Answer:
y = 2x + 7
Step-by-step explanation:
y = mx + b The point (-2,3) gives us an x value and a y value that we can use. We are also give the slope (m). All we need to do is figure out the b (y-intercept) value.
y = mx + b
3 = 2(-2) + b
3 = -4 + b Add for to both sides
7 = b We know have every thing that we need to write the equation. We have the slope (m) which is 2 and the b (y-intercept) that we just figured out is 7
y = 2x + 7
Answer:
140
Step-by-step explanation:
Solve 40% of 350.
Answer:
The prime factors of 168 are 2, 3, and 7.
Step-by-step explanation:
Answer:
18.66 ft/s
Step-by-step explanation:
The distance between you and the elevator is given by:
![h=\sqrt{x^2+y^2}](https://tex.z-dn.net/?f=h%3D%5Csqrt%7Bx%5E2%2By%5E2%7D)
The rate of change for the distance between you and the elevator is given by:
![\frac{dh}{dt}=\frac{dh}{dy}*\frac{dy}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7Bdh%7D%7Bdy%7D%2A%5Cfrac%7Bdy%7D%7Bdt%7D)
![-16=\frac{dh}{dy}*\frac{dy}{dt}](https://tex.z-dn.net/?f=-16%3D%5Cfrac%7Bdh%7D%7Bdy%7D%2A%5Cfrac%7Bdy%7D%7Bdt%7D)
![\frac{dh}{dy}=\frac{d}{dy} (\sqrt{x^2+y^2})\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdy%7D%3D%5Cfrac%7Bd%7D%7Bdy%7D%20%28%5Csqrt%7Bx%5E2%2By%5E2%7D%29%5C%5C)
Applying the chain rule:
![u=x^2+y^2\\\frac{dh}{dy}=\frac{d\sqrt u}{du} *\frac{du}{dy}\\\frac{dh}{dy}=\frac{1}{2\sqrt u} *2y\\\frac{dh}{dy}=\frac{y}{\sqrt {(x^2+y^2)}}](https://tex.z-dn.net/?f=u%3Dx%5E2%2By%5E2%5C%5C%5Cfrac%7Bdh%7D%7Bdy%7D%3D%5Cfrac%7Bd%5Csqrt%20u%7D%7Bdu%7D%20%2A%5Cfrac%7Bdu%7D%7Bdy%7D%5C%5C%5Cfrac%7Bdh%7D%7Bdy%7D%3D%5Cfrac%7B1%7D%7B2%5Csqrt%20u%7D%20%2A2y%5C%5C%5Cfrac%7Bdh%7D%7Bdy%7D%3D%5Cfrac%7By%7D%7B%5Csqrt%20%7B%28x%5E2%2By%5E2%29%7D%7D)
Therefore, at x=300 and y = 500, dy/dt is:
![-16=\frac{y}{\sqrt {(x^2+y^2)}}*\frac{dy}{dt}\\-16=\frac{500}{\sqrt {(300^2+500^2)}}*\frac{dy}{dt}\\\frac{dy}{dt}=-18.66\ ft/s](https://tex.z-dn.net/?f=-16%3D%5Cfrac%7By%7D%7B%5Csqrt%20%7B%28x%5E2%2By%5E2%29%7D%7D%2A%5Cfrac%7Bdy%7D%7Bdt%7D%5C%5C-16%3D%5Cfrac%7B500%7D%7B%5Csqrt%20%7B%28300%5E2%2B500%5E2%29%7D%7D%2A%5Cfrac%7Bdy%7D%7Bdt%7D%5C%5C%5Cfrac%7Bdy%7D%7Bdt%7D%3D-18.66%5C%20ft%2Fs)
The elevator is descending at 18.66 ft/s.
Step-by-step explanation:
The ratio of the two shorter legs of the top triangle is
![\dfrac{5}{4} = 1.25](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B4%7D%20%3D%201.25)
The bottom triangle has the following ratio:
![\dfrac{7.5}{6} = 1.25](https://tex.z-dn.net/?f=%5Cdfrac%7B7.5%7D%7B6%7D%20%3D%201.25)
Since their ratios are the same, this means that the two triangles are similar.