Answer:
First person: $107
Second person: $98
Third person: $93
Step-by-step explanation:
Let be "f" the amount of money (in dollars) that the first person contributed to the purchase, "s" the amount of money (in dollars) that the second person contributed to the purchase and "t" the amount of money (in dollars) that the third person contributed to the purchase.
With the information given in the exercise, you can set up the following equations:
Equation 1 → 
Equation 2 → 
Equation 3 → 
Substitute the Equations 2 and 3 into the Equation 1 and then solve for "f":
Finally, substitute the value of "f" into the Equation 2 and then into the Equation 3, in order to find the values of "s" and "t".
Therefore, you get:
Find, correct to the nearest degree, the three angles of the triangle with the vertices d(0,1,1), e( 2, 4,3) − , and f(1, 2, 1)
Ksju [112]
Well, here's one way to do it at least...
<span>For reference, let 'a' be the side opposite A (segment BC), 'b' be the side opposite B (segment AC) and 'c' be the side opposite C (segment AB). </span>
<span>Let P=(4,0) be the projection of B onto the x-axis. </span>
<span>Let Q=(-3,0) be the projection of C onto the x-axis. </span>
<span>Look at the angle QAC. It has tangent = 5/4 (do you see why?), so angle A is atan(5/4). </span>
<span>Likewise, angle PAB has tangent = 6/3 = 2, so angle PAB is atan(2). </span>
<span>Angle A, then, is 180 - atan(5/4) - atan(2) = 65.225. One down, two to go. </span>
<span>||b|| = sqrt(41) (use Pythagorian Theorum on triangle AQC) </span>
<span>||c|| = sqrt(45) (use Pythagorian Theorum on triangle APB) </span>
<span>Using the Law of Cosines... </span>
<span>||a||^2 = ||b||^2 + ||c||^2 - 2(||b||)(||c||)cos(A) </span>
<span>||a||^2 = 41 + 45 - 2(sqrt(41))(sqrt(45))(.4191) </span>
<span>||a||^2 = 86 - 36 </span>
<span>||a||^2 = 50 </span>
<span>||a|| = sqrt(50) </span>
<span>Now apply the Law of Sines to find the other two angles. </span>
<span>||b|| / sin(B) = ||a|| / sin(A) </span>
<span>sqrt(41) / sin(B) = sqrt(50) / .9080 </span>
<span>(.9080)sqrt(41) / sqrt(50) = sin(B) </span>
<span>.8222 = sin(B) </span>
<span>asin(.8222) = B </span>
<span>55.305 = B </span>
<span>Two down, one to go... </span>
<span>||c|| / sin(C) = ||a|| / sin(A) </span>
<span>sqrt(45) / sin(C) = sqrt(50) / .9080 </span>
<span>(.9080)sqrt(45) / sqrt(50) = sin(C) </span>
<span>.8614 = sin(C) </span>
<span>asin(.8614) = C </span>
<span>59.470 = C </span>
<span>So your three angles are: </span>
<span>A = 65.225 </span>
<span>B = 55.305 </span>
<span>C = 59.470 </span>
$ 25 was the cost of each ticket before applying the service fee.
<u>Step-by-step explanation:</u>
Given that the cost of two tickets including the service fee = $59
So, the cost of one ticket including the service fee = 
Service fee on each ticket = 18%
Let the cost of 1 ticket without including the service fee = x
So, according to the data given in the question,
Hence, cost of each ticket before applying the service fee = $25
10
random words to fill up 20 character minimum for answering questions :P
Division of two quantities is expressed as the quotient of those two quantities.
The word quotient is derived from the Latin language. It is from the Latin word "quotiens" which means "how many times." A quotient is the answer to a divisional problem. A divisional problem describes how many times a number will go into another. The first time that this word was known to have been used in mathematics was around 1400 - 1500 AD in England.
There are two different ways to find the quotient of two numbers. One of them is through Fractions. The quotient of a fraction is the number obtained when the fraction is simplified. The other way to find a quotient is by employing the long division method where the quotient value is positioned above the divisor and dividend.
