WILL GIVE BRAINLY AND POINTS PLZZZ Which linear function has a positive slope?
2 answers:
You might be interested in
Length of the side = 9 cm
Diagonal = cm
Solution:
Area of the square = 81 square centimeters
In square all sides are equal.
Area of the square = side × side
Side × side = 81
Side² = 9² (∵81 = 9²)
Taking square root on both sides, we get
Side = 9 cm
Length of the side = 9 cm
To find the length of the diagonal:
In square all the angles are right angle.
Diagonal splits the square into two right angle triangle.
Using Pythagoras theorem,
<em>In right triangle, square of the hypotenuse is equal to the sum of the square of the other two sides.</em>
Here, diagonal is the hypotenuse.
Taking square root on both side,
Diagonal = cm
If your directrix is a "y=" line, that means that the parabola opens either upwards or downwards (as opposed to the left or the right). Because it is in the character of a parabola to "hug" the focus, our parabola opens upwards. The vertex of a parabola sits exactly halfway between the directrix and the focus. Since our directrix is at y = -2 and the focus is at (1, 6) AND the parabola opens upward, the vertex is going to sit on the main transversal, which is also the "line" the focus sits on. The focus is on the line x = 1, so the vertex will also have that x coordinate. Halfway between the y points of the directrix and the focus, -2 and 6, respectively, is the y value of 2. So the vertex sits at (1, 2). The formula for this type of parabola is where h and k are the coordinates of the vertex and p is the DISTANCE that the focus is from the vertex. Our focus is 4 units from the vertex, so p = 4. Filling in our h, k, and p:
. Simplifying a bit gives us
. We can begin to isolate the y by dividing both sides by 16 to get
. Then we can add 2 to both sides to get the final equation
, choice 4 from above.