catmg

It's solved now. :)))

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-7x = 4x + 22

-11x = 22

x = -2

y = 14

(-2, 14)

I hope this helped. :))

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The first thing to notice is that the triangles are similar, and right triangles. 

BC = 2sqrt(6)

ABC side ratios are 

5 : 2sqrt(6) : 7

DAC side ratios are

? : 7 : x, where x = CD

Looking for x, 7/(2sqrt(6))*7 = 49sqrt(6)/12

I hope this helped. :)))

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Hi Guest!

To solve this question, you can use case work. :))

4 digit plus 1 digit

abcd + e = 2247

*note abcd is written as 1000a + 100b + 10c + d. 

dcba + e = 4353

4 digit plus 2 digit

abcd + ef = 2247

dcba + fe = 4353

4 digit plus 3 digit

abcd + efg = 2247

dcba + gfe = 4353

4 digit plus 4 digit

abcd + efgh = 2247

dcba + hgfe = 4353

Try solving these cases by yourself. I wish you best of luck. :)))

If you need help, feel free to respond and I'll try to help more. 

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f(m,n)=9(5m+4n)

5m+4n has to be an integer, and the smallest positive integer is 1. You can achieve this in many ways, one is (m = 1, n = -1). 

But we need to mulitply it by 9, so our answer is 9. 

I hope this helped. :))

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/4/3/2 is because the 4 math books are the same. 

So there 4*3*2 ways the arrange 4 seperate things, but since all of them are the same, we divide 4, 3, and 2. 

Same with 3/2 because the 3 english books are the same. 

I'm sorry, I'm not a teacher nor good at explaining. 

If you're still confused, here's a video: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:combinations/v/introduction-to-combinations

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(x+y+z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx

Now, we just need to plug in some values. 

(x+y+z)^2 = 18 + 2*9

(x+y+z)^2 = 36

x+y+z = 6

*Note that x+y+z could be -6, but we're looking for absolute value. 

So our answer is 6. :)))

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7*6*5*4*3*2/4/3/2/3/2 = 35 ways. 

I hope this helped. :)))

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Hi Guest!

z = a + bi

(a + bi)^2 = i/2

a^2 - b^2 - 2abi = i/2

2a^2 - 2b^2 - 4abi = i

2a^2 - 2b^2 = 0

a^2 = b^2 (Important)

4abi = i

ab = 1/4 (Important)

So |a| and |b| are the same number. 

And since ab = 1/4 (positive), they must be both negative or both positive. 

So a = 1/2 and b = 1/2 or a = -1/2 and b = -1/2. 

z = 1/2 + i/2

z = -1/2 - i/2

I hope this helped. :)))

=^._.^=

Hello Guest!

2*(n+1)!+6*n!=4*(n+1)!

6n! = 2(n+1)!

6n! = 2n! * (n+1)

3 = n + 1

2 = n

I hope this helped. :))

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