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2 years ago

What is the equation of the given line? Y= -3x y= -3 x= -3 x=3

Mathematics

1 answer:

iVinArrow [24]2 years ago

4 0

Answer:

y = -3x

An explanation is not needed for this is quite simple.

(Sorry for my bad English, I'm Japanese, lol.)

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If x=y-7 what is the value of 3x-3 in terms of y

beks73 [17]

$\bf \boxed{x}=y-7
\\\\\\
3x-3\implies 3\left( \boxed{y-7} \right)-3\implies 3y-21-3\implies 3y-24$

7 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

Solve the system of equations:

iVinArrow [24]

$(-1,-2) \: \: \: \: \: and \: \: \: \: \: (3,6) \\ Answer: A$

Step-by-step explanation:

$y = 2x \\ y = {x}^{2} - 3 \\ \\ 2x = {x}^{2} - 3 \\ {x}^{2} - 2x - 3 = 0 \\ (x + 1)(x - 3) = 0 \\ x + 1 = 0 \: \: \: \: \: or \: \: \: \: \: x - 3 = 0 \\ x = - 1 \: \: \: \: \: or \: \: \: \: \: x = 3$

When x = -1

Substitute x = -1 into y = 2x

y = 2(-1)

y = -2

( -1, -2)

When x = 3

Substitute x = 3 into y = 2x

y = 2(3)

y = 6

( 3, 6)

5 0

3 years ago

A tennis shop sold twenty $100 racquets at an 8% profit and ten $80 bags at a 15% loss. The profit on the combined transaction w

Sergeeva-Olga [200]

So first let me assume that the Total profit of the racquets are 8 percentage and not individually.

Now to find the profit we can do

20 x 100= 2000

Now
8=x/2000*100
X= 160

And now for loss
10x80=800

Now

15= x/800*100
X=120

Now profit =

160-120 = 40

The profit was only 40

4 0

2 years ago

Read 2 more answers

Please answer it now

Sergeeva-Olga [200]

Answer:

s= 15 (nearest integer), 14.8 (to nearest 10ths)

Step-by-step explanation:

here you need to apply the cosine rule,

${s}^{2} = {u}^{2} + {t}^{2} - 2ut \cos(s)$