Step-by-step explanation:
The simplest possible form of f(n) is:
f(n) = n² + bn + c
f(n) / (n + 1) has a remainder of -12, so:
n² + bn + c = (n + p) (n + 1) − 12
n² + bn + c = n² + (1 + p)n + p − 12
b = 1 + p and c = p − 12
f(n) / (n + 2) has a remainder of -24, so:
n² + bn + c = (n + q) (n + 2) − 24
n² + bn + c = n² + (2 + q)n + 2q − 24
b = 2 + q and c = 2q − 24
Setting the expressions equal:
1 + p = 2 + q and p − 12 = 2q − 24
1 = p − q and p = 2q − 12
Solving the system of equations:
1 = q − 12
q = 13
p = 14
b = 15, c = 2
Therefore, f(n) is:
f(n) = n² + 15n + 2
Using grouping:
f(n) = n² + 3n + 2 + 12n
f(n) = (n + 1) (n + 2) + 12n
f(n) / ((n + 1) (n + 2) = 1 + (12n) / ((n + 1) (n + 2))
The remainder is 12n.
Answer:
x < 7
Step-by-step explanation:
Answer:
m = undefined
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Coordinates (x, y)
- Parallel lines have the same slope but different y-intercepts
- An undefined line is a vertical line
- Slope Formula:
Step-by-step explanation:
<u>Step 1: Define</u>
Point (3, 2)
Point (3, 1)
<u>Step 2: Find slope </u><em><u>m</u></em>
Simply plug in the 2 coordinates into the slope formula to find slope <em>m</em>
- Substitute in points [Slope Formula]:
- [Fraction] Subtract:
- Simplify: m = undefined
<h2>
Conditional statement.</h2>
A mathematical statement of the form 'If A Then B' is a conditional statement.
<h3>
Explanation:</h3>
A conditional statement in geometry is an if-then statement consisting of a hypothesis and a dependent conclusion. The structure of a conditional statement is:
<em>If (......hypothesis......), then (......conclusion......)</em>
If hypothesis = A and conclusion = B, the mathematical expression for a conditional statement is: <u>A → B</u> and it is read as <u>If A then B.</u>
A conditional statement is always true unless the hypothesis is true and the conclusion is false.
A conditional statement can be written in form of its converse, inverse and contrapositive.
<u>Example of a conditional statement is</u>
A = I am 18 years old
B = I am an adult
A conditional statement is of the form (<u>A → B</u>) "If A then B"; therefore
If I am 18 years old, then I am an adult.
Answer:
In a 30 60 90 triangle, the side opposite the 60 degree angle = the hypotenuse * ((square root of 3) / 2)
side opposite 60 degree angle = 2 * (square root of 3) * ((sq root of 3) / 2)
side opposite 60 degree angle = 3.4641016151 * 0.8660254038
side opposite 60 degree angle = 3
Step-by-step explanation: