Hi, can anyone help me with this one here? Thanks.

Mathematics

1 answer:

Nezavi [6.7K]1 year ago

8 0

Answer:

Option 4

Step-by-step explanation:

Let $f(x)=ax^2+bx+c$ .

$f(0)=a(0)^2+b(0)+c=-4 \implies c=-4 \\ \\ f(-1)=a-b-4=-3 \implies a-b=1 \\ \\ f(2)=4a+2b-4=6 \implies 2a+b=5 \\ \\ \therefore (a-b)+(2a+b)=6 \implies a=2 \implies b=1 \\ \\ \therefore f(x)=2x^2+x-4$ .

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Pls instruct me on this.

Levart [38]

For x = ay - bz:

Add bz to both sides:

ay = x + bz

Divide a on both sides:

y = (x + bz)/a

For xy + yz = 10:

Distribute y from the left side:

y * (x + z) = 10

Divide by x + z:

y = 10/(x + z)

For (ab - ac)/z = x:

Multiply by z on both sides:

ab - ac = xz

Take out a from the left side:

a * (b - c) = xz

Divide by b - c on both sides:

a = xz/(b - c)

8 0

3 years ago

A colony of bees doubles in size every month. If there are initially 5000 bee, create a model for the bee population

Temka [501]

we know that the colony is doubling, namely the rate of growth is 100% of whatever is existent, thus

$\textit{Amount of Population Growth} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &5000\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=\textit{elapsed time}\dotfill &t\\ \end{cases} \\\\\\ A = 5000e^{1\cdot t}\implies \boxed{A = 5000e^t}$