Arrange the parabolas represented by the equations in increasing order with respect to the y-values of their directrixes.
tiles
y = -x2 + 3x + 8
y = 2x2 + 15x + 18
y = x2 + 13x + 5
y = -2x2 + 4x + 8

3rd Parabola < 2nd parabola < 4th parabola < 1st parabola.

Step-by-step explanation:

We are given with equation of parabolas.

We need to arrange them in increasing order with respect to y-values of their directrixes.

First we convert given equations in Standard form then find their directrix.

The standard form is (x - h)² = 4a (y - k),

then directrix is  y = k - a

1). y = -x² + 3x + 8

using completing the square method,

Now, by comparing with standard equation

So, Directrix,

2). y = 2x² + 15x + 18

using completing the square method,

Now, by comparing with standard equation

So, Directrix,

3). y = x² + 13x + 5

using completing the square method,

Now, by comparing with standard equation

So, Directrix,

4). y = -2x² + 4x + 8

using completing the square method,

Now, by comparing with standard equation

So, Directrix,

So, from above

y = 37.5 < y = -10.25 < y = 10.125 < y = 10.5

Therefore, 3rd Parabola < 2nd parabola < 4th parabola < 1st parabola.

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing im pretty sure that is the right answer

step-by-step explanation:

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !