catmg

Hi Guest!

1001 prime factorzation is 7*11*13.

GCD that are possible and 2 digit is 11, 13, 77, and 91. 

So 11 has the numbers: 11, 22, 33, 44, 55, 66, 77, 88, and 99: or 9 numbers. 

And 13 has the numbers: 13, 26, 39, 52, 65, 78, and 91: or 7 numbers. 

Total there are 99 numbers, and 9+7+1+1 have double digit gcds. 

So the answer is 99 - (9+7) = 83. 

So the answer is 83. 

I hope this helped. :))

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Hi Guest!

5.75(p) - 3.25 = c

If he buys 5 pounds, we just replace p with 5. 

5.75(5) - 3.25 = c

c = 25.5

I hope this helped. :)))

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The time tables are a table that show you multiplication answers. 

https://www.mathsisfun.com/tables.html

Here's the link to one. 

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Hi GR0001!

10(e - 4) = 20(f - e)

10e - 40 = 20f - 20e

e - 4 = 2f - 2e

3e = 2f + 4

20(f - 4)=10(e+f)

2(f - 4) = e + f

2f - 8 = e + f

f = e + 8

3e = 2(e + 8) + 4

e = 20

f = 20 + 8

f = 28. 

So e = 20 and f = 28. 

I hope this helped. :)))

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If we start listing out the gcds, you'll notice that they repeat, 1, 2, 1, 4. 

I'm pretty sure this is due to the +4 in 3n + 4. 

So the possible values are 1, 2, and 4. 

1 + 2 + 4 = 7

I hope this helped. :)))

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If you do it enough times in mod 5, you'll notive a pattern of 2, 4, 1, 2, 4, 1. 

100/3 = 33 remainder 1. 

So our answer is 2. 

I hope this helped. :)))

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6*5/2 = 15 (total ways to paint 2 faces)

2 and 4 are the only way to have the product of 2 numbers 1-6 equal 8.

15 - 1 = 14

14 is our answer.

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f(-7) = 2(-7)  + 9

f(-7) = -14 + 9

f(-7) = -5

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x+(x+12)=124

2x + 12 = 124

2x = 112

x = 56

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Hi Guest!

Vieta's Formula

To solve these problems we're going to need the vieta's formula. 

Here's a link to them if you need them: 

https://artofproblemsolving.com/wiki/index.php/Vieta%27s_Formulas

Problem 1

1/a + 1/b = (a+b)/(a*b)

a + b = 4/5 (Veita's)

a * b = 11/5 (Veita's)

(4/5) * (11/5) = 44/25

Our answer is 44/25

Problem 2

u/v + v/u = (u^2+v^2)/(u*v)

u^2+v^2 = (u+v)^2 - 2uv

u + v = 7/3

u * v = -7/5

u^2 + v^2 = (7/3)^2 - -14/5

u^2 + v^2 = 49/9 + 14/5

u^2 + v^2 = 371/45

u/v + v/u = (371/45)/(-7/5)

u/v + v/u = -53/9

Our answer is -53/9

*Please note that for the second problem, simply solving for the roots by factoring may be a better method. 

I hope this helped. :))))

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