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Vlada [557]
3 years ago
10

Solve system of equations for x + y: -4x + 9y = -11 & -3x + 7y =-9

Mathematics
1 answer:
Aloiza [94]3 years ago
8 0

Answer:

x = -3   and   y = -4

x + y = -3-4 = -7

Step-by-step explanation:

-4x + 9y = -11 ------------------------------------------------------------------------(1)

-3x + 7y = -9--------------------------------------------------------------------------(2)

multiply through  equation (1) by 3   and multiply through equation(2) by 4

-12x + 27y = -33 -----------------------------------------------------------------------(3)

-12x + 28y   = -36 ----------------------------------------------------------------------(4)

subtract equation (1) from equation (2)

y = -3

substitute y = -3 into equation (2)

-3x + 7(-3) = -9

-3x -21 = -9

add 21 to both-side of the equation

-3x -21 + 21 = -9 + 21

-3x = 12

divide both-side of the equation by -3

-3x/-3 = 12/-3

x = -4

x = -3   and   y = -4

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There is a bag filled with 5 blue and 6 red marbles.
Afina-wow [57]

Answer:

The probability of getting two of the same color is 61/121 or about 50.41%.

Step-by-step explanation:

The bag is filled with five blue marbles and six red marbles.

And we want to find the probability of getting two of the same color.

If we're getting two of the same color, this means that we are either getting Red - Red or Blue - Blue.

In other words, we can find the independent probability of each case and add the probabilities together*.

The probability of getting a red marble first is:

\displaystyle P\left(\text{Red}\right)=\frac{6}{11}

Since the marble is replaced, the probability of getting another red is: \displaystyle P\left(\text{Red, Red}\right)=\frac{6}{11}\cdot \frac{6}{11}=\frac{36}{121}

The probability of getting a blue marble first is:

\displaystyle P\left(\text{Blue}\right)=\frac{5}{11}

And the probability of getting another blue is:

\displaystyle P\left(\text{Blue, Blue}\right)=\frac{5}{11}\cdot \frac{5}{11}=\frac{25}{121}

So, the probability of getting two of the same color is:

\displaystyle P(\text{Same})=\frac{36}{121}+\frac{25}{121}=\frac{61}{121}\approx50.41\%

*Note:

We can only add the probabilities together because the event is mutually exclusive. That is, a red marble is a red marble and a blue marble is a blue marble: a marble cannot be both red and blue simultaneously.

4 0
2 years ago
-6 4/9 -3 2/9 -8 2/9<br> -
Zinaida [17]

Answer:

-17.8884

Step-by-step explanation:

- 6.444 - 3.2222 - 8.2222 = -17.8884

8 0
3 years ago
Read 2 more answers
What are equivalent fraction to 33/48 with the numeration as 11
Vera_Pavlovna [14]

Answer:

11/16

Step-by-step explanation:

The first thing I would do is see 11 times what will get me 33

The answer is 3

Next I would ask myself 48 divided by 3 is what

The answer is 16

To double check my work I would do 3 x 11 = 33

                                                              3 x 16 = 48

5 0
2 years ago
The difference of the square of a number and 24 is equal to 5 times that number. Find the negative solution.
vampirchik [111]

Answer:

the "negative solution" is -3

Step-by-step explanation:

Represent the number by n.

Then n^2 - 24 = 5n

We rewrite this in standard quadratic form:

n^2 - 5n - 24 = 0

This factors as follows;  (n + 3)(n - 8) = 0

The roots are n = -3 and n = 8.  Thus, the "negative solution" is -3

8 0
3 years ago
309 ,009 ,990 in expanded form
Mrac [35]

300 + 0 +9,

0 + 0 + 9

900 + 90

8 0
3 years ago
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