Write the equation for a parabola with a focus at (5,-5) and a directrix at y= -4

y = (-1/2)(x-5)^2 - 4.5

Step-by-step explanation:

The general formula for a vertical parabola is 4py=x^2.

Here the vertex is not at (0,0), but rather is at (5, -4.5) (halfway between the focus and the directrix).  The graph of the parabola opens down, because the directrix is higher up the y-axis than the focus.

Thus, this equation becomes 4p(x+4.5) = (x-5)^2.

Here p = half the distance between the focus and the directrix, or 0.5.  Because the graph opens downward, use p = -0.5.

Then we have 4(-0.5)(y+4.5) = (x-5)^2, or

                            -2   (y + 4.5) = (x-5)^2, or

                                    y + 4.5 = (-1/2)(x-5)^2, or

                                     y = (-1/2)(x-5)^2 - 4.5

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!

30 feet

step-by-step explanation:

that would be 2 1/2 * 12

= 24 + 6

= 30 feet   (answer)