Answer: 1
Step-by-step explanation: first you need to pretend that the absolute value bars are parentheses. Then substitute a with any number less that five, for example z=3
Now we can write our new equation: (3-6)-(3-5) now we have to determine if the final answer inside the parentheses is positive or negative. In the first parentheses 3-6=-3 with is negative. In our second parentheses we have 3-5=-2 which is a also negative.
Knowing that both parentheses are negative results we can set up an equation using z instead of 3:
-(z-6)-(-(z-5)) is our new equation. If we simplify this equation we get 1 for an answer
Answer:
Distance = 10 km
Step-by-step explanation:
Let x be the number of hours taken from school to town and y be the number of hours taken back to the school
Then distance covered during first trip would be 10x (distance = speed*time) and during the second trip would be 8y. Both distances are equal.
=> 10x = 8y
Dividing both sides by 2
=> 5x = 4y
=> 5x-4y = 0 ------------------(1)
<u><em>The total time for both the trips is:</em></u>
=> x + y = 2.25 -------------------(2)
Multiplying eq (2) by 5
=> 5x+5y = 11.25 ---------------(3)
Subtacting (3) from (1)
=> 5x-4y-5x-5y = 0-11.25
=> -4y-5y = -11.25
=> -9y = -11.25
Dividing both sides by -9
=> y = 1.25 hrs
Putting in (2)
=> x + 1.25 = 2.25
=> x = 2.25 - 1.25
=> x = 1 hr
<u><em>Now, Calculating the Distance</em></u>
=> Distance = 10x
=> 10 ( 1 )
=> Distance = 10 km
Answer:
$625,000
Step-by-step explanation:
The maximum revenue will be found where the derivative of the revenue function is zero.
r'(x) = 50 -2x = 0
50 = 2x
x = 25
When 2500 gallons are sold, the revenue is ...
r(25) = 50(25) -25(25) = (50 -25)(25) = 25(25) = 625 . . . thousands
The maximum revenue is $625,000.
Answer:
A. 70 miles per hour B. 620 miles from home
Step-by-step explanation:
This function is a linear equation, following the slope-intercept form of a line. This standard form is y = mx + b, where m is the slope and b is the y-intercept. The slope of a line is the rate at which the steepness of the line is changing. The y-intercept is where the function is "starting".
In our case, the number in the rate of change position is 70. It is being multiplied by t. If t = 1, that means that after 1 hour, we have gone 70 miles. If t = 2, that means after 2 hours we have gone 140 miles. If t = 3, that means that after 3 hours, we have gone 210 miles; etc. That number in the slope position represents the rate at which you are traveling PER HOUR; the slope.
The "starting" position of day 2 is found in the y-intercept. Replacing x with 0, meaning NO time has gone by at all, at the beginning of the second day, we are starting 620 miles from home.