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Alex17521 [72]
3 years ago
13

What are the methods of substitution?

Mathematics
1 answer:
anyanavicka [17]3 years ago
8 0

Answer:

-<u>One Equation</u>: is set equal to a variable

Example:

y = 2x + 1

x + 3y = -12

You already have y, plug it back into x + 3y = -12

x + 3(2x + 1) = -12

x + 6x + 3 = -12

7x + 3 = -12

(Subtract 3 from each side)

7x = -15

(Divide by 7)

x = - 2.14

-<u>No Equation</u>: is set equal to a variable

Example:

2x + y = 10

4× + 2y = -3

Subtract 2x from each side of 2x + y = 10, you should get y= -2x + 10. Now that you have found y, substitute y into 4x+ 2y = -3.

4x + 2(-2x + 10) = -3

4x + -4x + 20 = -3

(Subtract 20 from each side)

4x + -4x = -23

(Add 4x and -4x)

0 = -23

No Solution

<u>-Both</u><u> </u><u>Equations</u>: are set equal to a variable

Example:

y = x + 5

y = -x + 3

(you already have y so plug it into the other equation to solve for x)

-x + 3 = x + 5

(Add -x on both sides)

3 = 2x + 5

(subtract 5 from both sides)

-2 = 2x

(Divide by 2 on each side)

x = -1

I hope this helped!

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What is 98=3y-4 i need answer
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If you would like to solve the equation 98 = 3 * y - 4, you can calculate this using the following steps:

98 = 3 * y - 4
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The correct result would be 34.
4 0
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A cookie jar starts off with 36 cookies in it, and each day 4 cookies are eaten. After a certain number of days, there are 4 coo
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Answer:

8 days until there will be only 4 cookies left in the jar

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3 0
3 years ago
Determine the domain of each graph:
ycow [4]

Answer:

The 1st

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The second

Domain is (R)

The 3rd

Domain = (R)

The 4th

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Respectively

8 0
3 years ago
On a given day, a particular raccoon will eat the trash from one of three different houses. If he eats from the trash of a parti
pashok25 [27]

Answer:

Step-by-step explanation:

On a given day , a particular raccoon will eat the trash from one of three different houses.

Let assume Y_n be a random variable that illustrating  the house raccoon will eat on an unknown given nth day.

If he eats from the trash of a particular house, he has a 50% chance to eat from the same house the next day, and a 25% chance each to eat from one of the other two houses.

There are three states given in the above statement.

So, we can have state 1, state 2 and state 3

Assuming that:

state 1 = house 1

state 2 = house 2

state 3 = house 2

If he eats from the trash of a particular house,

For state 1 : he has a 50% chance to eat from the same house the next day

i.e state 1 = 0.50

and a 25% chance each to eat from one of the other two houses.

For state 2 and state 3: = 0.25

i.e state 2 = 0.25

state 3 = 0.25

NOW:

\mathtt{P[Y_{n+1 }= 0  \ |  \  Y_n = 0] = 0.5}

\mathtt{P[Y_{n+1 }= 1  \ |  \  Y_n = 0] = 0.25}

\mathtt{P[Y_{n+2}= 2   \ |  \  Y_n = 0] = 0.25}

\mathtt{P[Y_{n+1 }= 0  \ |  \  Y_n = 1] = 0.25}

\mathtt{P[Y_{n+1 }= 1  \ |  \  Y_n = 1] = 0.5}

\mathtt{P[Y_{n+1 }= 2  \ |  \  Y_n = 1] = 0.25}

\mathtt{P[Y_{n+1 }= 0  \ |  \  Y_n = 2] = 0.25}

\mathtt{P[Y_{n+1 }= 1  \ |  \  Y_n = 2] = 0.25}

\mathtt{P[Y_{n+1 }= 2  \ |  \  Y_n = 2] = 0.5}

The stochastic matrix for this scenario can be computed as:

                  0          1       2

P = \left\begin{array}{c}0\\1\\2\end{array}\right  \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]

\mathbf{ P =\left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right] }

5 0
4 years ago
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