Answer:
3
Step by Step:
Subtract the tip ($6) from the total ($39)
11x=33
Then divide 33 by 11, leaving you with the value of x.
x=3
The lesson was 3 hours long.
P1=(0,0)=(x1,y1)→x1=0, y1=0
P2=(3,-2)=(x2,y2)→x2=3, y2=-2
Slope: m=(y2-y1)/(x2-x1)
m=(-2-0)/(3-0)
m=(-2)/3
m=-2/3
Point-slope equation:
y-y1=m(x-x1)
y-0=(-2/3)(x-0)
y=-(2/3)x
Answer: The equation of the line is: y=-(2/3)x
Answer:
Max Value: x = 400
General Formulas and Concepts:
<u>Algebra I</u>
- Domain is the set of x-values that can be inputted into function f(x)
<u>Calculus</u>
- Antiderivatives
- Integral Property:
- Integration Method: U-Substitution
- [Integration] Reverse Power Rule:
Step-by-step explanation:
<u>Step 1: Define</u>
<u>Step 2: Identify Variables</u>
<em>Using U-Substitution, we set variables in order to integrate.</em>
<u>Step 3: Integrate</u>
- Define:
- Substitute:
- [Integral] Int Property:
- [Integral] U-Sub:
- [Integral] Rewrite:
- [Integral - Evaluate] Reverse Power Rule:
- Simplify:
- Back-Substitute:
- Factor:
<u>Step 4: Identify Domain</u>
We know from a real number line that we cannot have imaginary numbers. Therefore, we cannot have any negatives under the square root.
Our domain for our integrated function would then have to be (-∞, 400]. Anything past 400 would give us an imaginary number.
Answer:
Step-by-step explanation:
f(x)=(x-0)(x-1)(x-2)
=x(x^2-3x+2)
or f(x)=x^3-3x^2+2x