Suppose that α and β belong to GF(81)*, with |α| = 5 and |β| = 16.Show that αβ is a generator of GF(81)*.

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A: According to Fidelity Investment Vision Magazine, the average weekly allowance of children varies di...

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Q: Construct a field of order 27.

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Q: Solve the following inequality graphically in two-dimensional plane: x + y < 5

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Q: Draw v = [ 4/1 ] and w = [ -2/2 ] and v+w and v-w in a single xy plane.

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Q: Solve the following system of inequality graphically: x + y ≥ 4, 2x – y < 0

A: We will make table for the auxiliary equations of the inequalities  x+y=4 x 0 4 y 4 0   2x-y...

Q: Define Universal set in algebra. State example.

A: Universal set is the set of all elements under consideration in a given discussion. In other words, ...

Q: How do you factor out x^4+18x+81

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Q: The sum of two consectutive even integers is 106. What are the integers?

A: Let the first even integer be 2x Second consecutive even integer is 2x+2

Q: Let A = {1, 2, 3,...,14}. Define a relation R from A to A by R = {(x, y) : 3x – y = 0, where x, y ∈ ...

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Q: The second angle of a triangle is 3 times as large as the first angle. The third angle is 30 degrees...

A: Let, measure of first angle of triangle is x. Then

Q: For Exercise, write the domain of the function in interval notation. 2х — 3 r(х) 4x + 3x

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Q: Fred is 4 years older than Barney. Five years ago the sum of their ages was 48. How old are they now...

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Q: For Exercise, solve the system. -2r + 3y = 10 5x² + 2y² = 13

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Q: For Exercise, simplify the expression and state the restrictions on the variable. Зр — Зт хт — хр + ...

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Q: Ann and Kate have 80 dollars together. If Kate buys ice-cream for 5 dollars, then  Kate will have do...

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Q: Let f (x) be a nonconstant element in Z[x]. Prove that k f (x)l is notmaximal in Z[x].

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Q: use a formula to solve this problem How far would a car go in 4h at an average speed of 55mi/h?

A: The average speed of a car is 55mi/h.   

Q: For the given function, find each of the components. You will upload a picture of your work (not jus...

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Q: The total cost for tuition plus room and board at State University is S2,584.Tuition costs S704 more...

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Q: Find the length and width of a rectangle whose perimeter is equal to 160 cm and its length is equal ...

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Q: Given: 5x -3(2x-7) > 3x – 1 < 7 + 4x; then x can take which of the following values? a) 6 b) 9...

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Q: Solve y < 2 graphically.

A: To solve the inequality y<2 graphically, first plot the line y=2 by finding some points on the li...

Q: When 18 is subtracted from six times a certain number, the result is − 42.What is the number?

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Q: Find a2, a3, a4, a1= -3,  an= 10+2an-1

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Q: For what values of k the equation           -x2 + 2kx - 4 = 0 has one real solution?

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Q: determine all eigenvalues and corresponding eigenvectors of the given matrix.

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Q: What should be added to 5(2x-y) to obtain 4(2x – 3y) + 5(x + 4y)?

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Q: If 4x + i(3x – y) = 3 + i (– 6), where x and y are real numbers, then findthe values of x and y.

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Q: 15. Graph. x-3 if x 2

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Q: The sum of three consecutive integers is 93. What are the integers?

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Q: How many elements of the cyclic group GF(81)* are generators?

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Q: Expand the following expression:  (2x – 3)6

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Q: An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second...

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Q: Solve the following system of inequality graphically: 4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0

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Q: The sum of two consecutive even integers is 106. What are the integers?

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Q: SimplifY ( (46 ) 2 )4 A 42.4 63.2.4 B463.2.4 C. C 463+2+4 D 4+2+4 63+2+4

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Q: Explain what is a finite set. Give relevant example along with.

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Q: Suppose that f (x) and g(x) are irreducible over F and that deg f (x)and deg g(x) are relatively pri...

A: We have to show that g(x) is irreducible over F(a).

Q: Bamboo plants grow rapidly. A bamboo plant is 130 inches tall. Tomorrow it will be 143 inches tall, ...

A: It is given that, the height of the bamboo tree at first day is 130 inches. Let it be “a”. It is giv...

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.