Answer:
- 9 student tickets and 8 general admission tickets
Step-by-step explanation:
Let the number of student tickets is s and general admission tickets - g.
<u>Set equations and solve:</u>
<u>Double the first equation and subtract from the second to eliminate s:</u>
- 2s + 3g - 2s - 2g = 42 - 2*17
- g = 8
<u>Find s:</u>
1/4 + 2/5 = 5/20 + 8/20 = 13/20
Answer:
x=-1/85; y=-283/85; z=2/17
Step-by-step explanation:
Using an algebraic method like elimination or substitution would take a lot of steps which could lead to mistake the calculations. In this case, I decided to use the Gaussian elimination. We can express the system in matrix form as follows:
![\left[\begin{array}{ccc}2&-4&6\\9&-3&1\\5&0&9\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}14\\10\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-4%266%5C%5C9%26-3%261%5C%5C5%260%269%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D14%5C%5C10%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
To begin the calculations, we write the system in augmented matrix form and use the Gaussian elimination:
![\left[\begin{array}{ccccc}2&-4&6&|&14\\9&-3&1&|&10\\5&0&9&|&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D2%26-4%266%26%7C%2614%5C%5C9%26-3%261%26%7C%2610%5C%5C5%260%269%26%7C%261%5Cend%7Barray%7D%5Cright%5D)
By applying the Gaussian elimination, the final matrix is the following:
![\left[\begin{array}{ccccc}1&0&0&|&-1/85\\0&1&0&|&-283/85\\0&0&1&|&2/17\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%260%260%26%7C%26-1%2F85%5C%5C0%261%260%26%7C%26-283%2F85%5C%5C0%260%261%26%7C%262%2F17%5Cend%7Barray%7D%5Cright%5D)
In order to verify the results, it´s enough to substitute the calculated values in the original equations to see if the equalities are correct. Here you can see the verification for all of the equations:

As the sum of two complementary angles = a + b = 90
degree -------(1)
Difference of two complementary angles = a – b
According to question;
The difference of two complementary angles exceed the
sume (90) by 86.
So
a – b = 90 – 86 = 4 -------(2)
adding equation (1) and (2);
2a = 90 + 4 = 94
a = 94 / 2 = 47
putting a = 47 in equation (1);
47 + b = 90
b = 90 – 47 = 43
<span>
So angle a = 47 and
angle b = 43</span>
The answer is B. Parabola is a symmetrical open plane bend framed by the crossing point of a cone with a plane parallel to its side. The way of a shot affected by gravity in a perfect world takes after a bend of this shape.