Answer:
Step-by-step explanation:
The system of equations (a) is the correct one for this situation. We must now solve this system for x and y, which are the unit costs.
Multiplying the 2nd equation by (-3/2) yields -12x - 18y = -168.
Now eliminate x by combining the two equations
12x + 5 y = 116
-12x -18y = - 168
-------------------------
-13y = -52, or y = 4.
If y = 4 then 12x + 5y = 116, or
12x +5(4) = 116, or
12x + 20 = 116, or
12x = 96, or x = 8
Roller pens are $8/dozen and ball point pens are $4 per dozen.
Answer:
<em>The rate of the boat is 75.17 km/h and the rate of the stream is 17.83 km/h</em>
Step-by-step explanation:
<u>System of Equations</u>
Let's call:
B = speed (rate) of the boat in still water
S = speed (rate) of the stream
The boat travels 172 km in 3 hours when going upstream, that is when the speed of the stream subtracts its own speed. The speed is the distance divided by the time, thus:
Multiplying by 3:
3B - 3S = 172 [1]
The boat travels 372 km in 4 hours downstream when the speed of the current adds to its own:
B + S = 93
Solving for B:
B = 93 - S [2]
Substituting in [1]
3(93 - S) - 3S = 172
Operating:
279 - 3S - 3S = 172
279 - 6S = 172
Subtracting 279:
- 6S = 172 - 279
- 6S = -107
Multiplying by -1 and solving for S:
From [2]:
Subtract 28 from 49 which is 21 picked in the second hour
Answer:
The function in the form of fog(x) is written as 48 x² + 336 x + 590
Step-by-step explanation:
Given function as :
f(x) = 3 x² - 6 x + 5
g(x) = - 4 x - 13
So, The function in the form of fog(x) is written as
We, substitute the value of g(x) into f(x)
∴ fog(x) = 3 (g(x))² - 6 (g(x)) + 5
Or, fog(x) = 3 (- 4 x - 13 )² - 6 ( - 4 x - 13 ) + 5
or, fog(x) = 3 (16 x² + 169 + 104 x) + 24 x + 78 + 5
or , fog(x) = 48 x² + 507 + 312 x + 24 x + 78 + 5
or , fog(x) = 48 x² + 336 x + 590
So, The function in the form of fog(x) = 48 x² + 336 x + 590
Hence The function in the form of fog(x) is written as 48 x² + 336 x + 590 Answer
