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  1. Asked: September 23, 2021In:

    Multiplying polynomials

    acedstud
    acedstud

    Multiply two at a time using the distributive property (foil). Multiply $(x^4+3x^2-1)(4x^3+x^2-x+3)=x^4(4x^3+x^2-x+3)+3x^2(4x^3+x^2-x+3)-(4x^3+x^2-x+3)$ $=4x^{4+3}+x^{4+2}-x^{4+1}+3x^4+12x^{2+3}+3x^{2+2}-3x^{2+1}+9x^2-4x^3-x^2+x-3$ $=4x^7+x^6-x^5+3x^4+12x^5+3x^4-3x^3+9x^2-4x^3-x^2+x-3$ Collect likeRead more

    Multiply two at a time using the distributive property (foil).

    Multiply (x^4+3x^2-1)(4x^3+x^2-x+3)=x^4(4x^3+x^2-x+3)+3x^2(4x^3+x^2-x+3)-(4x^3+x^2-x+3)

    =4x^{4+3}+x^{4+2}-x^{4+1}+3x^4+12x^{2+3}+3x^{2+2}-3x^{2+1}+9x^2-4x^3-x^2+x-3

    =4x^7+x^6-x^5+3x^4+12x^5+3x^4-3x^3+9x^2-4x^3-x^2+x-3

    Collect like terms; terms with the same exponent:

    =4x^7+x^6+11x^5+6x^4-7x^3+8x^2+x-3

    Now, multiply (4x^7+x^6+11x^5+6x^4-7x^3+8x^2+x-3)(x^6-2)

    =x^6(4x^7+x^6+11x^5+6x^4-7x^3+8x^2+x-3)-2(4x^7+x^6+11x^5+6x^4-7x^3+8x^2+x-3)

    =4x^{6+7}+x^{6+6}+11x^{6+5}+6x^{6+4}-7x^{6+3}+8x^{6+2}+x^{6+1}-3x^6-8x^7-2x^6-22x^5-12x^4+14x^3-16x^2-2x+6

    =4x^{13}+x^{12}+11x^{11}+6x^{10}-7x^{9}+8x^{8}+x^{7}-3x^6-8x^7-2x^6-22x^5-12x^4+14x^3-16x^2-2x+6

    Collect like terms; terms with the same exponent

    4x^{13}+x^{12}+11x^{11}+6x^{10}-7x^{9}+8x^{8}-7x^{7}-5x^6-22x^5-12x^4+14x^3-16x^2-2x+6

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  2. Asked: April 22, 2021In:

    Evaluate the following combinations

    acedstud
    acedstud

    The combination of n objects taking r at a time is given by C(n, r) = $\dfrac{n!}{r!(n-r)!}$. Thus, $C(4, 2)=\dfrac{4!}{2!(4-2)!}=\dfrac{4!}{2!2!}=\dfrac{4\times3\times2\times1}{2\times1\times2\times1}$ $=3\times2=6$ Therefore, 2C(4, 2) - 10 = 2(6) - 10 = 12 - 10 = 2.

    The combination of n objects taking r at a time is given by C(n, r) = \dfrac{n!}{r!(n-r)!}.

    Thus, C(4, 2)=\dfrac{4!}{2!(4-2)!}=\dfrac{4!}{2!2!}=\dfrac{4\times3\times2\times1}{2\times1\times2\times1}

    =3\times2=6

    Therefore, 2C(4, 2) – 10 = 2(6) – 10 = 12 – 10 = 2.

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  3. Asked: April 17, 2021In: ,

    multiple choice ( geometry )

    acedstud
    acedstud

    A square pyramid has a square base and 4 triangular faces which meet at a point, called the vertex. Therefore, a square pyramid has a total of 5 faces.

    A square pyramid has a square base and 4 triangular faces which meet at a point, called the vertex.

    Therefore, a square pyramid has a total of 5 faces.

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  4. Asked: April 21, 2021In: ,

    Probability and Statistics

    acedstud
    acedstud

    First, let us confirm that all the class' scores were covered by making sure that the sum of all probabilities is 1. Thus, $\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}=\dfrac{3}{6}+\dfrac{2}{6}+\dfrac{1}{6}=\dfrac{6}{6}=1$. Thus, the scores of the entire class are represented. The LCD of the denominatorsRead more

    First, let us confirm that all the class’ scores were covered by making sure that the sum of all probabilities is 1.

