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Tysm :D

C  =  5n + 40

        ______     multiply both sides by 9

            9

9C  =  5n + 40       subtract 40 from both sides

9C - 40  =  5n       divide both sides by 5

9C - 40

______    = n      notice that we can split th left side up as

     5

9C              40

___     -      __             =     n

  5               5

(9/5)C  -  8  = n           answer  "A"

You did not confuse me, thank you so much ^-^

p(x)   is  the answer that goes in the top left box

x cannot be > 1  in this function because we would have a negative under the square root

q(x)  is the answer that goes in the bottom left box

x cannot be > -1  ...for instance...if x  = 0, we get -1 under the root which isn't real

r(x)  goes in the top right box

x cannot be < -1   ...we get a negative under the radical

s(x) goes in the bottom right box

If x < 1, we get a negative under the radical

I hope I haven't confused you, RP

thanks Cphill

Ax + By  = C  is standard form

y = -A/Bx + C/B

This form would be helpful to find the y intercept  [ and the slope ]

"B" is correct

If x  =  0...then y = 100

Thus....one of the two bottom graphs must be correct

Notice in the bottom left graph that 2 appears to be a root.....testing this in the polynomial should produce a result of 0

y=2^4−6(2)^3−11(2)^2+60(2)+100   =  144

So...the bottom right graph is correct

 x²y^-3z^-1  =

  x²

____

y³ z

The 14th term is

27  + 4(14 - 1)   =  79

The sum is given by

[ 27 + 79]  * 14/2   =  742

The 10th term  is

455 +  16 (10 - 1)   =  599

Th sum is given by :

( 455 + 599) * 10/2   =   5270

Guest please stop..I did not remembered. But thank you all for answering it

....and you didn't learn the answer?   You didn't remeber asking the question just a day or two ago?

You didn't want to take the time to look up the answer that was given then?

  Are we just doing every bit of your homework?  Are you learning anything?  Are you TRYING to learn how the answers are derived? 

Because my teacer asked me again

Definitely converges, OBT

The geometric ratio is 2/3

The sum is

2/3  / [ 1 - 2/3]  =

2/3 / [1/3]  =

2

Sigma  notation

   inf

   ∑ (2/3)ⁿ

n = 1

You know you asked this EXACT SAME QUESTION a couple of days ago!!!!!!????  AND it was answered...........

    Why post it AGAIN?

I do not know what the  poly remain theorem is, but if you put in '5' fo 'x' , the result is

f(5) = 469

It is a parabola....

if 'a' is positive it is open upwards like a bowl

if 'a' is negative it is open downward like a dome

imaginary     as in    ' i '

Gretchen has eight socks, two of each color: magenta, cyan, black, and white.

She randomly draws four socks.

What is the probability that she has exactly one pair of socks with the same color?

\(\text{Let ${\color{magenta}{m}} = {\color{magenta}{magenta}}$ } \\ \text{Let ${\color{cyan}{c}} = {\color{cyan}{cyan}}$ } \\ \text{Let ${\color{black}{b}} = {\color{black}{black}}$ } \\ \text{Let ${\color{grey}{w}} = {\color{grey}{white}}$ } \)

The Set is\(\{ {\color{magenta}{m_1}},{\color{magenta}{m_2}}, {\color{cyan}{c_1}},{\color{cyan}{c_2}}, {\color{black}{b_1}},{\color{black}{b_2}}, {\color{grey}{w_1}},{\color{grey}{w_2}} \} \)

The number of all the possibilities is \(^8C_4=\dbinom{8}{4} = \mathbf{70 }\)

