Answer:
4 km per hour and 6 km per hour.
Step-by-step explanation:
The combined running rate = 30/3 = 10 km/h.
If one runner's speed = x then the other one's speed is x+2 km/h.
So x + x + 2 = 10
2x = 8
x = 4
So one runs at 4 km/h and the other at 6 km/h.
Answer:
x=6
Step-by-step explanation:
81^x = 27 ^(x+2)
81 = 3^4 and 27 =3^3 so replace 81 and 27 in the equation
3^4^x = 3^3^(x+2)
When we have a power to a power we can multiply the exponents
a ^b^c = a^(b*c)
3^(4x) = 3^(3*(x+2))
Since the bases are the same, the exponents have to be the same
a^b = a^c means b=c
4x = 3(x+2)
Now we can solve for x
Distribute
4x = 3x+6
Subtract 3x from each side
4x-3x = 3x-3x+6
x = 6
Answer:
The (constant) rate of change with respect to the variable x of a linear function y = f(x) is the slope of its graph. If x and f have units in Definition 2, then the units of the rate of change are those of f divided by those of x.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Lets use the compound interest formula provided to solve this:
<em>P = initial balance</em>
<em>r = interest rate (decimal)</em>
<em>n = number of times compounded annually</em>
<em>t = time</em>
First, change 6% into a decimal:
6% -> 
-> 0.06
Since the interest is compounded semi-annually, we will use 2 for n. Lets plug in the values now and your equation will be:
Answer:
Step-by-step explanation:
Let's say that the time it took him to get to work in the morning is t hours. Then the time it took him to get home in the afternoon must be 1 - t hours. We know that for any trip, distance equals rate times time or d = rt . That means that the distance he drove to work is given by , but we also know that the distance he drove to get home must be the same distance, because he took the same route (and, presumably, no one picked up him house and moved it while he was at work) so for the trip home we can say d = 30 × (1 - t) and since the distances are equal, we can say:
45t = 30 × (1 - t)
45t = 30 - 30t
45t + 30t = 30
75t = 30
t = 30/75
t = 2 /5 hour to drive to work at 45mph
Since , d = rt
d = 45 ×(2/5) = 18miles
