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2 years ago

How to graph a line that passes through (-1,-7) and has a slope of 4

Mathematics

1 answer:

lana [24]2 years ago

5 0

Answer:

y=4x-3

Step-by-step explanation:

First, write your equation as y=4x+b. Plug in your coordinate to the equation, it should look like this: -7=4(-1)+b. Multiply 4 by -1 to get -4. It should look like this: -7= -4+b. Add 4 to both sides to get your y-intercept of -3. Go back to your original equation and plug in -3 to b. This is your final equation: y=4x-3. Hope this helped!

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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

{(12*3)+6}-3^2 divided by (9-6)

Mrac [35]

33. 12*3=36 the u add 6 so it becomes 42. 3^2 is 9 so if u subtract 9 from 42 it becomes 33.

6 0

3 years ago

In the given right triangle find the missing length 24m 10m c

nirvana33 [79]

The missing length: sqrt (24^2 + 10^2) m Answer: 26 m

3 0

3 years ago

Read 2 more answers

The admission fee at a local zoo is $1.50 for children and $5.00 for adults. On a certain day, 3000 people enter the zoo and $9,

vlabodo [156]

1600 children and 1400 adults attended

<h3>How to determine the number of adults?</h3>

Let the children be x and adult be y.

So, we have the following equations:

x + y = 3000

1.5x + 5y = 9400

Make x the subject in x + y = 3000

x = 3000 - y

Substitute x = 3000 - y in 1.5x + 5y = 9400

1.5(3000 - y) + 5y = 9400

Expand

4500 - 1.5y + 5y = 9400

Evaluate the like terms

3.5y = 4900

Divide both sides by 3.5

y = 1400

Substitute y = 1400 in x = 3000 - y

x = 3000 - 1400

Evaluate

x = 1600

Hence, 1600 children and 1400 adults attended

Read more about system of equations at:

brainly.com/question/14323743

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8 0

1 year ago

What is the y coordinate of the solution 3x+2y=12

Tomtit [17]

Answer:

Step-by-step explanation:

3x+2y=12

2y=-3x+12

y=-3/2+12

Honestly you dont have to do any of this work but i did it anyways, The y coordinate is always at the end of the point intercept form (y=mx+b form)

5 0

3 years ago