\(\begin{array}{|rcll|} \hline && \dfrac{ \dbinom{ {\color{magenta}{2} } }{ 2 }\times \left[ \dbinom{{\color{cyan}{2}}}{1}\dbinom{{\color{black}{2}}}{1}\dbinom{\color{grey}{2}}{0} +\dbinom{{\color{cyan}{2}}}{1}\dbinom{{\color{black}{2}}}{0}\dbinom{\color{grey}{2}}{1} +\dbinom{{\color{cyan}{2}}}{0}\dbinom{{\color{black}{2}}}{1}\dbinom{\color{grey}{2}}{1} \right] \\ + \dbinom{ {\color{cyan}{2} } }{ 2 }\times \left[ \dbinom{{\color{magenta}{2}}}{1}\dbinom{{\color{black}{2}}}{1}\dbinom{\color{grey}{2}}{0} +\dbinom{{\color{magenta}{2}}}{1}\dbinom{{\color{black}{2}}}{0}\dbinom{\color{grey}{2}}{1} +\dbinom{{\color{magenta}{2}}}{0}\dbinom{{\color{black}{2}}}{1}\dbinom{\color{grey}{2}}{1} \right] \\ + \dbinom{ {\color{black}{2} } }{ 2 }\times \left[ \dbinom{{\color{cyan}{2}}}{1}\dbinom{{\color{magenta}{2}}}{1}\dbinom{\color{grey}{2}}{0} +\dbinom{{\color{cyan}{2}}}{1}\dbinom{{\color{magenta}{2}}}{0}\dbinom{\color{grey}{2}}{1} +\dbinom{{\color{cyan}{2}}}{0}\dbinom{{\color{magenta}{2}}}{1}\dbinom{\color{grey}{2}}{1} \right] \\ + \dbinom{ {\color{grey}{2} } }{ 2 }\times \left[ \dbinom{{\color{cyan}{2}}}{1}\dbinom{{\color{black}{2}}}{1}\dbinom{\color{magenta}{2}}{0} +\dbinom{{\color{cyan}{2}}}{1}\dbinom{{\color{black}{2}}}{0}\dbinom{\color{magenta}{2}}{1} +\dbinom{{\color{cyan}{2}}}{0}\dbinom{{\color{black}{2}}}{1}\dbinom{\color{magenta}{2}}{1} \right] } {70} \\\\ &=& \dfrac{ 1\times \left[ 2\cdot 2\cdot 1 + 2\cdot 1\cdot 2 + 1\cdot 2\cdot 2 \right] \\ + 1\times \left[ 2\cdot 2\cdot 1 + 2\cdot 1\cdot 2 + 1\cdot 2\cdot 2 \right] \\ + 1\times \left[ 2\cdot 2\cdot 1 + 2\cdot 1\cdot 2 + 1\cdot 2\cdot 2 \right] \\ + 1\times \left[ 2\cdot 2\cdot 1 + 2\cdot 1\cdot 2 + 1\cdot 2\cdot 2 \right] } {70} \\\\ &=& \dfrac{ ( 4+4+4 ) + (4+4+4) + (4+4+4) + (4+4+4) } {70} \\ &=& \dfrac{ 12 + 12 + 12 + 12 } {70} \\ &=& \dfrac{ 4\cdot 12 } {70} \\\\ &=& \dfrac{ 2\cdot 12 } {35} \\\\ &\mathbf{=}&\mathbf{ \dfrac{ 24 } {35} } \\ \hline \end{array}\)

The probability that she has exactly one pair of socks with the same color is \(\mathbf{ \dfrac{ 24 } {35} }\)

-3 and -1 are the zeros ie values of x so that f(x) = 0

By the Pythagorean identity...

( sin(-θ) )² + ( cos(-θ) )²  =  1

                                                 We are given that  cos(-θ) = 4/5

( sin(-θ) )² + ( 4/5 )²  =  1

( sin(-θ) )² + 16/25  =  1

                                                 Subtract  16/25  from both sides of the equation.

( sin(-θ) )²  =  1 - 16/25

( sin(-θ) )²  =  9/25

                                                 Take the  ±  square root of both sides.

sin(-θ)  =  ±√[ 9/25 ]

sin(-θ)  =  ± 3 / 5

Since cos(-θ) is positive,  -θ  must be in Quadrant I or Quadrant IV.

Since tan θ > 0 ,  θ  must be in Quadrant I or III. That means  -θ  must be in Quadrant IV or II .

So  -θ  has to be in Quadrant IV, and  sin(-θ) has to be negative.

sin(-θ)  =  - 3 / 5

well this seems like trig, so i hope it is.

you have the base and heighth, 2 and 7

so that is tangent, when you have to legs

so use a calculator for inverse tan of 7/2

using atan(7/2) on web2.0 's caculator it says 74

radical form means the root symbol and they are in all the answers

distribute that 2/3 exponent to each term so we multiply exponents

x^(3*2/3) = x^2, only one answer with that, the second one

but lets do y for fun

y^(4*2/3) = y^8/3

so the Y^6/3 comes out to y^2 and we are left with Y^2/3

which is the second answer also.

extra work when we already eliminate the other answers before.

looking at this, you be like what?

kind of want to get rid of some fractions.

lets multiply everything by 4, cause of that 1/4 at the front will go away.

5x/12 - 3/4 > 4x + 1/3, a little better

we could multiply everything by 12 now and get rid of all fractions

or we could start moving terms around and combining.

i think i will try  times 12  to all terms, cause of that 5/12 in front.

one would only do this if all fractions were reduced by this. 

if there was a 1/5 then 12 would not work cause 12/5 does not become a whole number

5x - 9 > 48x + 4 is what we get after *12 to all terms

now we can move and combine.

5x to the right, 4 to the left, change signs

-9 -4 > 48x - 5x

-13 > 43x

divide by 43 to x alone

-13/43 > x

seems to be the last answer

just multiply x to each term in the second equation

the multiply -3 to each term in the second equation.

then combine like terms.

all answers have the same fron and last terms so what about the middle ones.

x and -x = - x^2

-3 and 2x^2 = - 6x^2

add those for -7x^2 so we cut our answers in half

x and 3 = 3x

-3 and -x = 3x

add those for 6x

now we know it is the last answer