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3 years ago

Please Help, Lots of points

Mathematics

1 answer:

Andrei [34K]3 years ago

3 0

Answer:

9 cats

Step-by-step explanation:

x = cat

y = dog

Set up equations.

x + y = 30

4.5x + 8.5y = 219

Multiply first equation by 4.5 and subtract.

4.5x + 4.5y = 135

-(4.5x + 8.5y = 219)

-4y = -84

y = 21

Substitute this y value into the first equation

x + y = 30

x + 21 = 30

x = 9

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5x – 12y – 17 = 0<br> 1*9(x + 2) - (y + 1) + 3 = 0

valentina_108 [34]

Answer: $x=\frac{12y+17}{5}$

$y=\frac{-5x+17}{-12}$

$x=\frac{y-20}{9}$

y=9x+20

Step-by-step explanation:

5x-12y-17=0 (plus 17 from both sides)

5x-12y=17 (plus 12y from both sides)

5x=12y+17 (divide 5 from everything)

$x=\frac{12y+17}{5}$

5x-12y-17=0 (plus 17 from both sides)

5x-12y=17 (minus 5x from both sides)

-12y=-5x+17 (divide everything by -12)

$y=\frac{-5x+17}{-12}$

1*9(x+2)-(y+1)+3=0 (distribute 9 to x and to 2) (distribute -1 to y and to 1)

1*9x+18-y-1+3=0 (times 9x by 1)

9x+18-y-1+3=0 (combine like terms)

9x-y+20=0 (minus 20 from both sides)

9x-y=-20 (plus y to both sides)

9x=y-20 (divide 9 from both sides)

$x=\frac{y-20}{9}$

1*9(x+2)-(y+1)+3=0 (distribute 9 to x and to 2) (distribute -1 to y and to 1)

1*9x+18-y-1+3=0 (times 9x by 1)

9x+18-y-1+3=0 (combine like terms)

9x-y+20=0 (minus 20 from both sides)

9x-y=-20 (minus 9x from both sides)

-y=-9x-20 (divide -1 from everything)

y=9x+20

3 0

3 years ago

Eight rooks are placed randomly on a chess board. What is the probability that none of the rooks can capture any of the other ro

Brums [2.3K]

Answer:

9.11*10^-4 %

Step-by-step explanation:

To find the probability, you simply need to find the possible outcomes that allows no rooks to be in danger, and the possible amount of ways to place the rooks.

For the first outcome, you start by putting 1 rook in the first columns, you have 8 possible rows to do this. The next rook in the next column will only have 7 possible rows, as you have to exclude the one where the previous rook is located. The next rook, 6 possibilities, the next 5, and so on. So we conclude that the total amount of ways so that none of the rooks can capture any of the other rooks is 8*7*6*5*4*3*2*1 = 8! = 40320

In order to find the total amount of ways to place the rooks, you can just use a combinatoric:

$\left[\begin{array}{ccc}64\\8\end{array}\right]= \frac{64!}{8!(64-8)!} = 4.43*10^9$

Then:

P = $\frac{40320}{4.43*10^9}*100\%=9.11*10^{-4}\%$

5 0

3 years ago

Which equation is equivalent to log Subscript 3 Baseline (x 5) = 2?.

grin007 [14]

The equivalent equation is x - 4 = 0.

<h2>Linear system</h2>

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.