All categories

3 years ago

The vertex of this parabola is at (-2, 5). Which of the following could be its equation?

Mathematics

1 answer:

LenKa [72]3 years ago

5 0

Answer:

y=3(x+2)^2+5

Step-by-step explanation:

The vertex is (p, q) where the "p" value is the x-coordinate of the vertex and the "q" is the y-coordinate of the vertex.

Given the vertex (-2, 5) the "p" here is -2 and "q" here is 5, so plugging into the vertex form we get y=3(x+2)^2+5

You might be interested in

When you find the surface area of a cube, you ________ the length of the cube and multiply by 6.

ryzh [129]

Answer:

A-square

Step-by-step explanation:

example:

sa=(4cm)^2x6

sa=16x6

sa=96

3 0

2 years ago

A model for the population in a small community after t years is given by P(t)=P0e^kt.

LUCKY_DIMON [66]

$\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\\
\end{cases}$

a)

so, if the population doubled in 5 years, that means t = 5. So say, if we use an amount for "i" or P in your case, to be 1, then after 5 years it'd be 2, and thus i = 1 and A = 2, let's find "r" or "k" in your equation.

$\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &2\\
I=\textit{initial amount}\to &1\\
r=rate\\
t=\textit{elapsed time}\to &5\\
\end{cases}
\\\\\\
2=1\cdot e^{5r}\implies 2=e^{5r}\implies ln(2)=ln(e^{5r})\implies ln(2)=5r
\\\\\\
\boxed{\cfrac{ln(2)}{5}=r}\qquad therefore\qquad \boxed{A=e^{\frac{ln(2)}{5}\cdot t}} \\\\\\
\textit{how long to tripling?}\quad 
\begin{cases}
A=3\\
I=1
\end{cases}\implies 3=1\cdot e^{\frac{ln(2)}{5}\cdot t}$

$\bf 3=e^{\frac{ln(2)}{5}\cdot t}\implies ln(3)=ln\left( e^{\frac{ln(2)}{5}\cdot t} \right)\implies ln(3)=\cfrac{ln(2)}{5} t
\\\\\\
\cfrac{5ln(3)}{ln(2)}=t\implies 7.9\approx t$

b)

A = 10,000, t = 3

$\bf \begin{cases}
A=10000\\
t=3
\end{cases}\implies 10000=Ie^{\frac{ln(2)}{5}\cdot 3}\implies \cfrac{10000}{e^{\frac{3ln(2)}{5}}}=I
\\\\\\
6597.53955 \approx I$

3 0

3 years ago

A worker is paid $9.80 per hour, with time and a half for any hours over 40 per week. If he works 44 hours in a week, what will

bezimeni [28]

b. 450.80

you multiply 40 x 9.80 ...equals 392.

take 1/2 of 9.80...that equals 4.90. 
4.90 plus 9.80 equals $14.70 x 4 = 58.80 

$58.80 plus 392. equals $450.80

4 0

3 years ago

What is the volume of this right triangular prism 5cm 4.5 cm in 8 cm

Tresset [83]

The Volume Of The Right Triangular Prism Is 180 cm

8 0

3 years ago

The solution for the following system of linear equation 3m-2n=13 is (2,-1) true or false

Tanya [424]

Answer:

Not True

Step-by-step explanation:

>_<

4 0

3 years ago

Read 2 more answers