The area is 25π
Hope this helps
Answer: x = 8
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I'm going to use the notation log(2,x) to indicate "log base 2 of x". The first number is the base while the second is the expression inside the log (aka the argument of the log)
log(2,x) + log(2,(x-6)) = 4
log(2,x*(x-6)) = 4
x*(x-6) = 2^4
x*(x-6) = 16
x^2-6x = 16
x^2-6x-16 = 0
(x-8)(x+2) = 0
x-8 = 0 or x+2 = 0
x = 8 or x = -2
Recall that the domain of log(x) is x > 0. So x = -2 is not allowed. The same applies to log(2,x) as well.
Only x = 8 is a proper solution.
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You can use the change of base rule to check your work
log base 2 of x = log(2,x) = log(x)/log(2)
log(2,(x-6)) = log(x-6)/log(2)
So,
(log(x)/log(2)) + (log(x-6)/log(2)) = 4
(log(8)/log(2)) + (log(8-6)/log(2)) = 4
(log(8)/log(2)) + (log(2)/log(2)) = 4
(log(2^3)/log(2)) + (log(2)/log(2)) = 4
(3*log(2)/log(2)) + (log(2)/log(2)) = 4
3+1 = 4
4 = 4
The answer is confirmed
Answer:
1.2 centimeters
Step-by-step explanation:
Answer:
x = 14.375
Step-by-step explanation:
Ok, so we know that a triangle has a total interior degree of 180°. And since we already have a 95° angle, we just need to subtract 95 from 180.
180° - 95° = 85°
Now, we already have indicators that two of the three sides are equal. And we already got the angle of the side that does not have a matching partner. So we just need to divide what we already have by 2.
85° / 2 = 42.5°
Now that we know each side is 42.5 degrees, we just need to grab our given equation and put and equal sign at the end with what we already know is the answer (since we are trying to solve for <em>x</em>).
(4x - 15) = 42.5
Now, let's just get rid of those useless parentheses.
4x - 15 = 42.5
Next, we just need to have the variable on its own side, all by itself. So, in order to do that, we just add 15 to both sides.
4x = 57.5
Now, for our final step, we just need to divide each side by our variables' factor (which is a positive 4). In which we get our final answer of:
x = 14.375
The sequence seems to be that you add 1 and then multiply by 2, and then add 1 and multiply by 3, so I would assume you do 9 + 1 = 10, and then multiply by 4 to get 40 as your next number. I hope this helps!
