<h3>
Answer: x = 1/2</h3>
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Explanation:
Recall that quadratic form is ax^2+bx+c.
So we need an x^2 term followed by an x term, then a constant at the end.
It may not look it, but the given equation is nearly in quadratic form.
Rewrite 9^(2x) as (9^x)^2
We get this equivalent equation (9^x)^2 - 2*(9^x) - 3 = 0
From here, let's make w = 9^x. Replace every copy of '9^x' with 'w' and we end up with this new simpler equation: w^2 - 2w - 3 = 0
From here we can use the quadratic formula or factor. I'll factor.
w^2 - 2w - 3 = 0
(w - 3)(w + 1) = 0
w-3 = 0 or w+1 = 0
w = 3 or w = -1
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Now we use these values of w to find x
If w = 3, then,
w = 9^x
3 = 9^x
log(3) = log(9^x)
log(3) = x*log(9)
x = log(3)/log(9)
x = log(3)/log(3^2)
x = log(3)/(2*log(3))
x = 1/2
At the last step, we have the log(3) terms cancel.
Repeat for w = -1
w = 9^x
-1 = 9^x
log(-1) = log(9^x)
We run into a problem. The log of any negative number is not a real number output. In other words, 9^x is never negative. Raising any positive number to a real number output leads the result to be positive. Take a look at the graph of y = 9^x to confirm this.
In short, w = -1 is extraneous so it doesn't lead to any x value solution.
So only w = 3 is useful.
Ultimately, the only solution is x = 1/2.
Answer:
The appropriate answer is "0.437".
Step-by-step explanation:
Given:
P(rain) = 0.14
then,
P(no-rain) = 1-P(rain)
= 1-0.14
= 0.86
P(delay) = 0.16
P(rain and on time) = 0.79
then,
By using the conditional probability, we get
⇒ 
or,
⇒ 
By substituting the values, we get
⇒ 
⇒ 
I hope this helps... if not let me know and I'll try to help again :)
The answer would be 1:4 because when you divide 2:8 by 2 you get 1:4
