Answer:
Step-by-step explanation:
We are given the polynomial:
And we want to determine the value of <em>k</em> such that (<em>x</em> - 2) is a factor of the polynomial.
Recall that the Factor Theorem states that a binomial (<em>x</em> - <em>a</em>) is a factor of a polynomial P(x) if and only if P(a) = 0.
Our binomial factor is (<em>x</em> - 2). Thus, <em>a</em> = 2.
Hence, by the Factor Theorem, P(2) must equal zero.
Find P(2):
This must equal zero. Hence:
In conclusion, <em>k</em> = 34/3.
That's 7.68% = 7.7% (rounded)
Note: C(5, 4) is the number of combinations of 5 things taken 4 at a time. You may have seen this written as
In general,
Answer:
9 inches deep
Step-by-step explanation:
12 inches - 3 inches = 9 inches
Let's start by understanding that the graph is a linear line. We have a common difference if 4.5 for every 10x we have more.
We can start by finding the gradient, using rise over run. Let's take (10, 4.5) and (20, 9)
Our rise is 9 - 4.5 = 4.5 and our run is 10. Then, our gradient becomes 4.5/10 = 0.45
Now, we can substitute points using the point-slope form.
y - 4.5 = 0.45(x - 10)
y - 4.5 = 0.45x - 4.5
Hence, our line becomes y = 0.45x and you can verify by substituting in points from the table.
Answer:
14
Step-by-step explanation:
