The answer is 43 hope this helps:)
<h2>
Question:</h2>
Find k if (x+1) is a factor of 2x³ + kx² + 1
<h2>
Answer:</h2>
k = 1
<h2>
Step-by-step explanation:</h2>
The factor of a polynomial F(x) is another polynomial that divides evenly into F(x). For example, x + 3 is a factor of the polynomial x² - 9.
<em>This is because;</em>
i. x² - 9 can be written as (x - 3)(x + 3) which shows that both (x - 3) and (x + 3) are factors.
ii. If x = -3 is substituted into the polynomial x² - 9, the result gives zero. i.e
=> (-3)² - 9
=> (9) - 9 = 0
Therefore, if (x + a) is a factor of a polynomial, substituting x = -a into the polynomial should result to zero. This also means that, if x - a is a factor of a polynomial, substituting x = a into the polynomial should give zero.
<em><u>From the question</u></em>
Given polynomial: 2x³ + kx² + 1
Given factor: x + 1.
Since x + 1 is a factor of the polynomial, substituting x = -1 into the polynomial should give zero and from there we can calculate the value of k. i.e
2(-1)³ + k(-1)² + 1 = 0
2(-1) + k(1) + 1 = 0
-2 + k + 1 = 0
k - 1 = 0
k = 1
Therefore the value of k is 1.
Answer:
r = 50 degrees.
Step-by-step explanation:
r = 50 degrees ( vertical angles are congruent).
Answer:
a) The table of values represents the ordered pairs formed by the elements of the sequence (
) (range) and their respective indexes (
) (domain):

1 6
2 11
3 16
4 21
5 26
b) The algebraic expression for the general term of the sequence is
.
c) The 25th term in the sequence is 126.
Step-by-step explanation:
a) Make a table of values for the sequence 6, 11, 16, 21, 26, ...
The table of values represents the ordered pairs formed by the elements of the sequence (
) (range) and their respective indexes (
) (domain):

1 6
2 11
3 16
4 21
5 26
b) Based on the table of values, we notice a constant difference between two consecutive elements of the sequence, a characteristic of arithmetic series, whose form is:
(1)
Where:
- First element of the sequence.
- Arithmetic difference.
- Index.
If we know that
and
, then the algebraic expression for the general term of the sequence is:

c) If we know that
and
, then the 25th term in the sequence is:


The 25th term in the sequence is 126.
Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Geometry</u>
- Volume of a Rectangular Prism: V = lwh
<u>Calculus</u>
Derivatives
Derivative Notation
Differentiating with respect to time
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
<u>Step 1: Define</u>
<u />
<u />
<u />
<u>Step 2: Differentiate</u>
- Rewrite [VRP]:

- Differentiate [Basic Power Rule]:

<u>Step 3: Solve for Rate</u>
- Substitute:

- Multiply:

Here this tells us that our volume is decreasing (ice melting) at a rate of 360 cm³ per hour.