Answer: option B. it has the highest y-intercept.
Explanation:
1) point -slope equation of the line
y - y₁ = m (x - x₁)
2) Replace (x₁, y₁) with the point (5,3):
y - 5 = m (x - 3)
3) Expand using distributive property and simplify:
y - 5 = mx - 3m ⇒ y = mx + 5 - 3m
4) Compare with the slope-intercept equation of the line: y = mx + b, where m is the slope and b is the y-intercept
⇒ slope = m
⇒ b = 5 - 3m = y - intercept.
Therefore, for the same point (5,3), the greater m (the slope of the line) the less b (the y-intercept); and the smaller m (the slope) the greater the y - intercept.
Then, the conclusion is: the linear function with the smallest slope has the highest y-intercept (option B).
Answer:
a) 1296 bacteria per hour
b) 0 bacteria per hour
c) -1296 bacteria per hour
Step-by-step explanation:
We are given the following information in the question:
The size of the population at time t is given by:
We differentiate the given function.
Thus, the growth rate is given by:
a) Growth rates at t = 0 hours
b) Growth rates at t = 3 hours
c) Growth rates at t = 6 hours
The new shower head dispenses 3 gallons of water per minute, as shown in the equation y = 3x.
So, 3 x 8 = 24.
Then, to find out how much he saves each day, you would find how much he used before,
11 x 8 = 88
Next we want to see how much Nathan saved, so we subtract the total,
88 - 24 = 64
Nathan saved 64 gallons.
Answer:
50 times
Step-by-step explanation:
You are going to flip a coin 100 times. There are 2 sides. So, what you would do is divide 100 by two because there are two sides. There is a 50% chance that the coin will land on heads, and a 50% chance it will land on tails.
Please let me know if you have any more questions. Hope this helps!
