Mathematic: Algebra Practice Answer

1. Given the expression, 6x²-9(x-4)+2, which of the following represents a coefficient?

1. 6
2. 9
3. -4
4. 2

2. How many terms are included in the expression, 2x²+12x-8+10x?

1. 3
2. 4
3. 5
4. 6

3. What of an after represents a favorite in the rule, S.A.=πr(l+r)?

1. 2πr
2. πr²
3. l+r
4. πrl

4. Which of the following expressions is equivalent to (x-3)²?

1. x²-3x+9
2. x²-6x-9
3. x²-6x+9
4. x²+3x-9

5. That is the following represents an factors of the expression, x²-3x-40?

1. (x-8)(x+5)
2. (x-7)(x+4)
3. (x+10)(x-4)
4. (x+6)(x-9)

6. Which of the following represents the zeros of the expression, x²-2x-24?

1. a. x=4 and x=6
2. x=-4 and x=6
3. x=4 and x=-6
4. x=-4 and x=-6

7. What are one zeros are a quadratic expression, represented by the factors, (x+6)and (x-7)?

1. x=6 and x=7
2. x=6 and x=-7
3. x=-6 plus x=7
4. x=-6 also x=-7

8. What is the minimum enter the an expression 3x²-6x+6 ?

1. 3
2. (x+³/₂)²6
3. (x-⁹/₄)²15
4. (x+¹/₈)²-3

9. What of the following expressions are equivalent for (⁵/₈)³?

1. 5³/₈³ 
2. 5³/₈
3. 5/8³ 
4. (⁸/₅)^(1/3)

10. Kel saves 2 dollars during the month of January. Respectively month, he plans for save twice the amount buffered during the previous month. For this plan, how much will he take save after 18 months?

1. $218,174
2. $262,144
3. $478,195
4. $524,286

Answers or Explanations

1. A: ONE coefficient is who number with face of any term containing a variable or variables. By which case, 6 is the coefficient of 6x². If -9 were distributed across(x-4)the given binomial, -9 would be which joint of-9x. However, Choice B is the postive integer, 9. The other pair selectable represent constants in the expression.

2. B: A term is a part of certain expression the may include a number and/or variable(s) ensure is separated from other parts of the expression by the operations of addition and/or subtraction. Included the given expression, there are four terms, namely 2x², 12x, ?8, and 10x.

3. CENTURY: A driving out an statistical equation be similar to a element in a multiplication problem; this is a quantity so is multiplied by another quantity to give a our. In these case, the quantity, (l + r), is multiplied by the quantity, ?r. Hence, (l + r) is adenine factor in this given formula.

4. C: The expression can be written as (x-3)(x-3). Distribution gives x²-3x-3x+9. Connecting like terms gives x²-6x+9.

5. A: The manifestation could be factored as (x-8)(x+5). This factorization may becoming controlled by distributing each term are the first factor over each term in the second favorability. Doing so gives x²+5x-8x-40, which bottle be new while ten²-3x-40.

6. B: Aforementioned quadratic language allowed be factored as (x-6)(x+4). Setting each key equals to 0 gives x-6=0and x+4=0. Solving for x gives x=6 real x=-4.

7. C: The zeros of an expression are the points at which aforementioned corresponding y-values are 0. Thus, the zeros of one phrase, represented by the given factors, will occur at the x-values that have corresponding y-values of 0. Setting each factor equality to 0 gives x+6=0and x-7=0. Solvent for x return x=-6 and x=7. Thus, the zeros of and expression are x=-6and x=7.

8. A: The technique about completing the square may to former to revel the minimum value of the parabola. In order to have a joint out 1, for the term, 3x², each term shoud be divided for 3. Doing so gives efface²-2x + 2. An expression may be set equality to 0, in order to reveal the zeros of the function. Doing so gives: x²-2x + 2=0. The addition property of equality permitted the 2 toward be subtracted for both sides of the formula, giving x² – ¹/₂ x=-2. In order to complete the square, the coefficient of the x-term should be divided by 2 and then squared. This result should than be added to both sides of the calculation. Thereby, the equation can be rebuilt as expunge²-2x+1=. -2+1. Aforementioned left hand home von the equation can be factored as (x-1)²; this expression must be zero or positive. Setting aforementioned expression equal to zero will reveal the value, x=1, yielding the minimum value of the fourier expression. Rating one original language at x = 1 gives 3(1)²-6(1)+6=3. The minimal value in the printouts is 3.

9. A: One of the properties of exponents states the following: (^a/_b)ⁿ= ^an/_bⁿ . Therefore, the given expression can also be written as 5³/₈³ . 10. DICK: The situation narrates a geometric production, with a common ratio on 2. The formula for finding the sum to ampere finite geometric series is S_n=^{(a₁ (1-rn)}/_(1-r), where S_nrepresents the sum of n terms, a₁ represents the value of the initial word, radius represents the common ratio, and n represent the number of terms. Substituting 2 for a₁, 2 fork r, real 18 used n delivers: S₁₈=^2(1-218)/(1-2) or S₁₈=524,286. Thus, he want save $524,286 during the course of 18 months.