Answer:
a-bi
Step-by-step explanation:
If a quadratic equation lx^2+mx+n=0 has one imaginary root as a+bi then the other root is the conjugate of a+bi = a-bi
Because we have l, m and n are real numbers and they are the coefficients.
Sum of roots = a+bi + second root = -m/l
When -m/l is real because the ratio of two real numbers, left side also has to be real.
Since bi is one imaginary term already there other root should have -bi in it so that the sum becomes real.
i.e. other root will be of the form c-bi for some real c.
Now product of roots = (a+bi)(c-bi) = n/l
Since right side is real, left side also must be real.
i.e.imaginary part =0
bi(a-c) =0
Or a =c
i.e. other root c-bi = a-bi
Hence proved.
Given that the directrix is at y = 4 and the focus is at (0, -4), then the vertex is at (h, k) = (0, 0).
p is the distance between the vertex and the focus and between the vertex and the directrix = 4 and since the focus is below the directrix, p is negative, i.e. p = -4
Equation of a parabola is given by (x - h)^2 = 4p(y - k)
Therefore, the required equation is (x - 0)^2 = 4(-4)(y - 0)
x^2 = -16y
y = -1/16 x^2
Answer:
x = 8
y = -7
Step-by-step explanation:
3y - 5x = -61
-----------------------+
-9x = -72
x = 8
3y -5(8) = -61
3y - 40 = -61
3y = -21
y = -7
For the triangle, x is 12 units long.
Step-by-step explanation:
Step 1:
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The hypotenuse is the side which is the longest in the triangle and is always opposite the right angle.
In the given triangle, the hypotenuse is 13 units long. The other two sides measure 5 units and x units.
Step 2:
By substituting the known values, we get
Rounding this off to the nearest hundred, we get that x is 12 units long.
Answer:
x = -4
Step-by-step explanation:
First lets add 82 + 55 which equals 137, then 137 +47 which equals 184
Now we know that a triangle equals 180 degrees (cannot go over 180), so this tells us x is a negitive number.
-x + 184 = 180
-x = -4
Another way to look at it is; 184 minus what equals 180? 4 does, so it translates into -4.
