The equation k(x) = x^2 is quadratic equation, and the value of n in p (x) = k (x) + n is -6
<h3>How to determine the value of n?</h3>
The equations are given as:
k(x) = x^2
p (x) = k (x) + n
From the graph, we can see that the graph of k(x) is shifted down by 6 units.
This means that the equation of p(x) is
p (x) = k (x) - 6
By comparison;
n = -6
Hence, the value of n in p (x) = k (x) + n is -6
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Answer:
c/sin C = b/sin C
Step-by-step explanation:
Look at the statement in the previous step and the reason in this step.
c sin B = b sin C
Divide both sides by sin B sin C:
(c <em>sin B</em>)/(<em>sin B</em> sin C) = (b <em>sin C</em>)/(sin B <em>sin C</em>)
c/sin C = b/sin B
Cardinality is the number of elements in a set. Both of the sets E and O have infinite elements, but there are different types and sizes of infinity. Luckily, all you have to do to prove that two sets have the same cardinality is describe an explicit one-to-one correspondence between the two.
For odds and evens, this is a relatively easy thing to do - all odds are just one less than an even. So, the function that relates the two sets is
f(n) = n + 1
or, depending on how you write it,
E(n) = O(n) + 1
Answer:
5 hours
Step-by-step explanation:
The ratio of speeds is 3 : 4 with a multiplier of 6 mph. They are at right angles to each other, so the speed vectors form a right triangle with side ratios 3:4:5. The separation speed of the cyclists is 5·(6 mph) = 30 mph. It will take them 5 hours to be separated by 150 miles.
time = distance/speed = 150 mi/(30 mi/h) = 5 h
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<em>Alternate solution</em>
The distance (d) between the cyclists can be written in terms of their respective distances as a function of time. If the first one has distance n(t) = 18t from the start, and the second has distance e(t) = 24t from the start, then the distance between them is given by the Pythagorean theorem as ...
