<u>Answer:</u>
8
<u>Step-by-step explanation:</u>
We are given the following expression and we are to find the simplest form of this expression:
First of all, we will factor the coefficient:
Rewriting it as:
Applying the exponent rule 
to get:
Answer:
n = (123 - 3a) / 0.1
Step-by-step explanation:
Given:
3a + 0.1n = 123
Solve for n
3a + 0.1n = 123
Subtract 3a from both sides
3a + 0.1n - 3a = 123 - 3a
0.1n = 123 - 3a
Divide both sides by 0.1
n = (123 - 3a) / 0.1
The resulting equation if 3a + 0.1n = 123 is solved for n is n = (123 - 3a) / 0.1
To minimize the cost, we take the straight distance from the refinery to the other side of the river as 2 km. Also, the 7 km will be the distance that has to be traveled by the pipeline in land. The total cost, C, is therefore,
total cost = (2 km)($800,000/km) + (7 km)($400,000 /km)
total cost = $4,400,000
Thus, the total cost of the pipeline is approximately $4,400,000.00.
Answer:
(x, g(x)) = {(-2, -2), (0, 0), (2, 2), (4, -3), (6, -3)}
Step-by-step explanation:
The first three values of x in the table are all less than or equal to 2, so the first part of the function definition applies. The y-value is equal to the x-value. The ordered pairs are ...
(-2, -2), (0, 0), (2, 2)
The last two values of x in the table are more than 2, so the last part of the function definition applies. For those values of x, the y-value is -3. The ordered pairs are ...
(4, -3), (6, -3)
Answer:
see below
Step-by-step explanation:
(ab)^n=a^n * b^n
We need to show that it is true for n=1
assuming that it is true for n = k;
(ab)^n=a^n * b^n
( ab) ^1 = a^1 * b^1
ab = a * b
ab = ab
Then we need to show that it is true for n = ( k+1)
or (ab)^(k+1)=a^( k+1) * b^( k+1)
Starting with
(ab)^k=a^k * b^k given
Multiply each side by ab
ab * (ab)^k= ab *a^k * b^k
( ab) ^ ( k+1) = a^ ( k+1) b^ (k+1)
Therefore, the rule is true for every natural number n
