A movie theater offers three types of tickets: child, student, and adult. Ticket sales for two movies are shown in the table.
1 answer:
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Answer:
x = 2 , y = 0 , z = 3
Step-by-step explanation:
Cramer's rule is a rule through which we can find the solution of linear equation.
we have the three linear equations as
x+2y+3z=11
2x+y+2z=10
3x+2y+z=9
AX=B
A: coefficient matrix
X= unknown vectors(x,y,z)
D = values of the linear equation (11 , 10 , 9)
now we find the determinant of the given linear equation
determinant of the matrix will be
A = = 1(1-4) - 2(2-6) + 3(4 - 3)
= 1(-3) - 2(-4) + 3(1)
= -3+8+3 = 8
also D
so the determinant is Non zero we can apply Cramer's rule
we will be replacing the first column of the coefficient matrix A with the values of D
by replacing the first column we will get the value of the variable 'x'
Dx = = 11(1-4) -2(10-18) + 3(20-9) = -33+16+33 = 16
x = =
= 2
similarly
Dy = = 1(10-18) -11(2-6) + 3(18 -30) = -8 +44 -36 = 0
y = = 0
Dz= = 1(9 - 20) -2(18 - 30) + 11(4 -3) = -11 +24 +11 = 24
z = =
so we have the solution as
x = 2 , y = 0 , z = 3
Therefore the solution for the given linear equations is (2,0,3).
Using relations in a right triangle, it is found that the length of AC is of 14 cm.
<h3>What are the relations in a right triangle?</h3>The relations in a right triangle are given as follows:
- The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
- The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
- The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
Researching this problem on the internet, we have that:
- The opposite leg to angle A is of 48 cm.
- sin(A) = 0.96.
Hence the hypotenuse is found as follows:
sin(A) = 48/h
0.96 = 48/h
h = 48/0.96
h = 50 cm.
The length of side AC is the other leg of the triangle, found using the Pythagorean Theorem, hence:
x = 14 cm.
More can be learned about relations in a right triangle at brainly.com/question/26396675
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