Answer:
y = 1/12 (x − 5)²
Step-by-step explanation:
We can solve this graphically without doing calculations.
The y component of the focus is y = 3. Since this is above the directrix, we know this is an upward facing parabola, so it must have a positive coefficient. That narrows the possible answers to A and C.
The x component of the focus is x = 5. Since this is above the vertex, we know the x component of the vertex is also x = 5.
So the answer is A. y = 1/12 (x−5)².
But let's say this wasn't a multiple choice question and we needed to do calculations. The equation of a parabola is:
y = 1/(4p) (x − h)² + k
where (h, k) is the vertex and p is the distance from the vertex to the focus.
The vertex is halfway between the focus and the directrix. So p is half the difference of the y components:
p = (3 − (-3)) / 2
p = 3
k, the y component of the vertex, is the average:
k = (3 + (-3)) / 2
k = 0
And h, the x component of the vertex, is the same as the focus:
h = 5
So:
y = 1/(4×3) (x − 5)² + 0
y = 1/12 (x − 5)²
Answer:
A| 12, 3
Step-by-step explanation:
The polynomial can be factored by looking for factors of 36 that sum to -15. The sum being negative while the product is positive means both factors will be negative. The answer choices suggest ...
y = (x -12)(x -3)
A quick check shows this product is ...
y = x^2 -12x -3x +36 = x^2 -15x +36 . . . . as required
The factors are zero when x is either 12 or 3.
The zeros of the equation are 12 and 3.
____
Once you realize the constants in the binomial factors both have a negative sign, you can immediately choose the correct answer (A).
Or, you can use Descartes' rule of signs, which tells you that the two sign changes in the coefficients (+-+) mean there are 2 positive real roots.
Answer:
140
Step-by-step explanation:
560. 1
____. ÷. ______
1. 4
Cross out the numbers that are divisible
560/4 = 140
C=1500+4x where x is cds, C is cost
R=10x where R is revenue
then, P=R-C
P=10x-1500-4x
P=6x-1500
set P=0
1500=6x
x=250
check, C=1500+4*250, R=10*250
C=250, R=250
They need to sell 250 cds before they make profit
Answer:
Step-by-step explanation:
To calculate the angles of the given triangle, we can use the law of cosines:
Then, given the sides a=2, b=9, and c=8.
For B:
