Answer: 16
Solution:
1) Use letters to identify the variables:
Number of trumpets: t
Number of clarinets: c
2) Translate each statement into algebraic (mathematical) language.
2.1) Sold a total of 27 used trumpets and clarinets
=> t + c = 27
2.2) Trumpets cost $149 and clarinets cost $99
Total cost of the trumpets: 149t
Total cost of clarinets: 99c
Total cost = 149t + 99c
2.3) Total sales were $3223
=> 149t + 99c = 3223.
3) State the system of equations:
Equation (1) t + c = 27
Equation (2) 149t + 99c = 3223
4) Solve the system of equations:
4.1) Multiply equation 1 by 149:
=> 149t + 149c = 4023
4.2) Subtract the equation (2) from the equation obtained in 4.1
=> 149c - 99c = 4023 - 3223
=> 50c = 800
=> c = 800 / 50 = 16
5) Verify the solution:
From equation (1) t = 27 - 16 = 11
Total cost = 149*11 + 99*16 = 3223
Now you have a verified answer: they sold 16 clarinets
Four different ways to solve a quadratic equation are factoring, completing the square, quadratic formula, and graphing. all methods start with setting the equation equal to zero.
to determine the zeros of a quadratic graph, find the points where the graph of the quadratic equation crosses the x-axis. to determine the vertex, you convert the quadratic form to vertex form, you use this process of completing the square. to determine the axis of symmetry, you cut the graph vertically to see the symmetrical sides.
hope this helps, God bless!
Answer: 6.8829172362
Explanation:
sin35=e/12
Multiply 12 on each side
12sin35=e
Answer:
x=54°
Step-by-step explanation:
x+36°=90°
x=90°-36°
x=54°
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<em><u>HAVE A GREAT DAY</u></em>
Answer:
The question is incomplete, the complete complete question will be:
Lucy drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Lucy drove home, there was no traffic and the trip only took 4 hours. If her average rate was 40 miles per hour faster on the trip home, how far away does Lucy live from the mountains?
Lucy live at a distance of 288 miles from the mountains.
Step-by-step explanation:
DATA:
To the mts DATA:
Time = 9 hrs
Rate = r mph
Distance = 9r miles
From the mts DATA:
time = 4 hrs
rate = r+40 mph
distance = 4(r+40) miles
SOLUTION
Distance to = Distance from
9r = 4r + 160
5r = 160
r = 32 mph
RESULT:
Distance = 9r = 9*32 = 288 miles
