Everything looks good but the only thing you didn't do in the very last step is to cancel out the 5 in both the numerator and denominator. Everything is being multiplied together so you're not doing anything "illegal" by canceling the 5's. In fact, if you're simplifying, you NEED to cancel the 5's.
Answer:
412.3 feet
Step-by-step explanation:
A canoe rental shop is being built near a river. An equation of the line representing the river is y=1/4x+8. Each unit in the coordinate plane corresponds to 100 feet. Approximately how far is the canoe rental shop from the river? Round your answer to the nearest whole foot. The rental shop is at (-3,3).
Solution:
The distance between a point and a line is the perpendicular distance. The perpendicular distance is the shortest distance between the point and the line.
Given a point (
) and a line with the equation Ax + By + C = 0, the perpendicular distance (d) is given as:
![d=\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2} }](https://tex.z-dn.net/?f=d%3D%5Cfrac%7B%7CAx_1%2BBy_1%2BC%7C%7D%7B%5Csqrt%7BA%5E2%2BB%5E2%7D%20%7D)
Given the equation of the line y = 1/4 x + 8
y - 1/4 x - 8 = 0
Therefore A = -1/4, B = 1 and C = -8
The point is (-3,3), therefore ![x_1=-3,y_1=3](https://tex.z-dn.net/?f=x_1%3D-3%2Cy_1%3D3)
![d=\frac{|-1/4(-3)+(1*3)+(-8)|}{\sqrt{(-1/4)^2+1^2} }\\\\d=4.123\ unit\\\\but\ 1\ unit=100\ feet\\\\ d=4.123\ unit*1\ feet=412.3\ feet](https://tex.z-dn.net/?f=d%3D%5Cfrac%7B%7C-1%2F4%28-3%29%2B%281%2A3%29%2B%28-8%29%7C%7D%7B%5Csqrt%7B%28-1%2F4%29%5E2%2B1%5E2%7D%20%7D%5C%5C%5C%5Cd%3D4.123%5C%20unit%5C%5C%5C%5Cbut%5C%201%5C%20unit%3D100%5C%20feet%5C%5C%5C%5C%20d%3D4.123%5C%20unit%2A1%5C%20feet%3D412.3%5C%20feet)
Answer:
A = 1000 ( 1 + .031/12) ^(12t)
The approximate monthly interest rate is .2583 percent
Step-by-step explanation:
A=1000(1.031)^t
The formula for compound interest is given by
A = P(1 + r/n) ^ (nt)
Take 1.031 and subtract 1
.031 is the yearly rate in decimal form
A = 1000 ( 1 + .031/12) ^(12t)
Change to a percent = 3.1 %
Divide by 12
3.1/12 = .2583333333(repeating) %
This would be the monthly rate
First you can solve the triangle. complete the triangle my making the final side which would equal 12 because the top and bottom are bith 6. and the bottom is 12 then you do 1/2(12)(12) to find the area which would be 72. the area of the rectangle would be 18 so the total would be 90ft^2 when you add them together