Answer: Herba has a greater balance and Nour has more debt.
Step-by-step explanation: Herba's account balance is a positive number and is clearly greater than Nour's account balance; therefore, Herba has a much greater balance. On the other hand, Nour's account balance is a negative number and is clearly less than Herba's; therefore, Hour is in more debt since he has to pay back the money that he borrowed.
Answer: 2x + h - 2
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Work Shown:
Part 1
![f(x) = x^2 - 2x + 8\\\\f(x+h) = (x+h)^2 - 2(x+h) + 8\\\\f(x+h) = (x+h)(x+h) - 2(x+h) + 8\\\\f(x+h) = x(x+h)+h(x+h) - 2(x+h) + 8\\\\f(x+h) = x^2+xh+xh+h^2 - 2x-2h + 8\\\\f(x+h) = x^2+2xh+h^2 - 2x-2h + 8\\\\](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E2%20-%202x%20%2B%208%5C%5C%5C%5Cf%28x%2Bh%29%20%3D%20%28x%2Bh%29%5E2%20-%202%28x%2Bh%29%20%2B%208%5C%5C%5C%5Cf%28x%2Bh%29%20%3D%20%28x%2Bh%29%28x%2Bh%29%20-%202%28x%2Bh%29%20%2B%208%5C%5C%5C%5Cf%28x%2Bh%29%20%3D%20x%28x%2Bh%29%2Bh%28x%2Bh%29%20-%202%28x%2Bh%29%20%2B%208%5C%5C%5C%5Cf%28x%2Bh%29%20%3D%20x%5E2%2Bxh%2Bxh%2Bh%5E2%20-%202x-2h%20%2B%208%5C%5C%5C%5Cf%28x%2Bh%29%20%3D%20x%5E2%2B2xh%2Bh%5E2%20-%202x-2h%20%2B%208%5C%5C%5C%5C)
Part 2
![\frac{f(x+h)-f(x)}{h} = \frac{(x^2+2xh+h^2 - 2x-2h + 8) - (x^2-2x+8)}{h}\\\\\frac{f(x+h)-f(x)}{h} = \frac{x^2+2xh+h^2 - 2x-2h + 8 - x^2+2x-8}{h}\\\\\frac{f(x+h)-f(x)}{h} = \frac{2xh+h^2-2h}{h}\\\\\frac{f(x+h)-f(x)}{h} = \frac{h(2x+h-2)}{h}\\\\\frac{f(x+h)-f(x)}{h} =2x+h-2\\\\](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D%20%3D%20%5Cfrac%7B%28x%5E2%2B2xh%2Bh%5E2%20-%202x-2h%20%2B%208%29%20-%20%28x%5E2-2x%2B8%29%7D%7Bh%7D%5C%5C%5C%5C%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D%20%3D%20%5Cfrac%7Bx%5E2%2B2xh%2Bh%5E2%20-%202x-2h%20%2B%208%20-%20x%5E2%2B2x-8%7D%7Bh%7D%5C%5C%5C%5C%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D%20%3D%20%5Cfrac%7B2xh%2Bh%5E2-2h%7D%7Bh%7D%5C%5C%5C%5C%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D%20%3D%20%5Cfrac%7Bh%282x%2Bh-2%29%7D%7Bh%7D%5C%5C%5C%5C%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D%20%3D2x%2Bh-2%5C%5C%5C%5C)
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In part 1, I replaced every x with x+h. Then I expanded things out using the distributive property. This is to figure out what f(x+h) is equal to.
In part 2, I then computed the difference quotient. Notice how basically all of the terms in the original f(x) cancel out. Leaving nothing but h terms behind. We factor out h to cancel it with the denominator.
First lets add the 2 distances on the map:
3 3/4 + 5 1/4 = 9 inches ( 3/4 + 1/4 = 1, 3+5 = 8, 8+1 = 9 )
1/2 inch on the map = 4 miles
there are 2 1/2 inches to 1 inch so 4 miles x 2 = 8 miles to 1 inch
so now multiply 9 inches x 8 miles = 72 total miles
First month's profit of the company = $2,400.
After the first month, the profit is modeled by the function
J(t) = 2.5t + 1,250, t is the number of months after the first month the shop opened.
Now, P(t) describes the total profit earned by the company.
So, P(t) = (Profit earned from first month) + (Profit earned from remaining 11 months of the year)
= 2400 + (2.5t + 1250)
= 2.5t + 3650
Hence, total profit earned for the year = 2.5t + 3650.