Slope intercept form: y=mx+b
12x+3y=-18 subtract 12x on both side
3y=-12x-18 divide both sides by 3
y=-4x-6 is the answer
Answer:
The speeds of the cars is: 0.625 miles/minute
Step-by-step explanation:
We use systems of equations in two variables to solve this problem.
Recall that the definition of speed (v) is the quotient of the distance traveled divided the time it took :
. Notice as well that the speed of both cars is the same, but their times are different because they covered different distances. So if we find the distances they covered, we can easily find what their speed was.
Writing the velocity equation for car A (which reached its destination in 24 minutes) is:
![v\,*\,24\,min=d_A](https://tex.z-dn.net/?f=v%5C%2C%2A%5C%2C24%5C%2Cmin%3Dd_A)
Now we write a similar equation for car B which travels 5 miles further than car A and does it in 32 minutes:
![v\,*\,32\,min=d_A+5\,miles](https://tex.z-dn.net/?f=v%5C%2C%2A%5C%2C32%5C%2Cmin%3Dd_A%2B5%5C%2Cmiles)
Now we solve for
in this last equation and make the substitution in the equation for car A:
![v\,*\,32\,min=d_A+5\,miles\\d_A=v\,*\,32\,min-5\,miles\\\\v\,*\,24\,min=v\,*\,32\,min-5\,miles\\v\,(24\,min-32\,min)=-5\,miles\\v\,(-8\,min)=-5\, miles\\v=\frac{-5}{-8} \frac{miles}{min} \\v=0.625\,\frac{miles}{min}](https://tex.z-dn.net/?f=v%5C%2C%2A%5C%2C32%5C%2Cmin%3Dd_A%2B5%5C%2Cmiles%5C%5Cd_A%3Dv%5C%2C%2A%5C%2C32%5C%2Cmin-5%5C%2Cmiles%5C%5C%5C%5Cv%5C%2C%2A%5C%2C24%5C%2Cmin%3Dv%5C%2C%2A%5C%2C32%5C%2Cmin-5%5C%2Cmiles%5C%5Cv%5C%2C%2824%5C%2Cmin-32%5C%2Cmin%29%3D-5%5C%2Cmiles%5C%5Cv%5C%2C%28-8%5C%2Cmin%29%3D-5%5C%2C%20miles%5C%5Cv%3D%5Cfrac%7B-5%7D%7B-8%7D%20%5Cfrac%7Bmiles%7D%7Bmin%7D%20%5C%5Cv%3D0.625%5C%2C%5Cfrac%7Bmiles%7D%7Bmin%7D)
So this is the speed of both cars: 0.625 miles/minute
![\\ \sf{:}\implies (side)^3=14](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%7B%3A%7D%5Cimplies%20%28side%29%5E3%3D14)
![\\ \sf{:}\implies side=\sqrt[3]{14}](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%7B%3A%7D%5Cimplies%20side%3D%5Csqrt%5B3%5D%7B14%7D)
![\\ \sf{:}\implies side=2.5in](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%7B%3A%7D%5Cimplies%20side%3D2.5in)
Now
![\\ \sf{:}\implies Area=11(8)=88in^2](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%7B%3A%7D%5Cimplies%20Area%3D11%288%29%3D88in%5E2)
Cut it into 10 parts as per question(Open side means five sides hence it will be 5×2=10)
![\\ \sf{:}\implies 88/10=8.8in](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%7B%3A%7D%5Cimplies%2088%2F10%3D8.8in)
Now divide by previous side
![\\ \sf{:}\implies \dfrac{8.8}{2.5}=3.52=3.5](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%7B%3A%7D%5Cimplies%20%5Cdfrac%7B8.8%7D%7B2.5%7D%3D3.52%3D3.5)
Option D
It would be cos = 1 have a good day
Answer:
It takes 3 seconds over the interval [0,3]
Step-by-step explanation:
To find when the roller coaster reaches the ground, find when d=0.
![0=144-16t^2](https://tex.z-dn.net/?f=0%3D144-16t%5E2)
To solve divide each term by 16 and factor:
![\frac{0}{16}=\frac{144}{16} -\frac{-16t^2}{16} \\0= 9 - t^2\\0=(3-t)(3+t)](https://tex.z-dn.net/?f=%5Cfrac%7B0%7D%7B16%7D%3D%5Cfrac%7B144%7D%7B16%7D%20-%5Cfrac%7B-16t%5E2%7D%7B16%7D%20%20%5C%5C0%3D%209%20-%20t%5E2%5C%5C0%3D%283-t%29%283%2Bt%29)
Solve for t by setting each factor to 0.
t-3=0 so t=3
t+3=0 so t=-3
This means the car is in the air from 0 to 3 second.