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3 years ago

Y=3x-9 6x-2y=14 How many solutions does the linear system have?

Mathematics

1 answer:

Tcecarenko [31]3 years ago

7 0

Answer:

Step-by-step explanation:

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Help me plssssssssss

Amanda [17]

Answer:

Answer:  y = x + 1 

Step-by-step explanation:

${ \tt{y = - 3x + 5}}$

» At point of intersection:

${ \tt{2 = - 3x + 5}} \\ { \tt{ - 3x = - 3}} \\ { \tt{x = 1}}$

» Point of intersection is (1, 2)

• General equation of a line:

${ \tt{y = mx + c}}$

m is slope
c is y-intercept

» Consider point (1, 2);

${ \tt{2 = (1 \times 1) + c}} \\ { \tt{c = 2 - 1}} \\ { \tt{c = 1}}$

Equation:

${ \tt{y = x + 1}}$

8 0

2 years ago

If a substance decays at a rate of 25% every 10 years, how long will it take 512 grams of the substance to decay to 121.5 grams

Juliette [100K]

Answer:

It will take 50 years to decay from 512 grams to 121.5 grams.

Step-by-step explanation:

The decay formula :

$N=N_0e^{-\lambda t}$

where

N= amount of substance after t time

N₀= initial of substance

t= time.

A substance decays at a rate 25% every 10 years.

So, remaining amount of the substance is = (100%-25%)= 75%

$\frac{N}{N_0}=\frac{75\%}{100\%}=\frac{75}{100}=\frac34$ , t= 10

$N=N_0e^{-\lambda t}$

$\Rightarrow \frac {N}{N_0}=e^{-\lambda t}$

$\Rightarrow \frac34 =e^{-\lambda .10}$

Taking ln both sides

$\Rightarrow ln|\frac34| =ln|e^{-\lambda .10}|$

$\Rightarrow ln|\frac34|=-10\lambda$

$\Rightarrow \lambda=\frac{ ln|\frac34|}{-10}$

Now , N₀= 512 grams, N= 121.5 grams, t=?

$N=N_0e^{-\lambda t}$

$\therefore 121.5=512e^{-\frac{ln|\frac34|}{-10}.t}$

$\Rightarrow 121.5=512e^{\frac{ln|\frac34|}{10}.t}$

$\Rightarrow \frac{121.5}{512}=e^{\frac{ln|\frac34|}{10}.t}$

Taking ln both sides

$\Rightarrow ln|\frac{121.5}{512}|=ln|e^{\frac{ln|\frac34|}{10}.t}|$

$\Rightarrow ln|\frac{121.5}{512}|={\frac{ln|\frac34|}{10}.t}$

$\Rightarrow t=\frac{ln|\frac{121.5}{512}|}{\frac{ln|\frac34|}{10}}$

$\Rightarrow t=\frac{10.ln|\frac{121.5}{512}|}{{ln|\frac34|}}$

⇒t=50 years

It will take 50 years to decay from 512 grams to 121.5 grams.

8 0

4 years ago

30 POINTS AND BRAINLIEST PLS HELPP - Vanessa's bedroom floor is a rectangle 3m wide and 5m long. She chooses a new carpet that c

zzz [600]

Answer:

Carpet costs = 300£

Step-by-step explanation:

• First calculate the area of the floor:

Area of floor = length x width

= 5m² x 3m²

= 15m²

• As one m² of carpet costs £20, 15m² of carpet costs:

15 x 20

= 300£

7 0

2 years ago

13 please help.......

Nadusha1986 [10]

To find the average, or mean of data, we add them all up, and divide by the number of data points:

-1.2 + 0.8 + 0.65 - 3.4 + 5.8

>> 2.65

2.65 / 5

>> 0.53

4 0

4 years ago

If $3000 is deposited in an account that pays 5% interest, what is the difference in the amount after 4 years between the amount

Triss [41]

$\bf \qquad \textit{Simple Interest Earned Amount}\\\\
A=P(1+rt)\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to& \$3000\\
r=rate\to 5\%\to \frac{5}{100}\to &0.05\\
t=years\to &4
\end{cases}
\\\\\\
A=3000(1+0.05\cdot 4)\implies \boxed{A=3600}\\\\
-------------------------------\\\\$

$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$3000\\
r=rate\to 5\%\to \frac{5}{100}\to &0.05\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, thus once}
\end{array}\to &1\\
t=years\to &4
\end{cases}$

$\bf A=3000\left(1+\frac{0.05}{1}\right)^{1\cdot 4}\implies A=3000(1.05)^4\implies \boxed{A=3646.51875}\\\\
-------------------------------\\\\
\stackrel{\textit{compounded interest}}{3646.51875}~~-~~\stackrel{\textit{simple interest}}{3600}$

7 0

4 years ago