Organize the following polynomial expressions from least to greatest based on their degree: x 2xyz 9x3y2 18x2 5ab − 6y 4x4 3x2 −
1 answer:
The order will be IV, III, I, and II.
<h2>Polynomial</h2>Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
Given
I. x + 2xyz
II. 9x³y²
III. 18x² + 5ab - 6y
IV. 4 + 3x² - x - 4
The polynomial expressions from least to greatest are based on their degree.
<h3>How to organize?</h3>4 + 3x² - x - 4 is a biquadratic ploynolmial.
18x² + 5ab - 6y is a cubic polynomial.
x + 2xyz is a quadratic polynomial.
9x³y² is a monomial polynomial.
So the order will be IV, III, I, and II.
More about the polynomial link is given below.
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Answer:
The 1st and the 5th tables represent the same function
Step-by-step explanation:
* Lets explain how to solve the problem
- There are five tables of functions, two of them are equal
- To find the two equal function lets find their equations
- The form of the equation of a line whose endpoints are (x1 , y1) and
(x2 , y2) is
* Lets make the equation of each table
# (x1 , y1) = (4 , 8) and (x2 , y2) = (6 , 7)
∵ x1 = 4 , x2 = 6 and y1 = 8 , y2 = 7
∴
∴
- By using cross multiplication
∴ 2(y - 8) = -1(x - 4) ⇒ simplify
∴ 2y - 16 = -x + 4 ⇒ add x and 16 for two sides
∴ x + 2y = 20 ⇒ (1)
# (x1 , y1) = (4 , 5) and (x2 , y2) = (6 , 4)
∵ x1 = 4 , x2 = 6 and y1 = 5 , y2 = 4
∴
∴
- By using cross multiplication
∴ 2(y - 5) = -1(x - 4) ⇒ simplify
∴ 2y - 10 = -x + 4 ⇒ add x and 10 for two sides
∴ x + 2y = 14 ⇒ (2)
# (x1 , y1) = (2 , 8) and (x2 , y2) = (8 , 5)
∵ x1 = 2 , x2 = 8 and y1 = 8 , y2 = 5
∴
∴
- By using cross multiplication
∴ 2(y - 8) = -1(x - 2) ⇒ simplify
∴ 2y - 16 = -x + 2 ⇒ add x and 16 for two sides
∴ x + 2y = 18 ⇒ (3)
# (x1 , y1) = (2 , 10) and (x2 , y2) = (6 , 14)
∵ x1 = 2 , x2 = 6 and y1 = 10 , y2 = 14
∴
∴
- By using cross multiplication
∴ (y - 10) = (x - 2)
∴ y - 10 = x - 2 ⇒ add 2 and subtract y in the two sides
∴ -8 = x - y ⇒ switch the two sides
∴ x - y = -8 ⇒ (4)
# (x1 , y1) = (2 , 9) and (x2 , y2) = (8 , 6)
∵ x1 = 2 , x2 = 8 and y1 = 9 , y2 = 6
∴
∴
- By using cross multiplication
∴ 2(y - 9) = -1(x - 2) ⇒ simplify
∴ 2y - 18 = -x + 2 ⇒ add x and 18 for two sides
∴ x + 2y = 20 ⇒ (5)
- Equations (1) and (5) are the same
∴ The 1st and the 5th tables represent the same function