Which expression is equivalent to the given expression? 17x−32x
2 answers:
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Answer:
f(-3) = -20
Step-by-step explanation:
We observe that the given x-values are 3 units apart, and that the x-value we're concerned with is also 3 units from the first of those given. So, a simple way to work this is to consider the sequence for x = 6, 3, 0, -3. The corresponding sequence of f(x) values is ...
34, 10, -8, ?
The first differences of these numbers are ...
10 -34 = -24
-8 -10 = -18
And the second difference is ...
-18 -(-24) = 6
For a quadratic function, second differences are constant. This means the next first-difference will be ...
? -(-8) = -18 +6
? = -12 -8 = -20
The value of the function at x=-3 is -20.
_____
The attachment shows using a graphing calculator to do a quadratic regression on the given points. The graph can then be used to find the point of interest. There are algebraic ways to do this, too, but they are somewhat more complicated than the 5 addition/subtraction operations we needed to find the solution. (Had the required x-value been different, we might have chosen a different approach.)
The distance from the second destination back to Dallas is 918 miles
<h3>Given</h3>A triangle has points Dallas, destination 1, and destination 2.
The distance from Dallas to destination 1 is 720 miles
The distance from destination 1 and destination 2 is 290 miles
the angle formed between Dallas, destination 1, and destination 2 is 125 degrees.
He moves from destination 1 to Dallas then destination 2
We could use cosine law to find the distance
<h3>What is cosine law?</h3>The Law of cosines or cosine law means the relation between the length of sides of a triangle with respect to the cosine of its angle. It is also called the cosine rule
=
=84100+518400-417600 cos 125
=602500-417600*(-0.5735)
=602500+239493.6
=841993.6
b=917.6 miles
≅918 miles
The distance is 918 miles he will fly from the second destination back to Dallas
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