The line with a slope of 3 is steeper, they are alike because both are at a positive incline.
Sum of interior angles = (n-2) × 180<span> = (5-2) x 180 = 3 x 180 = 540
so
x + 90 + 107 + 144 + 138 = 540
x + 479 = 540
x = 540 - 479
x = 61</span>
<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.
= a/b * b/a + 2a/b + 2b/a + 4
= 1 + 2a/b + 2b/a + 4
= 5 +2a/b + 2b/a Answer
1. Rational.
2. Irrational (famous for being irrational).
3. Rational.
4. I think this is irrational.
