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thanks

Mistakes like this are no big deal Builderboi.

I actually even think they are advanatgeous.

Questions askers should always chaek the answers they are given and this error was very easy to pick up.

The asker was obviously only interested in copying your answer into an answer box.

It is a positive thing that he got it wrong.

Since  tan = y / x  and both the  x  value and the  y  value are negative in the third quadrant,

                               y = -4  and  x = -7.

Since  r = sqrt( x² + y² )    --->     r = sqrt( (-7)² + (-4)² )     --->     r = sqrt( 65 )

Since  cos = x / r    --->     cos = -7 / sqrt( 65 )

Hi  Elijah,

You can most definitely recommend other websites.

You should not ask public permission or give irrelevant preamble beforehand.

If you want to recommend some great site just do so.

In the sticky topics there is a post called 'reference material'

There are many recommended sites in there.

I just added your suggestion to the list.  

Thanks for your contribution.  

The formula for volume is length x width x height.

To calculate the volume in yards, we first have to convert everything into yards. Knowing that 3ft = 1 yard, we can convert them by dividing by 3. This means the dimensions in yards are: 12 yards x 8 yards x 0.25 yards. Using the formula for volume, we know the volume in yards is \(12 \times 8 \times 0.25 = \color{brown}\boxed{24}\)

To calculate the volume in feet, we don't have to do anything, because the dimensions are already in feet, the dimensions are: 36 ft x 24 ft x 0.75 ft. Thus, using the volume formula, we know the volume is \(36 \times 24 \times 0.75 = \color{brown}\boxed{648}\)

a + b = 14

Square both sides

a^2 + 2ab + b^2  =  196     ⇒   a^2 + b^2  =  196 - 2ab

a^3  + b^3 =  (a + b) ( a^2  - ab  +  b^2)

So

(a + b) (a^2 - ab + b^2)  =  812 +  4ab

(14)  ( 196 - 2ab - ab)  =  812  + 4ab

14 ( 196 - 3ab) =  812 + 4ab

2744 - 42ab  = 812 + 4ab

1932  =  46ab

42  = ab

42/a  =  b

a + b  =14

a + 42/a  = 14

a^2 + 42  = 14a

a^2 - 14a  =  -42

a^2  - 14a + 49  = -42 + 29

(a - 7)^2   =  7          take both roots

a - 7   =  ± sqrt 7

a = 7 + sqrt 7        and  b =   7 - sqrt 7

or

a  = 7 - sqrt 7    and b = 7 + sqrt 7

Thx for catching my error, BuilderBoi   !!!!

Oh, shoot... I made an arithmetic error, 13+14+14+14 is 54, not 57 

Thanks Alan!!!

Let \(DE = x\)

We know that \(AE = 3x\) and \(AD = \sqrt{10}x\)

We also know that \(\triangle ABC\) is similar to \(\triangle ADE\)

Because the scale factor is 2, we know that \(CB = 0.5x\)

Thus, the ratio is \({\sqrt{10} \over 0.5 } = \color{brown}\boxed{2\sqrt{10}}\)

We have a SSA  situation.....I'm assuming the  greater possible value  for BC

Use Law of Cosines to find   BC

9^2 = 10^2 + BC^2  -2 (10) (BC)cos 60

81 - 100  =  BC^2  - 10BC

-19  =  BC^2  - 10BC

BC^2  - 10BC  + 19   =  0

BC^2  -10BC =  -19                     complete the square on BC

BC^2  - 10BC  + 25  =  -19  + 25

(BC - 5)^2  =   6                take the positive root

BC - 5  =   sqrt 6

BC  =  5 +  sqrt 6

Area =  (1/2)(AC)(BC) sin 60  = (1/2) (5 +sqrt 6) (10) (sin 60)  =  5 (5 + sqrt 6) ( sqrt (3) / 2 )    ≈

32.26 units^2

Note that  x^2  - 8x + 15  =  (x - 5) ( x - 3)

So

lim                     (x - 5) ( x - 3)

x → 3                ____________  =          x - 5  =      3  -  5   =    -2

                               (x - 3 )

Umm what?

