Answer:
x = 2i, x = -2i and x = 4 are the roots of given polynomial.
Step-by-step explanation:
We are given the following expression in the question:
One of the zeroes of the above polynomial is 2i, that is :
Thus, we can write
Now, we check if -2i is a root of the given polynomial:
Thus, we can write
Therefore,
Dividing the given polynomial:
Thus,
X = 4 is a root of the given polynomial.
Thus, 2i, -2i and 4 are the roots of given polynomial.
If it has no real solutions, that means the graph does not intersect the x axis
since we have ax^2+bx+c=0, the parabola opens either up or down
since the vertex is in the second quadrant (x is negative and y is positive in this reigon) and the graph does not cross the x axis, the parabola must open up
if the value of 'a' is positive, then the parabola opens up
so 'a' must be positive
if it is translated to the 4th quadrant, then the vertex is now below the x axis
it will now have 2 x intercepts because the vertex is in the 4th quadrant and look at a graph of a parabola opening up with vertex in 4th quadrant and seehow many time it crosses the x axis
Parallel lines have the same slope.
To compare the slopes of two different lines, you have to get
both equations into the form of
y = 'm' x + (a number) .
In that form, the 'm' is the slope of the line.
Notice that it's the number next to the 'x' .
The equation given in the question is y = 3 - 2 x .
Right away, they've done something to confuse you.
You always expect the 'x' term to be right after the 'equals' sign,
but here, they put it at the end. The slope of this line is the -2 .
Go through the choices, one at a time.
Look for another one with a slope of -2 .
Remember, rearrange the equation to read ' y = everything else ',
and then the slope is the number next to the 'x'.
Choice #4: y = 4x - 2 . The slope is 4 . That's not it.
Choice #3: y = 3 - 4x . The slope is -4 . That's not it.
Choice #2). 2x + 4y = 1
Subtract 2x from each side: 4y = 1 - 2x
Divide each side by 4 : y = 1/4 - 1/2 x .
The slope is -1/2. That's not it.
Choice #1). 4x + 2y = 5
Subtract 4x from each side: 2y = 5 - 4x
Divide each side by 2 : y = 5/2 - 2 x .
The slope is -2 .
This one is it.
This one is parallel to y = 3 - 2x ,
because they have the same slope.
First, we need to know the smallest two digit prime number. It can't start with one, since one is not prime, so it must start with two (or be in the twenties.) 20 is divisible by 2, 4, 5, and 10, 21 is divisible by 7 and 3, 22 is divisible by 2 and 11, so the smallest prime number is 23.
Now we need the largest two-digit prime number. It cannot start with nine or eight, since both are composite, so it must start with seven (be in the seventies.) 79 is the largest integer in the seventies and also happens to be prime, so there's our largest two digit prime number.
now we just need to add them for the sum:
23+79=102
hope I helped, and let me know if you have any questions :D
Answer:
32 remaining cups for Kin
Step-by-step explanation:
