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Area = l x w        and   l = 10w

264 = 10w * w = 10w^2

w^2 = 26.4               (w = sqrt 26.4)            (l = 10 sqrt26.4)

w = 5.138      l = 51.38       

alcohol in ingredients = alcohol in final soln

x = 20% volume

40 = 50% volume

(x+40) = 30% volume

.20(x) + .50(40) = .30(x+40)

.2x + 20 = .3x + 12

.1x  = 8

x = 80 gallons of 20% alcohol needed

x    from -1 to -7 is  distance of -6       5 / (5+3)  = 5/8 ths  of this is added to -1 to get   x = -4 6/8 = -4.75

y    from -5 to 11 is  distance of 16      5/8 of this is added to -5 to get    y = 5                               

                      (  -4.75,5 )

https://web2.0calc.com/questions/please-help_32848

cos (5 R) = .28

so      sin (5 R) = y = -.96

Square both sides of the first equation:

\((z+\frac{1}{z})^2=1^2\\ z^2+2\cdot z \cdot \frac{1}{z} + \frac{1}{z^2} = 1\\z^2+\frac{1}{z^2}+2=1\\ \boxed{z^2+\frac{1}{z^2}=-1}\)

Given the points C(-1,-5) and D(-7,11), find the coordinates of point E on CD such that the ratio of CE to ED is 5:3

Hello Guest!

\(y_E=y_C+\frac{3}{5}(y_D-y_C)\\ y_E=-5+ \frac{3}{5}(11-(-5))=\color{blue}4.6\)

\(x_E=x_C-\frac{3}{5}(x_C-x_D)\\ x_E=-1-\frac{3}{5}(-1-(-7))=\color{blue}-4.6\)

The coordinates of point E are E (-4.6,4.6)

  !

100    +    100(.01) * 6 =  $.........    in six years  

7 p    2 d   3 n   just by looking at it .......

I do not know if my answer is corrector not...if it is, let me know and I will show you how I arrived to it

1024 ways     assuming the students are distiguishable

F_c =  mv² / r

14700 kg-m/s²    / 9.81 m/s² = 1498.47 kg    mass of car

52.5 km/hr = 14.583 m/s

     F_c  = 1498.47 * (14.583)² / (160)   = 1991.78 N

u_s = v² /( rg)   = 14.583² / (160 * 9.81) = .135      (coefficient of static friction)

I suspect it is a fountain (like a decorative water fountain in a garden etc) .... that is circular in shape ......   a circle of x diameter   or perhaps  x radius

128 500 = pv (1+ .065/2)^8*2       solve for pv           interest is then   128500 - pv

                           .065/2 is interest per period in decimal form (twice per year)   and there are 8*2 periods in eight years

3x+4y=-14  

 is the same as    y = -3/4 x - 14/4    slope, m  = -3/4        

               perpindicular slope = - 1/m = 4/3

point slope form    of new line  thru 5,7   

           y-7 = 4/3 (x-5)      re-arrange

           y = 4/3 x - 20/3 + 7

                                   take it from here......

Triangle side rule      any two sides summed must be greater than third side

   soooo    longest side cannot be greater than or equal to  1/2 of the perimeter, because the other two sides will not add up to be greater than...

      499        250   251  

Try writing out the number in decimal.

Do you know how?

The product expands as x^100 + 1.

Missing important numbers !  

f(x) =  y = 12.5 x

Rate of change = slope  = -3

or the derivative of -3x  is  -3

or take two points   say 2 and 4

               -3(2) = -6       -3(4) = -12           r.o.c = (-12 - - 6) /2 = - 3

There are two unit rates available    pages per day  99/3 = 33 pages/day    which I expect is what you want

but there is also  days per page   3 days/99 pages =  1/33   days /page

5 digits can make  10 000  plates    (00000 - 99999)

   multiplied by one of four letters =  40 000 plates

1/3 of the way from 0 to 9     is 3 = x

1/3 of the way from0 to 6      is 2 = y              sum = 5

My algebra was very long-winded and I have not finished it but

I used the first one to get a in terms of b       a(b)

then the last one to get b in terms of c          b(c)

then i substituted the b(c)  into the a to get a(b)  in terms of a(c)

Then I substituted this into the middle one and solved for c

etc

There is probably a better way.