    Thus, \dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}=\dfrac{3}{6}+\dfrac{2}{6}+\dfrac{1}{6}=\dfrac{6}{6}=1.

    Thus, the scores of the entire class are represented.

    The LCD of the denominators is 6x, so let the total number of students in the class be 6x, then 3x students scored 90, 2x students scored 87, and x students scored 89.

    Thus, the average grade of the entire class is given by \dfrac{90(3x)+87(2x)+89x}{6x}=\dfrac{270x+174x+89x}{6x}=\dfrac{533x}{6x}\approx88.83.

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  5. Asked: April 21, 2021In:

    How can you identify if the sequence is arithmetic or geometric

    acedstud
    acedstud
    This answer was edited.

    A sequence is an arithmetic sequence if each term is obtained by the addition or subtraction of a constant from the preceding term. A sequence is a geometric sequence if each term is obtained by the multiplication or division of a constant from the preceding term.

    A sequence is an arithmetic sequence if each term is obtained by the addition or subtraction of a constant from the preceding term.

    A sequence is a geometric sequence if each term is obtained by the multiplication or division of a constant from the preceding term.

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  6. Asked: April 21, 2021In: ,

    Algebraic Expression

    acedstud
    acedstud

    An algebraic expression is a mathematics statement where variables and constants are combined using the arithmetic operations of addition, subtraction, multiplication, and division.

    An algebraic expression is a mathematics statement where variables and constants are combined using the arithmetic operations of addition, subtraction, multiplication, and division.

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  7. Asked: April 21, 2021In: ,

    Mathematics Problem (Permutation)

    acedstud
    acedstud

    Any of the 8 swimmers can take the 1st prize. After the first price, there are 7 swimmers left, and any of the 7 swimmers can take the second prize. Similarly, after the second price, there are 6 swimmers left, and any of the 6 swimmers can take the third prize. Therefore, the number of possible outRead more

    Any of the 8 swimmers can take the 1st prize.

    After the first price, there are 7 swimmers left, and any of the 7 swimmers can take the second prize.

    Similarly, after the second price, there are 6 swimmers left, and any of the 6 swimmers can take the third prize.

    Therefore, the number of possible outcomes is 8\times7\times6=336.

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  8. Asked: April 17, 2021In:

    what type of algebraic equation is 2x+5?

    acedstud
    acedstud

    An algebraic expression that has 1 as the highest power of the exponent is called a linear expression. $2x+5$ has 1 as the highest power of the variable, $x$, thus it is a linear equation.

    An algebraic expression that has 1 as the highest power of the exponent is called a linear expression.

    2x+5 has 1 as the highest power of the variable, x, thus it is a linear equation.

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  9. Asked: April 17, 2021In: ,

    Mathematical question

    acedstud
    acedstud

    An algebraic term that contains three terms is called a trinomial.

    An algebraic term that contains three terms is called a trinomial.

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  10. Asked: April 18, 2021In: ,

    Probability of drawing in a deck of cards

    acedstud
    acedstud

    When two cards are picked from a deck of cards, there are two cases, namely, with replacement and without replacement. Case 1: With replacement There are 4 aces, 4 kings, and a total of 52 cards in a standard deck of card. The probability of picking an ace is $\dfrac{4}{52}=\dfrac{1}{13}$ and the prRead more

    When two cards are picked from a deck of cards, there are two cases, namely, with replacement and without replacement.

    Case 1: With replacement

    There are 4 aces, 4 kings, and a total of 52 cards in a standard deck of card.

    The probability of picking an ace is \dfrac{4}{52}=\dfrac{1}{13} and the probability of picking a king is \dfrac{4}{52}=\dfrac{1}{13}.

    Thus, the probability of picking an ace AND a king is \dfrac{1}{13}\times\dfrac{1}{13}=\dfrac{1}{169}.

     

    Case 1: Without replacement

    There are 4 aces, 4 kings, and a total of 52 cards for the first pick and a total of 51 cards for the second pick in a standard deck of card.

    The probability of picking an ace first is \dfrac{4}{52}=\dfrac{1}{13} and the probability of picking a king next is \dfrac{4}{51}.

    Thus, the probability of picking an ace AND a king is \dfrac{1}{13}\times\dfrac{4}{51}=\dfrac{4}{663}.

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