The slope-intercept formula can be written as follows:
y = mx + b
The variable "m" represents the slope of the line, while "b" represents the y-intercept. We'll start with the y-intercept.
We know that the y-intercept can be defined as the value of "y" when "x" is equal to zero. To do this, we will need to find point (0,y). The original problem gives us two points, one of which is (0,2). Because "x" is equal to zero, we know that the y-intercept is 2. Substitute this value into the slope-intercept formula:
y = mx + 2
Now we need to find the slope. Slope can be defined as the "rise" of the line over the "run" of the line. In other words, calculate the change in y-value over the change in x-value. To do this, we will use the "x" and "y" values of the two points given in the problem.
Starting with the y-values (rise), we have 2 and 4. The difference between these two values is 2. Moving on to the x-values (run), we have 0 and 8. The difference between these two values is 8. Now put rise over run and substitute this value into the slope-intercept formula:
y = (2/8)x + 2
Now simplify the right side of the equation:
y = (1/4)x + 2
We now have a complete slope-intercept formula of the line.
I hope this helps!
The distance travelled by an object at time t is given by: d = stwhere d is the distance, s is the speed and t is the time.
Given that the cheetah travels a maximum of 70mph, the distance travelled by the cheetah travelling at 70mph at time t is given by d = 70t
There are 60 mins in one hour, so the distance given in miles per minutes is d = 70/60t = 1.167 miles per minutes.
Part B:
Given that t = 10 minutes, the distance covered by the cheetah in 10 minutes is d = 1.167 x 10 = 11.67 miles.
Part C:
If the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes, then the number of minutes the cheetah have traveled in the first 8 minutes is given by
d = 1.167 x 8 = 9.33 miles.
Part D:
If the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes, then the number of minutes the cheetah have traveled in the second 8 minutes is given by
d = 40/60 x 8 = 5.33 miles
Part E:
The distance the cheetah traveled in the first 8 minutes more than in the second 8 minutes is given by
9.33 miles - 5.33 miles = 4 miles.
Part F:
The ratio of the distance travelled in the first 8 minutes to the distance travelled in the next minutes is given by
9.33 : 5.33 = 1.75 : 1.
Therefore, the distance traveled by the cheetah during the first 8 minutes is 1.75 times greater than the distance traveled during the second 8 minutes.
Answer:
The domain of a function is the complete set of possible values of the independent variable. The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Step-by-step explanation:
When finding the domain, remember:
The denominator (bottom) of a fraction cannot be zero
The number under a square root sign must be positive in this section
The range is the resulting y-values we get after substituting all the possible x-values.
-2y - 2y - 8 = -4
Move the -8 to the -4, and that makes
-2y -2y = 4
Add the -2ys together and that makes
-4y = 4
Then divide by -4, and you will get your answer of
y= -1