CPhill

Not necessarily, Anonymous.......here's a pretty good "duplicate" answer.......word for word !!!

So we have

√63 -√28 = √x     Simplify the left

√(9*7) -√(4*7) = √x

3√7 - 2√7 = √x

√7 = √x

And it's obvious that x = 7

y = 26t − 16t2

Rewrite as

y = -16t^2 + 26t

This is similar to the one I just did sally1, so we have

-b/2a =  -26/[2(-16)]  =  26/32   =    13/16    So to find max height, substitute this back into the original equation for "x"     This gives....

y = -16(13/16)^2 + 26(13/6) = 169/16 = 10.5625 ft.

-17F

3(4-2x) - x(7-4) = x over seven minus 2x over 3

Rewrite as

3(4-2x) - x(3) = x/7 - 2x/3       Simplify

12- 6x - 3x  = x/7 - 2x/3     

12 - 9x=  x/7 - 2x/3      Multiply both sides by the common denominator on the right (21)

252 - 189x = 3x - 14x     Simplify again

252 - 189x = -11x          Add 189x to both sides

252 = 178x                    Divide both sides by 178

252/178 = x = 126/89

f(x) = 9 − x −   1/2x^2   

Rewrite as

f(x) = -(1/2)x^2 - x + 9

This is a parabola that opens downward . so it will have only a maximum. If you haven't had calculus, the x coordinate of the max is given by -b/2a, where b = -1 and a = -1/2 ....So we have...

x = -(-1)/2(-1/2)  = 1/-1 = -1

Now, to find the y coordinate, we just substitute for x in the function.  So we have...

(-1/2)(-1)^2 - (-1) + 9 =   (-1/2) + 1 + 9 =  9.5

So the max occurs at (-1, 9.5)   ....  Here's the graph

This is a little off- topic, but let me show you how to turn a "repeating" decimal into a fraction........

Suppose we have  the decimal .127  where the '27" part repeats

Combine the non-repeating part (1) with the repeating part (27)...so we have... 127

Now from this, subtract the non-repeating part, so we have  127 - 1 = 126

Divide this by a number comprised of 9s and 0s, where the number of 9s = the number of repeating digits (2) and the number of 0s = the number of non-repeating digits (1). So the number we divide by = 990....so we have 

126/990 = .127(2727....)

Using your example, ND, of .454545

Combining the repeating part with the non-repeating part = 45  (The non-repeating part = 0, in this case)

Subtracting  the non-repeating part from the repeating part gives 45 - 0 = 45

Write this over 99  (the number of 9s = the number of repeated digits, we have no non-repeating ones, thus, there are no 0s)

So  45/99 = .4545(4545.....)

In effect, if there is no non-repeating part, we just write our repeating part over the number of 9s = the number of digits in the repeating part !!!

Note also that you may be able to reduce the resulting fraction to a more simple form.....

And that's it !!

(Try writing .817(1717.....) as a fraction using this procedure....)

Subtract 4/5 from each side    .....  we have...

(2/3)x = -(17/30) - (4/5)      and 4/5 = 24/30    ....so we have

(2/3)x = -(17/30) - (24/30)

(2/3)x = -41/30         multiply both sides by (3/2)

x = (-41/30) * ( 3/2)    (cancel the 30 and the 3 )

=    (-41/10) * (1/2) = (-41/20)

And that's it, ND.....

Here's another hint......if I sum the digits of a number and that sum is divisble by 3, then the number is divisible by 3. For instance, 54 = 5 + 4 = 9. Then 9 is divisible by 3 and so is 54.

I assume you want to "factor" this??

!0201 = 101^2