Answer: Yes A is correct
Step-by-step explanation:
Multiply the first equation by 3...
2x+3y=k+1 needs to be subtracted by 3x+3y=3k
which equals -x=-2k-1
Then you can multiply the equation by -1 to make them all positive. Resulting in x=2k+1
Answer: 100,000 + 80,000 + 6,000 + 200 + 80 + 2
Step-by-step explanation: Expanded form is writing out the number like I did tbh..hard to explain you just gonna practice but here ya go :)) !
Answer:
Step-by-step explanation:
This is a third degree polynomial because we are given three roots to multiply together to get it. Even though we only see "2 + i" the conjugate rule tells us that 2 - i MUST also be a root. Thus, the 3 roots are x = -4, x = 2 + i, x = 2 - i.
Setting those up as factors looks like this (keep in mind that the standard form for the imaginary unit in factor form is ALWAYS "x -"):
If x = -4, then the factor is (x + 4)
If x = 2 + i, then the factor is (x - (2 + i)) which simplifies to (x - 2 - i)
If x = 2 - i, then the factor is (x - (2 - i)) which simplifies to (x - 2 + i)
Now we can FOIL all three of those together, starting with the 2 imaginary factors first (it's just easier that way!):
(x - 2 - i)(x - 2 + i) =
Combining like terms and canceling out the things that cancel out leaves us with:
Remembr that , so we can rewrite that as
and
That's the product of the 2 imaginary factors. Now we need to FOIL in the real factor:
That product is
which simplifies down to
And there you go!
The required equation of the hyperbola is expressed as
The standard form for calculating the equation of a parabola along the x-axis is expressed as:
where:
(h, k) is the center
(k±c, h) are the foci
is the directrix
From the question given, we can see that foci = (±5, 0)
k±c, h = ±5, 0
k = 0
h = 0
c = 5
From the directrix,
Also, we need to know that;
a²+b² = c²
10 + b² = 5²
b² = 25 - 10
b² = 15
Substituting the gotten values into the equation of a hyperbola;
This gives the required equation of the hyperbola
Learn more on the equation of hyperbola here: brainly.com/question/20409089