The first question is c
the second is d
Answer: 20
Explanation: The equation is 175 - 15 (160) and then divide it by 8 (20)
X = first child
x +2 = 2nd child
x+ 4 = 3rd child
It doesn't matter if the ages are odd or even - there is two years between each child in age.
The sum would be
x + x + 2 + x + 4 or 3x + 6.
Lets try it with a sample age. Let's say the youngest is 5 middle is 7 and oldest is 9
The sum of their ages is 21 (5 + 7 + 9)
Using our answer of 3x + 6 where x is the age of the youngest child, we get
3(5) +6 which is also 21.
This could also be solved by having x represent the middle age child
x-2 is the youngest (2 years less than the middle)
x = the middle
x+2 is the oldest (2 years older than the middle)
The sum of these would be x-2 + x + x +2 or simply 3x (the 2's cancel out)
Since the middle child is 7 3x would mean 3 (7)=21
You could also set this up using x for the oldest child
x= oldest
x-2= middle
x-4= youngest (The sum of this is 3x - 6)
3 (9) -6 is also 21.
Answer:
B.
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
- Terms/Coefficients
- Exponential Rule [Rewrite]:
- Exponential Rule [Root Rewrite]:
<u>Calculus</u>
Derivatives
Derivative Notation
Derivative of a constant is 0
The definition of a derivative is the slope of the tangent line
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Implicit Differentiation
Step-by-step explanation:
<u>Step 1: Define</u>
<u>Step 2: Differentiate</u>
<em>Implicit Differentiation</em>
- [Function] Rewrite [Exponential Rule - Root Rewrite]:
- [Function] Basic Power Rule:
- [Derivative] Simplify:
- [Derivative] Rewrite [Exponential Rule - Rewrite]:
- [Derivative] Isolate term [Subtraction Property of Equality]:
- [Derivative] Isolate [Multiplication Property of Equality]:
- [Derivative] Simplify:
<u>Step 3: Evaluate</u>
<em>Find slope of tangent line</em>
- Substitute in point [Derivative]:
- [Slope] Exponents:
- [Slope] Simplify:
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Differentiation - Implicit Differentiation
Book: College Calculus 10e
The answer would be 2a-7 because a negative times a negative is a postive so -(-2a) is 2a and negative times a postive is a negative so -(7) is -7