<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.
With what? there’s no problem.
Answer:
72
Step-by-step explanation:
Sum of external angles= 360°
360 - (57+108+51+60) = 84
84-12= 72
Answer:
(5,-2)
Step-by-step explanation:
mapping is (x, y)=(-y,-x)
(2,-5)=(5,-2)
90° counterclockwise is (5,-2)
Thanks
Hope it helps
Answer:
24 feet
Step-by-step explanation:
According to the question, Patricia needs 10 yards of fabric to make curtains for her bedroom she also needs 3 yards of fabric to make a cover for her storage bench
So, she needs 13 yards
converting into feet
1 yard = 3 feet
13 yards x 3 = 39 feet
Now, she already has 15 feet of fabric.
Finding out the difference : 39 - 15= 24 feet
Therefore, she needs 24 feet more of fabric
