Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
2 answers:
Answer:
Valid solution: (35,5)
Time constraint: x+y≤40
Earning constraint: 25x+15y≥900
Step-by-step explanation:
x denote the number of hours Chris spends tutoring.
and y denotes the number of hours he spend referring.
It is given that:
- Chris can work a maximum of 40 hours per week.
so, the inequality that can be formed using this information is:
x+y≤40.
( Since he can't work more than 40 hours per week )
Similarly,
- His tutoring job pays $25 per hour and he also makes $15 per hour refereeing soccer matches.
He needs to make atleast $ 900 in order to cover his expenses.
So, the inequality is:
25x+15y≥900
Hence , we plot the graph of these system of inequalities to find the solution.
We see that the point:
(35,5) lies on the boundary line and hence it is a valid solution to the system of inequalities.
whereas the point (32,9) lies out of the feasible region and hence is not a valid solution.
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So firstly, multiply both sides by 4 (the reciprocal of 1/4):
Next, subtract both sides by 2 and your answer will be:
Answer:
a) 5.83 cm
b) 34.45°
Step-by-step explanation:
a) From Pythagoras theorem of right triangles, given right triangle ABC:
AB² + BC² = AC²
Therefore:
AC² = 5² + 3²
AC² = 25 + 9 = 34
AC = √34
AC = 5.83 cm
b) From triangle ACD, AC = 5.83 cm, AD = 4 cm and ∠A = 90°.
From Pythagoras theorem of right triangles, given right triangle ACD:
AD² + AC² = DC²
Therefore:
DC² = 5.83² + 4²
DC² = 34 + 16 = 50
DC = √50
DC = 7.07 cm
Let ∠ACD be x. Therefore using sine rule:
This one.
The doubly-shaded area is the solution set. The dashed line is not included.
The doubly-shaded area is the solution set. The dashed line is not included.