CPhill

5x + 3 = 10y - 2      add 2 to both sides

5x + 5 = 10y           divide both sides by 10

(1/2)x + 1/2  =  y

And this is just an equation of a line with a slope of 1/2  with a y interxrpt of 1/2

Remember that we need to take both roots of 16.....so we have

(x - 2)^2 = 16

x - 2 = ±√16

x - 2 = ± 4

So

x - 2 = 4        and       x - 2 = -4         add 2 to both sides of both of these

x = 6             and       x = -2

And those are the two solutions.....

Let x be the number of wireless keyboards sold. So the number of regular keyboards sold is three times this = 3x

So we have.....Quantity x Price = Revenue

x(105) +3x(84) = 4998       simplify

105x + 252x = 4998

357x  = 4998     divide both sides by 357

x = 14 = wireless keyboards sold

And 3x = 3(14) = 42 = regular keyboards sold

Let C be the total cost...so we have

C = 3(39.95) + 460(.68) = $432.65....so $400 won't be enough....

(1/4)C - 6

-5t^2 + 20t + 50    .....taking out the greatest common factor, we have

-5(t^2 - 4t - 10)

And that's it......!!! (the trinomial inside the parenhteses isn't factorable)

There are 16 ounces in a pound...so  6 x 16 = 96 ounces

And  96/5 = 19 full packages

Taking each different factor along with the highest power occurring on that factor, we have

2^2 * 3^3 * 5 * 7 =

4 * 27 * 35  =

3780

Perhaps you mean "a score??".....a "score" = 20...so.....a sum of "a score" + 13 = 33

Thanks, Anonymous....you are correct......I forgot about that!!!

The correct interval is (-√(2/3), √(2/3))

Let me add one proviso to what Anonymous said.......setting the second derivative to 0 and solving only indicates possible  inflection points. For instance...the second derivative of x^4 is 12x^2. Setting this to 0 gives us that x = 0. But this isn't an inflection point because this curve is always concave "up". To see this, pick a point on either side of 0 and "plug" them into the second derivative. Both results will be positive....indicating that the curve is concave "up" on both sides. Thus, there is no inflection point !!!