konstanta x。 adalah 5
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pengurangan dan perkalian pada polinomia Perhatikan contoh soal dibawah
Diketahui 7(x) = 3x ^ 4 - 2x ^ 3 + 5x ^ 2 - 4x + 3 , g(x) = 4x ^ 3 - 6x ^ 2 + 7x - 1
tentukaniah:
a. f (x) + g(x)
b. f(x) - g(x)
c. f(x) * xg(x)
Answer (4)
5. a lw a ys 6. a lw a ys
Two lines that do not intersect are parallel.- Sometimes
When two lines are cut by a transversal, if the alternate interior angles are equal in measure, then the lines are parallel. -Always
"Two lines that do not intersect are parallel" is sometimes true. In Euclidean** geometry**, if two lines do not intersect and lie in the same plane, they are parallel. However, if the lines exist in different planes or have different inclinations, they may never meet but are not parallel.
"When two lines are cut by a transversal, if the alternate interior angles are equal in** measure**, then the lines are parallel" is always true. This statement represents the Alternate Interior Angles Theorem, a fundamental concept in geometry.
When alternate interior angles are congruent, it guarantees that the two lines are parallel. This principle holds true universally within Euclidean geometry. If the angles formed by a **transversal **cutting two lines are equal, it ensures that those lines are indeed parallel, regardless of their orientation or position in the plane. This theorem forms the basis for many geometric proofs and constructions.
For more Question on Two lines
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The first statement is sometimes true, as it depends on the planes the lines exist in. The second statement is always true due to the Alternate Interior Angles Theorem, ensuring that equal alternate interior angles confirm parallelism. Therefore, the answers are: 5. Sometimes; 6. Always.
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Jawaban:soalDiketahui 7(x) = 3x ^ 4 - 2x ^ 3 + 5x ^ 2 - 4x + 3 , g(x) = 4x ^ 3 - 6x ^ 2 + 7x - 1tentukaniah:a. f (x) + g(x)b. f(x) - g(x)c. f(x) * xg(x) Diketahui: - f(x) = 3x⁴ - 2x³ + 5x² - 4x + 3- g(x) = 4x³ - 6x² + 7x - 1 a. f(x) + g(x) - f(x) + g(x) = (3x⁴ - 2x³ + 5x² - 4x + 3) + (4x³ - 6x² + 7x - 1)- Kumpulkan suku-suku sejenis:- 3x⁴ + (-2x³ + 4x³) + (5x² - 6x²) + (-4x + 7x) + (3 - 1)- Sederhanakan:- 3x⁴ + 2x³ - x² + 3x + 2 Jadi, f(x) + g(x) = 3x⁴ + 2x³ - x² + 3x + 2 b. f(x) - g(x) - f(x) - g(x) = (3x⁴ - 2x³ + 5x² - 4x + 3) - (4x³ - 6x² + 7x - 1)- Ubah tanda semua suku di g(x):- 3x⁴ - 2x³ + 5x² - 4x + 3 - 4x³ + 6x² - 7x + 1- Kumpulkan suku-suku sejenis:- 3x⁴ + (-2x³ - 4x³) + (5x² + 6x²) + (-4x - 7x) + (3 + 1)- Sederhanakan:- 3x⁴ - 6x³ + 11x² - 11x + 4 Jadi, f(x) - g(x) = 3x⁴ - 6x³ + 11x² - 11x + 4 c. f(x) × xg(x) - Pertama, kita hitung xg(x):- xg(x) = x * (4x³ - 6x² + 7x - 1)- xg(x) = 4x⁴ - 6x³ + 7x² - x- Kemudian, kita hitung f(x) × xg(x):- f(x) × xg(x) = (3x⁴ - 2x³ + 5x² - 4x + 3) * (4x⁴ - 6x³ + 7x² - x)- Kita akan kalikan setiap suku di f(x) dengan setiap suku di xg(x):- 3x⁴ * (4x⁴ - 6x³ + 7x² - x) = 12x⁸ - 18x⁷ + 21x⁶ - 3x⁵- -2x³ * (4x⁴ - 6x³ + 7x² - x) = -8x⁷ + 12x⁶ - 14x⁵ + 2x⁴- 5x² * (4x⁴ - 6x³ + 7x² - x) = 20x⁶ - 30x⁵ + 35x⁴ - 5x³- -4x * (4x⁴ - 6x³ + 7x² - x) = -16x⁵ + 24x⁴ - 28x³ + 4x²- 3 * (4x⁴ - 6x³ + 7x² - x) = 12x⁴ - 18x³ + 21x² - 3x- Kumpulkan dan sederhanakan suku-suku sejenis:- 12x⁸ + (-18x⁷ - 8x⁷) + (21x⁶ + 12x⁶ + 20x⁶) + (-3x⁵ - 14x⁵ - 30x⁵ - 16x⁵) + (2x⁴ + 35x⁴ + 24x⁴ + 12x⁴) + (-5x³ - 28x³ - 18x³) + (4x² + 21x²) - 3x- 12x⁸ - 26x⁷ + 53x⁶ - 63x⁵ + 73x⁴ - 51x³ + 25x² - 3x Jadi, f(x) × xg(x) = 12x⁸ - 26x⁷ + 53x⁶ - 63x⁵ + 73x⁴ - 51x³ + 25x² - 3x
