Consider the functions f(x) and g(x) shown below. For which of the following values of x does f(x) does not equal g(x)?
1 answer:
<h3>Answer: d) -3</h3>
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Explanation:
When f(x) = g(x) is true, this is where the two graphs intersect. So we have three solutions here because we have three different intersection points.
The x coordinates of those intersection points, from left to right, are: -3/2, 0, 3.
Note: -3/2 = -1.5 is exactly at the midpoint of -2 and -1.
In other words, if we plugged in x = 0 into both f(x) and g(x), then we'll get the same output value and hence f(x) = g(x) will be true. The same applies to -3/2 and 3 as well.
Recall that y = f(x) and y = g(x), so saying f(x) = g(x) really means they both have the same y outputs for that specific input x value. This explains why intersection points correspond to solutions.
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Since x = -3 is not on the list of solutions, this means this x value will make f(x) and g(x) be different outputs. The graph shows the curves do not intersect with each other when x = -3. Instead, g(x) is above f(x) at this location. So we can say g(x) > f(x) when x = -3.
In short, when x = -3, we have
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Answer: No, they would not get the same amount.
Step-by-step explanation:
Let the number of coins be x
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Answer:
cos(θ) = 3/5
Step-by-step explanation:
We can think of this situation as a triangle rectangle (you can see it in the image below).
Here, we have a triangle rectangle with an angle θ, such that the adjacent cathetus to θ is 3 units long, and the cathetus opposite to θ is 4 units long.
Here we want to find cos(θ).
You should remember:
cos(θ) = (adjacent cathetus)/(hypotenuse)
We already know that the adjacent cathetus is equal to 3.
And for the hypotenuse, we can use the Pythagorean's theorem, which says that the sum of the squares of the cathetus is equal to the square of the hypotenuse, this is:
3^2 + 4^2 = H^2
We can solve this for H, to get:
H = √( 3^2 + 4^2) = √(9 + 16) = √25 = 5
The hypotenuse is 5 units long.
Then we have:
cos(θ) = (adjacent cathetus)/(hypotenuse)
cos(θ) = 3/5
