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The graph of the equation 4x^2 + 20x + 4y^2 - 24y + 21 = 0 is a circle. Find the radius of the circle.

This is an exercise in completing the square: 3x^2 + 12x + 4 = 3(x + 1)^2 + 1, so (a,h,k) = (3,-1,1).  

2. Help!

4x^2 + 20x + 4y^2 - 24y + 21

Divide thrugh by 4

x^2 +5x +y^2-6y = -21/4      ' complete the square '   for x and y

(x+2.5)^2    +   (y-3)^2  = -21/4  + 6.25  + 9 

                                      =  -21/4  + 25/4 + 36/4 = 40/4 = 10

10 = r^2     r = sqrt 10

y= -2x +8      slope = -2     perpindicular slope =  -1 / -2 = 1/2

y = 1/2 x +b     sub in the given point

2 = 1/2 (9) + b     b= -2.5

y = 1/2 x -2.5

1/2 (12-p) *2 =   12-p  unit²

35 x   +   15 (55-x)   = 1325       solve fo x, the gallons used by the 35 mpg car.... then the other is   55-x

Amplitude is 13    so the wave goes from 13   to  -13     AND it is shifted UP by 24

    so max height will be   13 + 24 = 37ft       min height will be   -13 + 24 = 11 ft

Min height will be when the cos fxn = 1     

   when    cos (............) = -1     (0 degrees)

       pi x /60 - 5pi/12 = 0

          x = 25 min    or   8:25

Max height will occur   when    -13 ( cos ( pix/60 - 5pi/12) = 13

        or in other words, when      cos ( pi x / 60 - 5pi/12)   = -1      pi x/60 - 5pi/12 =   pi       x = 85 minutes =  9: 25

200 000 / 800 000    x 100% = 25 % increase

I found that a few other combinations of remainders are three 0 rems and two 2 rems and one 1 rem. I hope this will help...

Welcome !!

x        x+1       x+2        x+3     are the integers

3 ( x +  x+3)   = -5 ( x   +   x+1)   - 114       solve for x

6x + 9 = -10x -5 - 114

16x = - 128

x = -8

-8     -7     -6     -5     

Wow thx i forgot about the 90 degrees. THX i would not have gotten that right. Now i know how to solve this THX AGIAN

150 + two right angles + x = 360

150 + 90 + 90 + x = 360       

150 + two right angles + x = 360

150 + 90 + 90 + x = 360        

make 2x+1 the middle-ish integer   the two below will be  2x -1   and 2x -3     above will be 2x +3 

2x -3     2x-1     2x+1      2x+3 

5 ( 2x-3  + 2x+1)   = 22 +  (2x-1)(2x+3)  + (2x-1 + 2x+3)   solve for 'x'

5 ( 4x-2)   = 22 + ( 4x^2 +4x-3) + (4x+2)

20x-10      = 22  + 4x^2 +8x -1

0    =    4x^2 - 12x +31                       x = hmmmmmmmm     non integer

can you clarify this part?  ' 22 greater than the product of and the sum of the second and the fourth'

The amplitude is one-half the distance from the smallest value (38) to the largest value. (86)  (86 - 38)/2  =  24

The period is the x-distance that it takes to make one full wave:  one-half of a wave is made from 0 to 6, so one

full wave is made from 0 to 12:  12 = 0  =  12

The vertical shift is the shift from zero to the center y-value. The center y-value is 62, so the vertical shift is 62.

The generic form of a sinusoidal function is:

f(x) = A sin(2π/T x + B) + C

where A is the amplitude,

T is the period (time per revolution),

B is the horizontal offset (or phase shift),

and C is the vertical offset (or midline).

2π/T = 6

2π = 6T

T = π/3

T ≈ 1.05 s

The Answer is 1.05 sec

give me a like!

Thx

1. Find the equations of a line that is PARALLEL to y = 3/4x + 3 and passes through the point (3,-7). And it must but in point-slope form.

2. Find the equations of a line that is PERPENDICULAR to y = -3/2x + 3 and passes through the point (-6,4). And it must but in point-slope form.

lol i was wrong too, the result is 477,757,400/24=19,906,560

In general we would have f(x) = m(x)*x*(x-1)*(x-2) + u*x² + v*x + w

where m(x)*x*(x-1)*(x-2) is what I meant by the non-remainder part.  Clearly this part will be zero, when x = 0, 1 or 2.

477,757,400

ok, do you know what the answer is?

Sorry melody, thats incorrect

Thanks for the help guys