075t})\implies \log_e\left( \cfrac{103}{90} \right)=0.075t \\\\\\ \ln\left( \cfrac{103}{90} \right)=0.075t\implies \cfrac{\ln\left( \frac{103}{90} \right)}{0.075}=t\implies\stackrel{\textit{about 1 year and 291 days}}{ 1.8\approx t}$