Answer:
Step-by-step explanation:
The directrices in this case are vertical lines, so we have a horizontal ellipse. The equation for that ellipse is:
The center of the ellipse is (h,k), the diretrix is x = d and the foci are given by (h+c, k) and (h-c, k)
So, comparing the foci, we have that k = 0 and:
Adding these two equations, we have:
We can find the value of a^2 using the property:
Using c = 2 and d = 4, we have:
Now, to find b^2, we use the property:
So the equation of the ellipse is:
Answer:
114 marbles.
Step-by-step explanation:
Let the number of red marbles be r
Let the number of black marbles be b
<u>Given the following data;</u>
Total number of marbles = 120
Translating the word problem into an algebraic equation, we have;
.......equation 1
........equation 2
Substituting the value of "r" into equation 2, we have;
b = 6 marbles.
To find the number of red marbles;
From equation 1;
Substituting the value of "b" into equation 1, we have;
<em>r = 114 marbles.</em>
<em>Therefore, there are 114 red marbles in the bag. </em>