Answer:
$110
Step-by-step explanation:
Let a, b, and c represent the earnings of Alan, Bob, and Charles. The problem statement tells us ...
a + b + c = 480 . . . . . . the combined total of their earnings
-a + b = 40 . . . . . . . . . . Bob earned 40 more than Alan
2a - c = 0 . . . . . . . . . . . Charles earned twice as much as Alan
Adding the first and third equations, we get ...
(a + b + c) + (2a - c) = (480) + (0)
3a + b = 480
Subtracting the second equation gives ...
(3a +b) - (-a +b) = (480) -(40)
4a = 440 . . . . . . . . simplify
a = 110 . . . . . . . . . . divide by the coefficient of a
Alan earned $110.
_____
<em>Check</em>
Bob earned $40 more, so $150. Charles earned twice as much, so $220.
The total is then $110 +150 +220 = $480 . . . . as required
Answer:
The values of x is -30 degrees and undefined
None of these values fall within the given range
Thus, no value within the given range is the solution to the equation
Step-by-step explanation:
Here, we want to find the value of x that works for the equation in the selected range
2cot^2x = -3csc x
Mathematically, from trigonometry;
cot^2x = csc^2x - 1
Substitute this above
2(csc^2x - 1)= -3csc x
let csc x = b
2(b^2-1) = -3b
2b^2 - 2 + 3b = 0
2b^2 + 3b - 2 = 0
2b^2 + 4b - b - 2 = 0
2b(b+ 2) - 1( b + 2) = 0
(2b-1)(b + 2) = 0
2b = 1
b = -2
b = 1/2 = 0.5
or b = -2
Recall;
csc x = b
x = csc^-1 b
x = csc^-1 0.5
x = undefined
Secondly;
b = -2
x = csc^-1 (-2)
x = -30 degrees
As we can see , between the points
0 ≤ x < 360
None of our answers fall in these range
Answer:
irrational
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
they start from the same place so ya, that is proportional
