Answer:
Step-by-step explanation:
We see that diagonal AB is also the hypotenuse of a triangle where the other 2 side lengths are 4 and sqrt{45}. Using the Pythagorean theorem, we get that diagonal AB is
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:
x=24
Step-by-step explanation:
Answer:
Step-by-step explanation:
there is no question
Answer:
The answer is A and C
Step-by-step explanation:
The answer is A because 12.3 multiplied by 10 is 123, and 0.4 multiplied by 10 is 4.
12.3 * 10 = 123
0.4 * 10 = 4
So, this shows that this equation is the same as 12.3 divided by 0.4
The answer is C because 12.3 multiplied by 100 is equal to 1230, this is the same for 0.4
12.3 * 100 = 1230
0.4 * 100 = 40
So, the answer is both A and C.
Hope this helps! :)
