Answer:
X ≈ 117.9°
Step-by-step explanation:
The law of cosines formula is given. Solving it for C, we find ...
C = arccos((a^2 +b^2 -c^2)/(2ab))
where a and b are the sides adjacent to the angle of interest.
Here, we have ...
X = arccos((50^2 +55^2 -90^2)/(2·50·55)) = arccos(-2575/5500)
X ≈ 117.9°
Answer:
12 adults
Step-by-step explanation:
We can solve this in a couple of simple steps. First, since there are 3 adults for every 8 students we add these two numbers together
3+8 = 11
Now we simply divide this number by the total amount of people that went to the trip in order to get how many times this set of adults and students repeats itself.
44 / 11 = 4
Finally, we multiply this number by the set of 3 adults in order to find out how many adults went to the trip.
4 * 3 = 12 adults
8 * 3 = 32 Students
Answer: 11
Step-by-step explanation: To determine which number is not a solution for the inequality, first begin by substituting in 3 for <em>x</em>.
So we have (3) + 6 < 14.
(3) + 6 is 9 and we can see that 9 < 14.
This means that this is a solution so we need to continue.
Now substitute a 5 in for <em>x</em>.
So we have (5) + 6 < 14.
(5) + 6 is 11 and we can see that 11 < 14.
This means that this is a solution so we need to continue.
Now substitute a 7 in for <em>x</em>.
So we have (7) + 6 < 14.
(7) + 6 is 13 and we can see that 13 < 14.
This means that this is a solution so we need to continue.
Now substitute an 11 in for <em>x</em>.
So we have (11) + 6 < 14.
(11) + 6 is 17 and we can see than 17 < 14.
Notice that the inequality 7 < 14 is not a true statement however because 17 is greater than 14, not smaller. This means that 11 is not a solution.
Answer:
log 2 = 0.301
Step-by-step explanation:
We have to find the value of log 2 while the value of log 5 is given to be 0.6989.
Now, starting with log 10, we get,
log 10 = log (5 × 2) = log 5 + log 2
{Using the property of logarithm that, log AB = log A + log B}
⇒ ![\log 10^{1} = \log 5 + \log 2](https://tex.z-dn.net/?f=%5Clog%2010%5E%7B1%7D%20%3D%20%5Clog%205%20%2B%20%5Clog%202)
⇒ log 10 = 0.6989 + log 2
{Since
}
Again, we know that, log 10 = 1
⇒ 1 = 0.6989 + log 2
⇒ log 2 = 0.301 (Answer)
The laws of sines is already indicated in the provided images.
1. sin20/3.3 = sinC/5.4
Thus, angle C is 34.03 degrees. To find angle B: 180 - 20 - 34.03 = 126 degrees. Using the law of sines,
sin20/3.3 = sin(126)/b
b = 7.8 units
From this answer, we can already tell that the answer is letter C: <span>3 units and 7.8 units.
2. Angle J = 180 - 120 - 40 = 20 degrees. Then,
sin(20)/2 = sin(120)/k
k = 5.1 units</span>