Answer: The value of k is 5 units.
Step-by-step explanation:
Since we have given that
The graph of f(x)=0.5x is replaced by the graph of g(x) = 0.5x-k
If g(x) is obtained by shifting f(x) down by 5 units,
Then the graph of f(x) = 0.5x is replaced by the graph of g(x) = 0.5x-5
Hence, k = 5 units
Therefore, the value of k is 5 units.
270 degrees is at the bottom of the unit circle, and it splits the 3rd and 4th quadrants.
Its terminal point is (0, -1).
Hope this helps!
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.
For all of these, let n = the unknown number.
25) "Five less than a number" becomes 5 - n
"At least" tells you your number is greater than or equal to - 2.
Put it all together.
5 - n ≥ - 2
- n ≥ - 2 - 5
- n ≥ - 7
Divide by - 1 to isolate the variable. This flips the operation.
n ≤ 7
26) "The difference between a number and 6" tells you to do n - 6
"no more than" means this is a less than or equal to sign.
n - 6 ≤ 5
n ≤ 5 + 6
n ≤ 11
27) "The sum of a number and 7" becomes n + 7
"more than" is a greater than sign
n + 7 > 1
n > 1 - 7
n > - 6
28) "The difference between a number and 10" becomes n - 10
Obvious one, "greater than" is... just that.
n - 10 > 9
n > 9 + 10
n > 19
29) "Four less than a number" is 4 - n
Another obvious one in "less than"
4 - n < 11
- n < 11 - 4
- n < 7
Divide by - 1 on both sides to isolate the variable
n > - 7
First we need to determine the type of progression in the question.That's geometric progression. Because the pattern from one sequence to the others are about multiplying.
Second, determine the ratio of the progressionr = a₂/a₁
r = a₂ ÷ a₁
r = 1/2 ÷ 2
r = 1/2 × 1/2
r = 1/4
Third, determine the formula to know the recursive rulea₂ = a × 1/4
a₂ = 1/4 × a
Fourth, determine a₁. a₁ is the first term of the progressiona₁ = 2
Final answer:Recursive rule
![a_{n} = \frac{1}{4} a_{(n-1)}](https://tex.z-dn.net/?f=%20a_%7Bn%7D%20%3D%20%5Cfrac%7B1%7D%7B4%7D%20a_%7B%28n-1%29%7D%20)
a₁ = 2