Answer:
A and B
Step-by-step explanation:
When rotating a point (or any shape around a certain point), none of the diameters of the shape will change. So for example, with this circle, when you rotate it around a point, the radius and circumference will not change because it has just rotated. It wont be on the x-axis though because point P is not on the x-axis an it is being rotated 180 degrees about point P. Just know that when you are rotating, nothing about the shape changes, all angles or measurements will be the same, it is just moving to a different place.
Hope this helped ^-^
Answer:
<em>The coordinates of the vertex are (-1,-4).</em>
Step-by-step explanation:
<u>Equation of the Quadratic Function
</u>
The vertex form of the quadratic function has the following equation:

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.
We are given the function:

We must transform the equation above by completing squares:
The first two terms can be completed to be the square of a binomial. Recall the identity:

Thus if we add and subtract 1:

Operating:

The trinomial in parentheses is a perfect square:

Adding 4:

Comparing with the vertex form of the quadratic function, we have the vertex (-1,-4).
The coordinates of the vertex are (-1,-4).
Answer:
Quadrilateral MNOP is a rectangle.
Step-by-step explanation:
Answer:
30 mph
Step-by-step explanation:
Let d = distance (in miles)
Let t = time (in hours)
Let v = average speed driving <u>to</u> the airport (in mph)
⇒ v + 15 = average speed driving <u>from</u> the airport (in mph)
Using: distance = speed x time

Create two equations for the journey to and from the airport, given that the distance one way is 18 miles:

We are told that the total driving time is 1 hour, so the sum of these expressions equals 1 hour:

Now all we have to do is solve the equation for v:







As v is positive, v = 30 only
So the average speed driving to the airport was 30 mph
(and the average speed driving from the airport was 45 mph)