First pair goes to f(x) = 20x
Next pair goes to f(x) = 10x + 20
Third pair goes to f(x) = 10x + 25
Last pair goes to f(x) = 20x + 10
<span>SALES: 5x² + 2x – 80
</span>- COST: 5x² – x + 100
= ------------------
PROFIT: 0x²+3x-180
(+3x because we subtracted a negative (-x), which is called adding, similarly taking away 100 from negative 80 is -180.)
Checking:
5x² + 2x – 80
5(500)²+2(500)-80 = 1,250,920
5x² – x + 100
5(500)² – (500) + 100= 1,249,600
Profit = 1,250,920 - 1,249,600 = 1,320
0(500)²+3(500)-180 = 1,320 YAY! {:-)
Double Checking:
5x² + 2x – 80
5(5000)²+2(5000)-80 = 125,009,920
5x² – x + 100
5(5000)² – (5000) + 100= 124,995,100
Profit = 125,009,920 - 124,995,100 = 14,820
0(5000)²+3(5000)-180 = <span>14,820</span> YAY! {:-)
Let the number of hours be $x
Initial charges by Sanford's Plus = $125
Per hour charges = $165
Total cost of Sanford's Plus company = 125 + 165x
Initial charges by Quality Moving Company = $200
Per hour charges = $145
Total cost of Quality Moving Company = 200 + 145x
If either company were hired for hours, the total cost would be the same
125 + 165x = 200 + 145x
Add -125 on both sides
125 - 125 + 165x = 200 + 145x-125
165x = 75 + 145x
Add -145 on both sides
165x - 145x = 75
20x = 75
Divide both side by 20, to find the value of x
x = 75/20
x = 3.75 hours
Total cost of Sanford's Plus company = 125 + 165x
x = 12 hrs
Total cost of Sanford's Plus company = 125 + 165(12)
Total cost of Sanford's Plus company = 125 + 1980
Total cost of Sanford's Plus company = $2105
1st serving: 2/3 * 1/2 = 2/6 or 1/3
2nd serving: 1/3 * 1/2 = 1/6
3rd serving: 1/6 * 1/2 = 1/12
4th serving: 1/12 * 1/2 = 1/24
5th serving: 1/24 * 1/2 = 1/48
1/3 + 1/6 + 1/12 + 1/24 + 1/48
1/3 * 16/16 = 16/48
1/6 * 8/8 = 8/48
1/12 * 4/4 = 4/48
1/24 * 2/2 = 2/48
1/48 * 1/1 = 1/48
16/48 + 8/48 + 4/48 + 2/48 + 1/48 = 31/48
Bobby ate 31/48 of the cake in total.
Ok since the amount in the bank account will decrease the rate of change is negative and the bank account itself is positive. And the rate of change is 145 and the constant or y - intercept is 369. As a linear equation it would look like y = -145x + 369.
