Answer:
The answer is A.
Step-by-step explanation:
<span>7 x 7 = 49 area of square.</span>
<span /><span> The radius of the circle is half the diameter. 7 cm/2 = 3.5 </span>
<span> A = 3.14 × 3.5 cm × 3.5 cm = 38.465</span>
Finale step. Subtract the area of the circle from the area of the square.
49 cm^2 −38.465 cm^2 = 10.535 or round to 10.54 cm^2
D. 10.54
Answer:
x= 54°
Step-by-step explanation:
43 + x - 7 = 90°
36 + x = 90°
x= 90-36
x= 54°
Answer:
The answer to your question is x = 4
<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.
