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The largest possible value of b is 1/3.

∠3 = ∠17  = 140º

∠18 = 180 - 140 = 40º

The expected vaue is 5/12*pi, so a + b = 5 + 12 = 17.

Need clarification of the rules.  Can we use the same number more than once,

or are we limited to placing 0, 4, 5, 8, and 9 in the appropriate empty spaces? 

 The coordinates of P (4, 1)     Rotation is 90 degree clockwise

Hi Guest!

x and floor(x) must be similar, so I'll just do sqrt(70). 

sqrt(70) = 8.36660026534

So floor(x) = 8

Meaning that x = 70/8 = 8.75. 

So our answer is 8.75

I hope this helped. :)))

=^._.^=

Hi Guest!

A small side note, it really helps if you are more careful with the formatting, it makes reading a lot easier. 

x = hour from noon (note that since stock a starts at 9, it's x + 3)

12.25 + .07(x+3) = 12.75 - .15x

.07x + .21 = .5 - .15x

.22x = .29

x = 29/22

Well... that's not a very nice number for an hour. -.-

So ig the answer is 1:19 ish.

Maybe you can find the error in this?

Sorry I couldn't help more. 

=^._.^=

Hi Guest!

(a-4)(b-4) = ab - 4b - 4a + 16

(a-4)(b-4) = ab - 4(a+b) + 16

Now we need to use the vieta's formula. Here's an AOPS link if you need it: https://artofproblemsolving.com/wiki/index.php/Vieta%27s_Formulas

ab = -5/7

a + b = -1/7

Now, we just plug everything in. 

-5/7 - 4(-1/7) + 16 = (a-4)(b-4)

-5/7 + 4/7 + 16 = (a-4)(b-4)

16 - 1/7 = (a-4)(b-4)

111/7 = (a-4)(b-4)

I hope this helped. :)))

=^._.^=

3x^2 + 12x + 4 - 2x^2 + 11x - 7 = a(x - h)^2 + k

x^2 + 23x - 3 = a(x - h)^2 + k (Combining like terms)

(x+11.5)^2 = x^2 + 23x + 132.5 (factor)

(x+11.5)^2 - 135.5 = a(x - h)^2 + k (replacing)

And we have our answer :)))

(1, 11.5, -135.5)

I hope this helped

=^._.^=

The perpendicular distance between AB and CD = 4.899

5^(2x) = 5^x * 5^x

5^(2x) = 3 * 3

5^(2x) = 9

9 + 3 = 12

So our answer is 12. :)))

I hope this helped.

=^._.^=

The probability is 7/25.

Well said, cat, and I agree with you 100%.  Another thing that bugs me is when someone just posts the answer without showing how to obtain that answer.  I can't figure what they're thinking, maybe just showing off, but one thing that's for sure they aren't trying to help. 

_.

If ア is = 3 cm² then イ= 6 cm²

The two sides with the same length have to be longer than 7.

[8, 8, 12]

[9, 9, 10]

[10, 10, 8]

[11, 11, 6]

[12, 12, 4]

[13, 13, 2]

50 degrees

This was answered yesterday. Go look for it.

2, 6, 7

3, 5, 7

3, 6, 9

So 3 ways. :))

I hope this helped. :)))

=^._.^=

y=(x+3)^2 

y = x^2 + 6x + 9

6/1 = 6

I hope this helped. :)))

=^._.^=

8/5624 = 0.0014224751066856

Hi mintjellyxd!

Question 1

The demoinator of a fraction can't be 0 or negative, so anything less than or equal to -1 will be imposible. 

(-infinity, -1)

Question 2

There is no limit to the range of f(x) since x will always get bigger, but the minimum for the square is 0, so the minimum answer is 1.

[1, infinity)

I hope this helped. :)))

=^._.^=

Thanks!

5624/8=703

Hi Guest

Area of DAB

(2/sqrt(2))^2/2 = 1

Area of CDB

2^2/2 = 2

1 + 2 = 3

I hope this helped. :))

=^._.^=