Answer:
![\left\{\begin{array}{l}x+y\le360\\ \\\dfrac{x}{45}+\dfrac{y}{35}\le 8\end{array}\right..](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dx%2By%5Cle360%5C%5C%20%5C%5C%5Cdfrac%7Bx%7D%7B45%7D%2B%5Cdfrac%7By%7D%7B35%7D%5Cle%208%5Cend%7Barray%7D%5Cright..)
Step-by-step explanation:
Let x minutes be the time spent on skills and y minutes be the time spent on conditioning that Greg can complete this week.
1. To avoid excess fatigue, his coach requires Greg to spend no more than 360 minutes training in any week, then
![x+y\le 360.](https://tex.z-dn.net/?f=x%2By%5Cle%20360.)
2. When Greg trains, he either spends 45 minutes on skills or 35 minutes on conditioning. If Greg spends x minutes on skills, then
is the number of skills training sessions. If Greg spends y minutes on conditioning, then
is the number of conditioning training sessions. His schedule this week allows him to complete at most 8 training sessions, then
![\dfrac{x}{45}+\dfrac{y}{35}\le 8.](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B45%7D%2B%5Cdfrac%7By%7D%7B35%7D%5Cle%208.)
Therefore, the following system of inequalities can be used to determine the time spent on skills, x, and the time spent on conditioning, y, that Greg can complete this week
![\left\{\begin{array}{l}x+y\le360\\ \\\dfrac{x}{45}+\dfrac{y}{35}\le 8\end{array}\right..](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dx%2By%5Cle360%5C%5C%20%5C%5C%5Cdfrac%7Bx%7D%7B45%7D%2B%5Cdfrac%7By%7D%7B35%7D%5Cle%208%5Cend%7Barray%7D%5Cright..)
Answer:
D. (-1, 0) and (0, -6)
Step-by-step explanation:
The system of equations:
y = -6x - 6
y = x² - 5x - 6
We equate the two equations;
-6x - 6 = x² - 5x - 6
x² + x + 0 = 0
x² + x = 0
x(x + 1) = 0
So, x = 0 or -1
When x = 0,
Then y = -6(0) - 6 = -6
When x = -1,
Then y = -6(-1) - 6 = 6 - 6 = 0
So the answer is: (0, -6) and (-1, 0)
Answer:
It equals 420.
Step-by-step explanation:
Answer:
The correct option is B.
Step-by-step explanation:
The given function is
![f(x)=x^3](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E3)
The translation of a function is defined as
![g(x)=f(x+a)+b](https://tex.z-dn.net/?f=g%28x%29%3Df%28x%2Ba%29%2Bb)
If a>0, then the graph of f(x) shift a units left and if a<0, then the graph of f(x) shift a units right.
If b>0, then the graph of f(x) shift b units up and if b<0, then the graph of f(x) shift b units down.
It is given that the graph of f(x) shifts 4 units left and 2 units down. So, a=4 and b=-2.
![g(x)=f(x+4)+(-2)](https://tex.z-dn.net/?f=g%28x%29%3Df%28x%2B4%29%2B%28-2%29)
![[\because f(x)=x^3]](https://tex.z-dn.net/?f=%5B%5Cbecause%20f%28x%29%3Dx%5E3%5D)
![y=(x+4)^3-2](https://tex.z-dn.net/?f=y%3D%28x%2B4%29%5E3-2)
Therefore option B is correct.
Answer:
m ≥ 1229
Step-by-step explanation:
Use m for the number of minutes
30 + 0.05×m ≥ 91.45
0.05*m ≥ 91.45-30
0.05*m ≥ 61.45
m ≥ 1229