Point M is located at (3, 7). If point M is translated 2 units to the left and 4 units down, what are the coordinates of M’?
2 answers:
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The factor of the polynomial, the area of the pool and the simplified expression are all algebraic expressions
<h3>How to simplify the expressions?</h3><u>Factor of the polynomial</u>
The polynomial is given as:
2x^3 + 6x^2 + 6x + 18
Factor out 2
2x^3 + 6x^2 + 6x + 18 = 2(x^3 + 3x^2 + 3x + 9)
Factorize
2x^3 + 6x^2 + 6x + 18 = 2(x^2(x + 3) + 3(x + 3))
Factor out x + 3
2x^3 + 6x^2 + 6x + 18 = 2(x^2 + 3)(x + 3)
Expand
2x^3 + 6x^2 + 6x + 18 = (2x^2 + 6)(x + 3)
Hence, 2x^2 + 6 is a factor of the polynomial 2x^3 + 6x^2 + 6x + 18
<u>The length of the pool</u>
The given parameters are:
Area = 2x^3 - 29x + 12
Width = x + 4
The length is calculated as:
Length = Area/Width
This gives
Length = 2x^2 - 29x + 12/x + 4
Factorize the numerator
Length = (2x^2 - 8x + 3)(x + 4)/x + 4
Cancel out x + 4
Length = 2x^2 - 8x + 3
Hence, the length of the pool is 2x^2 - 8x + 3
<u>Simplify the expression</u>
The expression is given as:
(3s^2 - 2s + 1) (s^2 - s + 2)
Evaluate the quotient
3 + (s - 5)/(s^2 - 5 + 2)
Hence, the simplified expression is 3 + (s - 5)/(s^2 - 5 + 2)
Read more about algebraic expressions at:
Answer:
Realization :
since there are 3-variable. Therefore 2ⁿ = 2³ = 8
From the attached solution, f(x,y,z) = y' + xz'
also' see the circuit diagrams of my realizations of AND-OR and NAND-NAND
Step-by-step explanation:
See attached picture for minimal 2-level AND-OR and NAND-NAND of the logic function.
f(x,y,z) = y' + xz' was designed from the function f(x,y,z) = Σm(0,1,4,5,6)
Then, minimal 2-level AND-OR was designed and after was NAND-NAND designed as well.
