For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
Where:
m: It's the slope
b: It is the cut point with the y axis.
By definition, if two straight lines are parallel then their slopes are equal. Thus, the slope of the line sought will be ![m = 2.](https://tex.z-dn.net/?f=m%20%3D%202.)
![y = 2x + b](https://tex.z-dn.net/?f=y%20%3D%202x%20%2B%20b)
We substitute the given point to find b:
![2 = 2 (-1) + b\\2 = -2 + b\\2 + 2 = b\\b = 4](https://tex.z-dn.net/?f=2%20%3D%202%20%28-1%29%20%2B%20b%5C%5C2%20%3D%20-2%20%2B%20b%5C%5C2%20%2B%202%20%3D%20b%5C%5Cb%20%3D%204)
Finally the line is:
![y = 2x + 4](https://tex.z-dn.net/?f=y%20%3D%202x%20%2B%204)
Answer:
![y = 2x + 4](https://tex.z-dn.net/?f=y%20%3D%202x%20%2B%204)
<h2>
The top of the ladder is descending at 0.3 m/s.</h2>
Step-by-step explanation:
By Pythagoras theorem we know that
Hypotenuse² = Base² + Perpendicular²
h² = b² + p²
We have for ladder
h = 5 m
b = 3 m
5² = 3² + p²
p = 4 m
![\frac{db}{dt}=0.4m/s\\\\\frac{dh}{dt}=0](https://tex.z-dn.net/?f=%5Cfrac%7Bdb%7D%7Bdt%7D%3D0.4m%2Fs%5C%5C%5C%5C%5Cfrac%7Bdh%7D%7Bdt%7D%3D0)
Differentiating h² = b² + p² with respect to time
![2h\times \frac{dh}{dt}=2b\times \frac{db}{dt}+2p\times \frac{dp}{dt}\\\\5\times 0=3\times 0.4+4\times \frac{dp}{dt}\\\\\frac{dp}{dt}=-0.3m/s](https://tex.z-dn.net/?f=2h%5Ctimes%20%5Cfrac%7Bdh%7D%7Bdt%7D%3D2b%5Ctimes%20%5Cfrac%7Bdb%7D%7Bdt%7D%2B2p%5Ctimes%20%5Cfrac%7Bdp%7D%7Bdt%7D%5C%5C%5C%5C5%5Ctimes%200%3D3%5Ctimes%200.4%2B4%5Ctimes%20%5Cfrac%7Bdp%7D%7Bdt%7D%5C%5C%5C%5C%5Cfrac%7Bdp%7D%7Bdt%7D%3D-0.3m%2Fs)
The top of the ladder is descending at 0.3 m/s.
Answer:
peanuts=2/5
chocolate chips=1/8
coconut=3/10
rest=sprinkles
2/5+1/8+3/10
lcm=40
<u>16 + 5 + 12</u>
60
=33/60
60/60 -33/60
=27/60
=9 /20 apples are covered with sprinkles
9/20 x 120
<h2>
=63 apples are covered with sprinkles</h2>
Step-by-step explanation:
9514 1404 393
Answer:
2.25
Step-by-step explanation:
Add the square of half the x-coefficient to complete the square.
(-3/2)² = 9/4 = 2.25