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Readme [11.4K]
3 years ago
7

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:

3

Step-by-step explanation:

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Help me plssssssssss
Amanda [17]

Answer:

Answer: <u> </u><u>y</u><u> </u><u>=</u><u> </u><u>x</u><u> </u><u>+</u><u> </u><u>1</u><u> </u>

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]

<u>Answer:</u>

Carpet costs = 300£

<u>Step-by-step explanation:</u>

• 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}\\\\&#10;A=P(1+rt)\qquad &#10;\begin{cases}&#10;A=\textit{accumulated amount}\\&#10;P=\textit{original amount deposited}\to& \$3000\\&#10;r=rate\to 5\%\to \frac{5}{100}\to &0.05\\&#10;t=years\to &4&#10;\end{cases}&#10;\\\\\\&#10;A=3000(1+0.05\cdot 4)\implies \boxed{A=3600}\\\\&#10;-------------------------------\\\\

\bf \qquad \textit{Compound Interest Earned Amount}&#10;\\\\&#10;A=P\left(1+\frac{r}{n}\right)^{nt}&#10;\quad &#10;\begin{cases}&#10;A=\textit{accumulated amount}\\&#10;P=\textit{original amount deposited}\to &\$3000\\&#10;r=rate\to 5\%\to \frac{5}{100}\to &0.05\\&#10;n=&#10;\begin{array}{llll}&#10;\textit{times it compounds per year}\\&#10;\textit{annually, thus once}&#10;\end{array}\to &1\\&#10;t=years\to &4&#10;\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}\\\\&#10;-------------------------------\\\\&#10;\stackrel{\textit{compounded interest}}{3646.51875}~~-~~\stackrel{\textit{simple interest}}{3600}
7 0
4 years ago
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