Answer:
h(x) = 4·log₃(x) +2
Step-by-step explanation:
<h3>Part A:</h3>
h(x) = f(x) +g(x)
h(x) = (log₃(x) +3) +(log₃(x³) -1)
h(x) = log₃(x) +3·log₃(x) +2
h(x) = 4·log₃(x) +2 . . . . . "simplest" form
h(x) = log₃(9x⁴) . . . . . . . as a single logarithm
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<h3>Part B:</h3>
No system of equations is given. Perhaps you want to find x for f(x) = g(x).
log₃(x) +3 = log₃(x³) -1
log₃(x) +3 = 3·log₃(x) -1
4 = 2·log₃(x) . . . . . . . . . . . add 1-log₃(x)
2 = log₃(x) . . . . . . . . . . . . divide by 2
3² = x = 9 . . . . . . . . . . . . . take the antilog
The solution to f(x) = g(x) is x = 9.
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<em>Additional comment</em>
The relevant rules of logarithms are ...
a = log₃(b) ⇔ 3^a = b
log(a^b) = b·log(a)
log(ab) = log(a) +log(b)
Answer:
A) 53
B) 53%
C) 37%
D) 63%
E) Yes.
Step-by-step explanation:
A) 53 people did not get headaches at all.
B) To solve for the percentage of participants that reported they did not get a migraine headache, you will need to divide out of the TOTAL number of people:
53/100= .53 --> Convert to percentage--> .53×100 = 53%.
C) To find this value, you will need to divide out of the amount of people that took MEDICINE and got a headache:
22/60≈0.367--> Convert to percentage --> 0.367×100≈37%
D) This percentage will be found out of who did NOT take the medicine:
25/40= 0.625 --> Convert to percentage --> 0.625×100≈63%
E) The medicine did help prevent migraine headaches because the percentage that got <u>migraines with the medicine is lower</u> than the percentage that got <u>migraines WITHOUT the medicine.</u>
Answer: B. 62.8 cubic units :)
Answer:
47.7ft
Step-by-step explanation:
12.8ft+6.2ft+13.9ft+15.5ft=47.7ft
Given length of a lap = 5/8 mile.
Number of laps Carin ran = 3 1/2 laps.
3 1/2 can be read as 3 and a half. In improper fractions, it can be written as
(3*2+1)/2 = 7/2 laps.
In order to find the total distance covered in 3 1/2 or 7/2 laps, we need to multiply length of a lap by total number of laps ran.
Therefore, total distance covered = 7/2 × 5/8.
=
Multiplying across, we get
= 
=
Let us convert 35/16 into mixed fractions.
On dividing 35 by 16, we get 2 quotient and 3 remainder.
So, the mixed fraction would be 2 3/16.
Therefore, she ran 2 3/16 miles in 3 1/2 laps.