Triangle ACB  is similar to triangle ADE

Let  AE  = 6 

AE / DE = 3

Then DE =  2

Then  AD  =  sqrt  (6^2 + 2^2)  = sqrt 40 =  2sqrt 10

So AC = 1/2 AD =     sqrt 10

And AB =  (1/2) AE =    3

So

BC =  sqrt [  (sqrt (10)^2  - 3^2  ]   =  sqrt 1  =  1

So

AD / BC =   2 sqrt ( 10  )  /  1 =     2 sqrt 10

EDIT to correct a previous error   !!!

5x^2 + 6x  - 4   =  0 

333^1 mod 13 =   8      (1)

333^2  mod 13  =  12   (2)

333^3  mod 13  =  5     (3)

333^4 mod 13  = 1      (4)

333^5  mod 13  =  8

333^6 mod 13  =  12

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.

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The pattern has a repeating cycle of  4

So

(333 mod 4)   =   ( 1  )  =    8

The remainder =   8

Distance from origin  to  the line  =

 l 0 - 2(0) +  25  l   / sqrt  (1^2  + 2^2)   =

25 / sqrt  5  =

5sqrt (5)

This is the radius  of the  circle

Area =   pi ( 5sqrt (5) )^2    =    125 pi  units ^2

The  given line will have a slope of    1/2

The  equation  of   a  line  perpendicular to this  passing through the origin  has  the equation

y   =  -2x    (1)

The original line  can be written as

y  =  (1/2)x + 25/2     (2)

Set  (1)  =  (2)

-2x  = (1/2)x  + 25/2

-4x  = x  +  25

-5x  =  25

x = - 5    y =   -2(-5) =  10

Point of tangency =   (-5 , 10)

2 ^  ( 2x + 3)  =   14         

2^3  * 2^(2x)  =  14

8 * 2^(2x)  =  14

2^(2x)  = 14/8

2^(2x)  =  7/4

(2^x)^2  = 7/4      take the sq rt  of both sides

2^x  =   sqrt ( 7 )  / 2

Let x =  3      and set the two functions eaual

3(3)^2  +  2  =   a(3)  -  1

27 + 2  = 3a   -  1

29  =  3a    - 1

29   +  1  = 3a

30 =  3a

a  = 30   / 3   =    10

By a property of the  medians

EG = 25 (1/3)  =  25 /  3

AG =  15 (2/3)  = 10

Since triangle AGE is right...its area =   (1/2)product of legs EG and AG   =  (1/2)(25/3)(10) = 250 / 6

And by another median property, this area  = 1/6 the area of ABC

So

[ ABC ]  =  6 (250  /  6)  =   250 units ^2

0  ≥  64p - 144                        0 >  22 - 20p

144  ≥ 64p                               20p > 22

144/64  ≥  p                               p > 22/20

p ≤ 144/64                                 p >  11/10

p ≤  9/4

p  =   (11/10 , 9/4  ]

Thank you!

a +  b + c =  60

N = a - 7   ⇒   N + 7  =  a

N = b + 7  ⇒   N - 7   =b

N = 7c    ⇒     N / 7  =  c

So

(N - 7)  + ( N + 7)  +  N  /7  =   60

2N  +  N /7   =  60                      multiply through by 7

14N + N  =   420

15N  = 420

N =  420  /  15     =     28

This is an isosceles  triangle

The  height  = the length of  the median  drawn from  A

Using the Pythagorean Theorem  .....Height =  sqrt [ 8^2  - 1^2 ]  =  sqrt 63  =  3sqrt 7

AG  = (2/3)  Height   =  (2/3) * 3 sqrt 7   =   2 sqrt 7

5. Heights for 16-year-old girls are normally distributed with a mean of 64 in. and a standard
deviation of 1.9 in.
Find the z-score associated with the 90th percentile.
Find the height of a 16-year-old girl in the 90th perc

z score associated with  .90  = 1.29

( Height -  64 ) /  1.9   =  1.29 

Height   -64  =   1.29 * 1.9

Height  =   1.29 ( 1.9)  + 64   ≈    66.4  in