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y  =  (x - 2)(x - 3)(x + 3)

The zeros of this are the  x  values that make  y  be zero, that is, the  x  values when

0  =  (x - 2)(x - 3)(x + 3)

Set each factor equal to zero and solve each for  x  .

x  - 2  =  0     so     x  =  2

x  - 3  =  0     so     x  =  3

x + 3  =  0     so     x  =  -3

The zeros are  2, 3, -3

x + y   =   3     subtract  x  from both sides to get     y  =  3 - x

x² + y²   =   9       Substitute  3 - x  for  y  in this equation.

x² + (3 - x)²   =   9               Now we can solve this for  x .

x² + (3 - x)(3 - x)   =   9

x² + 9 - 6x + x²   =   9          Subtract  9  from both sides and combine like terms.

2x² - 6x   =   0                      Factor  x  out of both terms on the left side.

x(2x - 6)   =   0                     Set each factor equal to zero.

x  =  0          or          2x - 6  =  0

                                   x  =  3

Now we can use these values for  x  to find  y .

If   x = 0 ,     0 + y = 3    so    y = 3

If   x = 3 ,     3 + y = 3    so    y = 0

The solutions are   (0, 3)   and   (3, 0) .

Here's the way I thought about this one :

http://web2.0calc.com/questions/help-plz-im-having-some-good-old-trouble-with-this-one#r1

Don't feel bad....we all feel like "half-wits" from time to time....LOL!!!!

thx i was trying and tryng over and over.... i feel like a half wit lol thx so much!

To the best of my ability......answered here :

http://web2.0calc.com/questions/help_80357#r3

5x + 11 ≥  -9     subtract 11 to both sides    

5x ≥ -20       divide both sides by 5

x ≥ -4

10x  - 3  ≤  27     add 3 to both sides

10x ≤ 30      divide both sides by 10

x ≤  3

l  3x  +  1   l   =  1

We have two equations

3x +  1    =   1                                       3x  +  1   =   -1

                    subtract 1 from both sides

3x   =   0                                               3x  =  - 2

                   divide both sides by  3

x =  0                                                  x  =  -2 / 3

We can use any vowel  = 6 choices and any consonant  = 20 choices

And the vowel can come first or the consonant can come first  =  2 choices

So.....with one vowel we have  6 * 20 * 2  =  240 "words"

We can also use   a word with the same vowel repeated = 6 "words"

We can  also select any one of the vowels first  = 6 choices  and any one of the remaining vowels second  = 6 * 5  = 30 "words"

So......   240 +  6  +  30    =    276 "words"

-12x + 13y  = -10        we want to get y by itself

Add 12x to both sides

13y  =  12x  -  10       divide through by 13

y  =  (12/13)x  -  10/13     ⇒  slope (12/13), y intercept -10/13

4 - x + 20 = y - 10     simplify

24 - x  = y  - 10     rearrange as 

34  =  x + y

And  ( 4, 30)  ,  (24,10)   are the only solutions where x + y  =  34

Sure what you need to know?

y -  3  =  (4/7) ( x - 7)

Solve this for the x coordinate of the vertex  and axis of symmetry

6x - 2  =  0

Add 2 to both sides

6x  = 2

Divide both sides by 6

x  =  1/3

And the y coordinate  is  - 7

So......

(1/3, -7) , x  = 1/3   shifted to the right 1/3 units and down 7 units 

The last one

y  =  -16x^2 + 105x  + 12

Time to reach max ht  =    -105 / [ 2 * -16]  =  105/32  sec

Put  this into the function to find the max height  =

-16 (105/32)^2 + 105(105/32)  + 12   =  184.27 ft

And the time it takes to hit the ground  =

-16x^2  + 105x  + 12  =  0

( -105 ±√ [ 105^2   - 4(-16)(12) ]  )  /  [ 2 (-16)] 

( -105 ±√ 11793 )  /  -32     take the negative sign

( -105 - √11793 )  / -32  ≈  6.67  sec

We  have this  :

350 / tan (2°)  -  350 / tan (5.5°)  =  distance   =  6387.8 ft

x^4  + 5x^3  + 7x^2  - 3x - 10  = 0

If we  add the coefficients and constant term and get  0 then 1 is a root....so....

1 + 5 + 7  - 3  - 10   =    13  - 13   =    0

So 1  is a root

So.....we need to check  wheter 2  is a root...if not....then  -2 must be the other  rational root

So

(2)^4  + 5(4)^3 + 7(2)^2  - 3(2) - 10   >  0

So   -2  is the other rational root

So    -2, 1   are the rational roots

32pi  =  2*pi *r* (240/ 360)        divide both sides by pi

32  =   2 * (240/360) * r

32  = 240/180 * r

32  =  (4/3) * r

(32) (3/4)   = r

24  =  r

36pi  =  2* pi * 48  *  ( Angle / 360)

36    = (96/360)  * Angle

36 (360 / 96)  = Angle

(36/96)(360)  = Angle

(3/8)(360)  - Angle

135°  = Angle  =   (3/4)pi   rads

Quadrant iV ⇒  cosine positive, sine negative

4pi/5  *  (180) / pi  =  (4/5)(180)  =  144°

posive coterminal angle  = 2*360 - 32  =  688°

negative coterminal angle  = -360 - 32  =  -392°

[ if the negative coterminal angle is supposed to be between - 500 and -1000, we have 

-2*360 - 32  =  -752°  ]

257°   lies between  180°  and 270°....so......Quadrant III

3x^2 - 4 =  -x^4         add x^4 to both sides

x^4 + 3x^2  - 4  = 0     factor as

(x^2 + 4) (x^2 - 1)  = 0

(x^2 + 4)  (x + 1)  ( x-1)  = 0

Setting the last two factors to 0 and solving for x produces   x = -1 and x  = 1

Settting the first factor to 0, we have

x^2 +4  = 0   subtract 4 from both sides

x^2  =   -4         take both roots

x = ±√-4    =  ±2i

So the solutions are    1, -1, 2i, 2i

(s + 4v)^5  =

s^5  +  5(s^4)(4v) + 10(s^3)(4v)^2  + 10(s^2)(4v)^3  + 5(s)(4v)^4  + (4v)^5  

s^5  +  20s^4v  + 160s^3v^2   + 640s^2v^3  + 1280sv^4  +  1024v^5  [third answer ]

 When one unit of methane is consumed, one unit of carbon dioxide is produced. Simple but confusing.

6387.8

Can someone help me I do not understand the question

Simplify \(i^1+i^2+i^3+\cdots+ i^{97} + i^{98}+i^{99}.\)

Geometric sequence ratio = i

\(\begin{array}{|rcll|} \hline s_{99} &=& \frac{ i - i^{100} } {1-i} \qquad & | \qquad i^{100} = i^{2\cdot 50} = (i^2)^{50} = (-1)^{50} = 1 \\\\ s_{99} &=& \frac{ i - 1 } {1-i} \\\\ s_{99} &=& - \left( \frac{ 1 - i } {1-i} \right) \\\\ s_{99} &=& - 1 \\ \hline \end{array} \)