Answer:
9
-3x-12
9+6x-7-9x-5
(Group liked terms)
9+6x-9x-7-5
( subtract the numbers ) -7-5= -12
9+6x-9x-12
( add similar elements ) 6x-9x=-3x
9-3x-12
Step-by-step explanation:
Answer:
<u>32.97 inches</u>
Step-by-step explanation:
<u>Given</u>
- 27 in. is the length one of the legs
<u>Solving</u>
- cosine function gives the ratio of the adjacent side of the angle and the hypotenuse
- Take cos35°
- cos35° = 0.819
- cos35° = 27/z
- ⇒ 27/z = 0.819
- ⇒ z = 27/0.819
- ⇒ z = <u>32.97 inches</u>
Let the break even point in units be x,
57x = 18x + 7800
57x - 18x = 7800
39x = 7800
x = 7800/39 = 200
Thus break-even point in units is 200 units.
The break-even point in dollars is 57 x 200 = $11,400
Break-even point as a percent of capacity is 200 / 500 x 100 = 40%
c.) 57x = 18x + 7020
39x = 7020
x = 7020 / 39 = 180
Thus when fixed cost is reduced to $7020, the break-even point is $180.
78x = 18x + 7800
78x - 18x = 7800
60x = 7800
x = 130
Thus, when sellingprice is increased to $78 the break-even point in dollars is 78 x 130 = $10,140
Answer:
Step-by-step explanation:
The given function is
We want to find a function that shifts this function up by 5 units.
We let:
Then the transformed function we are looking for is
This implies that:
Hence the function we are looking for is
We can set up a system of equations.
x + y = 111
0.25x + 0.10y = 18.30
x + y = 111
Subtract 'y' to both sides:
x = -y + 111
Plug in '-y + 111' for 'x' in the 2nd equation:
0.25(-y + 111) + 0.10y = 18.30
Distribute 0.25 into the parenthesis:
-0.25y + 27.75 + 0.10y = 18.30
Combine like terms:
-0.15y + 27.75 = 18.30
Subtract 27.75 to both sides:
-0.15y = -9.45
Divide -0.15 to both sides:
y = 63
Plug this back into any of the two equations to find the 'x' value.
x + y = 111
x + 63 = 111
Subtract 63 to both sides:
x = 48
So there are 48 quarters and 63 dimes.
