Answer:
(x²-10x+33)/(-8) = y
Step-by-step explanation:
The distance between any point on a parabola from both its focus and directrix are the same.
Let's say we have a point (x,y) on the parabola. We can then say that using the distance formula,
is the distance between (x,y) and the focus. Similarly, the distance between (x,y) and the directrix is |y-1| (I use absolute value here because distance is always positive). We can find this equation by taking the shortest distance from the point to the line. Because the closest point to the line will be the same x value as the point itself, the distance is simply the distance between the y value of the point and the y value of the directrix.
Equating the two equations given, we have
square both sides to get
(x-5)²+(y+3)²=(y-1)²
expand the y components
(x-5)² + y²+6y+9 = y²-2y+1
subtract y²+6y+9 from both sides
(x-5)² = -8y - 8
expand the x components
x²-10x+25 = -8y - 8
add 8 to both sides to isolate the -8y
x²-10x+33 = -8y
divide both sides by -8 to isolate y
(x²-10x+33)/(-8) = y
Answer:
The equation is R = 20d + m(1)
Where R is the rental amount in dollars, d is the number of days and m is the number of miles driven
R for 3 days and 1000 miles is $1,060
Step-by-step explanation:
To properly represent the algebraic expression, we need to assign some variables.
Now, let the rental amount be R, the number of miles driven be m and the number of days rented for is d
Thus, we can say that:
R = 20d+ m(1)
Where R is rental amount, m is the number of miles driven and d is the number of days for which the truck was driven.
Now we are asked to calculate rental amount for 3 days and 1000 miles.
R = 20d + m(1)
R = 20(3) + 1000(1)
R = 60 + 1000
R = $1,060
Step-by-step explanation:
x+0.6+0.3-0.2=14.2
x+0.7=14.2
x=14.2-0.7
x=13.5
the answer is 10:20.
Hint for the future: be sure to write in the full problem. I only knew the answer because I had to do it myself, but people need more context if they are going to help you.
For this case we have the following expression:
For power properties we have:
Rewriting the exponents of the expression we have:
Using the cubic root we have:
![(\frac{1}{\sqrt[3]{8^2}} a^2)](https://tex.z-dn.net/?f=%20%28%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7B8%5E2%7D%7D%20a%5E2%29%20%20%20)
![(\frac{1}{\sqrt[3]{64}} a^2)](https://tex.z-dn.net/?f=%20%28%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7B64%7D%7D%20a%5E2%29%20%20%20)
![(\frac{1}{\sqrt[3]{4^3}} a^2)](https://tex.z-dn.net/?f=%20%28%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7B4%5E3%7D%7D%20a%5E2%29%20%20%20)
Simplifying the expression we have:
Answer:
The equivalent expression is given by:
