Consider the graph shown. Determine if the graph shows two quantities that vary directly. If possible, determine the constant of
proportionality. Explain your reasoning.
1 answer:
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Answer:
Step-by-step explanation:
log20 = 1.301 (when you see only "log" with no base, it is taken as a base 10)
This basically means:
(This is the log in exponential form)
Since we don't know what is equal to, we will say
= x
So to solve for = x, you do the same thing. (convert to exponential form)
Now you will notice that both of these equations are equal to 20.
Since 20 = 20,
we can say =
Another way of saying 100, is (make the bases the same)
Now we get
(we get 2x because an exponent to the power of an exponent () is the same as 2 * x)
Because you have the same base, you can just ignore the 10s and focus on the exponents. So you get:
2x = 1.301
x = 0.6505
Answer:
-3, 1, 4 are the x-intercepts
Step-by-step explanation:
The remainder theorem tells you that dividing a polynomial f(x) by (x-a) will result in a remainder that is the value of f(a). That remainder will be zero when (x-a) is a factor of f(x).
In terms of finding x-intercepts, this means we can reduce the degree of the polynomial by factoring out the factor (x-a) we found when we find a value of "a" that makes f(a) = 0.
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For the given polynomial, we notice that the sum of the coefficients is zero:
1 -2 -11 +12 = 0
This means that x=1 is a zero of the polynomial, and we have found the first x-intercept point we can plot on the given number line.
Using synthetic division to find the quotient (and remainder) from division by (x-1), we see that ...
f(x) = (x -1)(x² -x -12)
We know a couple of factors of 12 that differ by 1 are 3 and 4, so we suspect the quadratic factor above can be factored to give ...
f(x) = (x -1)(x -4)(x +3)
Synthetic division confirms that the remainder from division by (x -4) is zero, so x=4 is another x-intercept. The result of the synthetic division confirms that x=-3 is the remaining x-intercept.
The x-intercepts of f(x) are -3, 1, 4. These are the points you want to plot on your number line.
