They bought 8 orchestra seats and 6 mezzanine seats.
Step-by-step explanation:
Cost of one orchestra seat = $42
Cost of one mezzanine seat = $25
No. of people = 14
Amount spent = $486
Let,
x be the number of orchestra seats
y be the number of mezzanine seats
According to given statement;
x+y=14 Eqn 1
42x+25y=486 Eqn 2
Multiplying Eqn 1 by 25;

Subtracting Eqn 3 from Eqn 2 to eliminate y;

Dividing both sides by 17

Putting x=8 in Eqn 1

They bought 8 orchestra seats and 6 mezzanine seats.
Keywords: linear equation, elimination method
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To make that graph you follow these steps.
1) Set the cartesian coordinate system:
- vertical axis: y
- horizontal axis: x
- positive x-semi axis: to the right
- negative x-semi axis: to the left
- positive y-semi axis: upward
- negative y semi axis: dwonward
2) solve the inequality for y:
given: -2x + 5y > 15
transpose-2x: 5y > 15 + 2x
divide by 5: y > 3 + (2/5)x
3) Graph-
draw the line y = 3 + (2/5)x, using a dotted line (i.e. - - - - - -)
- remember that 3 is the y intercept, and 2/5 is the slope
- the line is dotted because
the solution does not include the points in the line.
- the solution is the
region above and to the left of the dotted line.
4) See the
figure attached for better visualization: the pink region is the solution of the inequality.
Answer:
Answer d)
,
, and 
Step-by-step explanation:
Notice that there are basically two right angle triangles to examine: a smaller one in size on the right and a larger one on the left, and both share side "b".
So we proceed to find the value of "b" by noticing that it the side "opposite side to angle 60 degrees" in the triangle of the right (the one with hypotenuse = 10). So we can use the sine function to find its value:

where we use the fact that the sine of 60 degrees can be written as: 
We can also find the value of "d" in that same small triangle, using the cosine function of 60 degrees:

In order to find the value of side "a", we use the right angle triangle on the left, noticing that "a" s the hypotenuse of that triangle, and our (now known) side "b" is the opposite to the 30 degree angle. We use here the definition of sine of an angle as the quotient between the opposite side and the hypotenuse:

where we used the value of the sine function of 30 degrees as one half: 
Finally, we can find the value of the fourth unknown: "c", by using the cos of 30 degrees and the now known value of the hypotenuse in that left triangle:

Therefore, our answer agrees with the values shown in option d)