Answer:
x=9
y=3
Step-by-step explanation:
since all three sides of an equlateral triangle are equal:
3x+y=30 then y=30-3x
4x-2y=30
4x-2(30-3x)=30
4x-60+6x=30
10x=90
x=9
3x+y=4x-2y
x=3y
y=3
Answer:
3164557/ 25000000
Step-by-step explanation:
Sub in what X and y are:
. Solve the exponents (if the exponent is 2 multiply the whole number by itself twice, if it were 3 you would multiply the whole number by itself three times): 3·3=9, 3·3=9: 9(9)= 81. :)
The enclosed shape is that of a trapezoid. The area of a trapezoid is the product of the height of it (measured perpendicular to the parallel bases) and the average length of the two parallel bases. The formula is generally written ...
... A = (1/2)(b₁ + b₂)·h
Here, the base lengths are the y-coordinates at x=4 and x=9. The height is the distance between those two x-coordinates: 9 - 4 = 5.
You are expected to find the y-values at those two points, then use the formula for the area of the trapezoid.
You can save a little work if you realize that the average of the two base lengths is the y-coordinate corresponding to the average x-coordinate: (9+4)/2 = 6.5. That is you only need to find the y-coordinate for x=6.5 and do the area math as though you had a rectangle of that height and width 5.
Going that route, we have
... y = 2(6.5) - 1 = 13 - 1 = 12
Then the trapezoid's area is
... A = 12·5 = 60 . . . . square units.
Since the focus is at (0, 2) and directrix is y = -2
point where both of these have the same x-value will be at (0, 2) for the focus and (0, -2) for the directrix.
The vertex will also have the same x-value so it will be (0, y).
y-value is half-way between the y-value of the focus, and the y-value of the directrix at x = 0.
Directrix y-value is -2 at x = 0 and for the focus it's 2 at x = 0.
Halfway between y = -2 and y = 2 is y = 0.
So the vertex of the parabola occurs at (0, 0).
So that's x^2 = 4ay = 4(2)y = 8y.
y = 1/8*x^2
hope it helps
