Step-by-step explanation:
LHS= sin 3x/sin x - cos 3x/cosx
Taking LCM,
<u>=</u><u>sin3xcosx- cos3xsinx</u>
sinxcosx
<u>=</u><u>sin(3x-x)</u>
sinxcosx
= <u>2sin2x</u>
2sinxcosx
=<u> </u><u>2sin2x</u><u> </u>
sin2x
=2
= RHS.
Proved.
C(x) = 200 - 7x + 0.345x^2
Domain is the set of x-values (i.e. units produced) that are feasible. This is all the positive integer values + 0, in case that you only consider that can produce whole units.
Range is the set of possible results for c(x), i.e. possible costs.
You can derive this from the fact that c(x) is a parabole and you can draw it, for which you can find the vertex of the parabola, the roots, the y-intercept, the shape (it open upwards given that the cofficient of x^2 is positive). Also limit the costs to be positive.
You can substitute some values for x to help you, for example:
x y
0 200
1 200 -7 +0.345 = 193.345
2 200 - 14 + .345 (4) = 187.38
3 200 - 21 + .345(9) = 182.105
4 200 - 28 + .345(16) = 177.52
5 200 - 35 + 0.345(25) = 173.625
6 200 - 42 + 0.345(36) = 170.42
10 200 - 70 + 0.345(100) =164.5
11 200 - 77 + 0.345(121) = 164.745
The functions does not have real roots, then the costs never decrease to 0.
The function starts at c(x) = 200, decreases until the vertex, (x =10, c=164.5) and starts to increase.
Then the range goes to 164.5 to infinity, limited to the solutcion for x = positive integers.
Answer:
Jared transfers $55 to his checking account from his savings account.
Jared spends $55 from his checking account to purchase a college Algebra textbook
Jared withdraws $55 from his checking account
Hope this helps!
Question:
A grocery store has 120 bottles of spring water in stock. The store orders bottles of spring water in cases of 24. The store wants to order enough cases of spring water so it has more than 500 bottles in stock. Which inequality best models this situation?
A. 24x + 120 > 500
B. 24x - 120 > 500
C. 24x + 500 > 120
D. 24(x+120) > 500
Answer:
Option A. 24x + 120 > 500 is the inequality that best models this situation.
Step-by-step explanation:
The Number of bottles of spring water in the stock = 120
Each case of the spring water bottles contains 24 bottles
The store wants to order enough cases of spring water so that it has over 500 bottles in stock.
So there are already 120 bottles in stock .
The store will order
24x +120 > 500
where x is the number of spring water bottle cases