CPhill

65% x 109  = $70.85  is the markup  [ the chair sells for $[ 109 + 70.85] = $ 179.85

I assume this is

0=26(sin60)t + (1/2)(-9.8)t^2      so we have

[ 26sqrt(3)/2] t - 4.9 t^2   = 0      factor out t

t [ 13sqrt(3) - 4.9t  ] = 0

Set both factors to 0.......  and t = 0   or t =  [ 13sqrt(3)]  / 4.9 = about  4.595

y=-6

4x+5y=-18        substitute the first equation into the second for y

4x + 5[ -6] = -18

4x - 30  = -18        add 30 to both sides

4x = 12    divide both sides by 4

x = 3    so   (x , y) = (3, -6)

This is an undetermined quantity......to see why....

0 /  0  = any real number  ......   because any real number *  the denominator of 0  = the numerator, 0  

If you look at the unit circle, the angle of 3pi/2 has its terminal point at  (x. y) = (0, -1)

And sin = y/r    and r = 1 on the unit circle.....so .....    sin (3pi/2) = y / r   = -1  1   = -1

I'm guessing that the "27"  in your equation was arrived at by cubing rhe sphere's radius......thus....the radius was 3 and the diameter, twice that  =  6

Here you go.......http://www.purplemath.com/modules/exponent3.htm

x+3(x+2(x-6)+6)+11/4  =

x + 3x + 6(x - 6) + 18 + 11/4  =

x + 3x + 6x - 36 + 18   + 11/4 =

10x - 18 + 11/4  =        

10x - 72/4 + 11/4  =

10x - 61/4

Sorry....I don't see this as a substitution or elimination problem......here's how I would solve it......

Let x be the lbs. of peanuts used....and we have

2.25x + 3.25 (14) =  2.65(14 + x)    simplify

2.25x + 45.50   = 37.10 + 2.65x       subtract 2.25x, 37.10 from both sides

8.40  = .40x      divide both sides by .40

21  = x   = 21 lbs. of peanuts

[Maybe someone else on here knows a different method]

Let L1 be the length of one of the legs and L2 be the lentgh of the other.......and by the Pythagorean Theorem ,we have that

[L1]^2 + [(1/2)L2] ^2 = 19^2     and

[L2]^2 + [(1/2)L1]^2  = 13^2   simplify

L1^2 + (1/4)L2^2  = 361     (1)

L2^2 + (1/4)L1^2  = 169     (2)

Rearranging (1),we  have

L1^2  = 361  - (1/4)L2^2   (3)    and subbing this into (2),we have

L2^2 +(1/4)[ 361 - (1/4)L2^2 ] = 169     multiply through by 16

16L2^2 + 4*361 - L2^2  = 2704

15L2^2  = 2704 - 4*361 

15L2^2 = 1260     divide by 15

L2^2 = 84   →  L2 = 2sqrt(21)

And using (3), we have

L1^2 = 361 - (1/4)L2^2

L1^2 = 361 - (1/4)84

L1^2  = 361 - 21

L1^2  = 340  →  L1 = 2sqrt(85)

So....the hypotenuse =  sqrt (84 + 340) =  sqrt (424) = 2sqrt (106)