CPhill

We can go  one step futher, Anonymous

4(x^2 + 8x - 33)  =

4(x + 11) ( x - 3)

And that's fully factored.....!!!!

27/ 50   = 54%

Obviously, you can only miss 20% of the questions to make an "80%"...so....

20%  of 135 =

.20 x 135 =

27 questions is the number you can miss....

I assume you might be wanting to know which term of the series = - 20....if so, we have......

-20 = [5 + 1/3] + (-1/3) (n-1)    simplify

-20 = 16/3 + (-1/3)(n-1)   multiply through by 3

-60  = 16 - 1(n - 1)       subtract 16 from both sides

-76 = -n + 1          subtract 1 from both sides

-77  = -n              multiply through by -1

77 = n

It will be the 77th term....!!!!

Notice that 1 in = 1/12 ft     so we have

850sq ft x 1/12 ft = about 70.83 cu ft.

And 1 cu yd = 27 cu ft....so

70.83cu ft x [1cu yd / 27 cu ft]    = about 2.62 cu yd.

1/4 + w = [6+ 1/3]   express [6 + 1/3] as an improper fraction

1/4 + w = 19/3        multiply through by the common denominator of 6 and 4, i.e., 12.....so we have

3 + 12w  = 76      subtract 3 from both sides

12w = 73             divide both sides by 12

w = 73/12  

So, we have.....

x^3 + x^2  = 230

It might be a little hard to find the soultion, algebraically.....we could use somerhing called "Newton's Method" to approximate a solution, but I prefer a graph......

Hey...c'mon guys.....haven't you ever heard of a "makeup" exam  ???

x-2/3-3=x-45         add 3 to both sides

x - 2/3 =  x - 42   

Notice that this has no solution, because  subtracting 2/3 from x can't be the same as subtracting 42 from  it....!!!

V_cone =(1/3)*pi * r^2 *h  =   (1/3)*pi*(4)^2 * 3 =  about 50.27cm^3