Math 1021 1.1-1.8 RA questions

Which of the following is a rational​ equation? a) 0.7x-3=0.09(x-5) b) 1/2x-1/3=4-x c) 6/x-1=4/x-12 d) 4-2(x-1)=x+3

c) 6/x-1=4/x-12

Which of the following statements best defines the term​ "extraneous solution"? a) An extraneous solution is an irrational solution to an algebraic equation. b) An extraneous solution is an approximate solution to an algebraic equation. c) An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation. d) An extraneous solution is a solution to a linear equation that contains fractions.

c) An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation.

Which of the following is not a property of​ inequalities? a) For c<0, if a<B, a/c>b/c b) For c<0, if a<b, ac>bc c) For c<0, if a<b, a-c>b-c d) For c>0, if a<b, ac<bc

c) For c<0, if a<b, a-c>b-c

If u is an algebraic expression and c is a real number such that c>0, then the inequality |u|<c is equivalent to... a) -c<u<c b) u<-c or u>c c) -c>u>c d) u<-c and u<c

a) -c<u<c

Which of the following statements is true about linear equations of the form ax+b=0? a) The constants a and b must be real numbers with the constant a never equal to zero. b)The constants a and b can never be fractions. c)The constants a and b can never be decimals. d)The constants a and b must be real numbers with the constant a always positive.

a) The constants a and b must be real numbers with the constant a never equal to zero.

Which of the following statements is​ true? a) Every linear equation is also a quadratic equation. b) All linear equations and all quadratic equations are polynomial equations. c) A polynomial equation is either a linear equation or a quadratic equation. d) Every quadratic equation is also a linear equation.

b) All linear equations and all quadratic equations are polynomial equations.

Which of the following is not a valid strategy when solving a polynomial equation of the form ax^3+bx^2=cx? a) Subtract cx from both sides. b) Divide the equation by x. c) Set the equation equal to zero and factor out an x. d) Subtract ax^3 and bx^2 from both sides.

b) Divide the equation by x.

Which of the following statements is true about rational​ equations? a) When solving a rational​ equation, it is never a good idea to multiply both sides of the equation by the least common denominator. b) It is important to check the solutions to a rational equation because it is possible to encounter extraneous solutions. c) Rational equations always have no solution. d) A rational equation can never lead to a linear equation.

b) It is important to check the solutions to a rational equation because it is possible to encounter extraneous solutions.

Suppose that you are solving a quadratic equation and realize that the discriminant is equal to 7. Which of the following statements best describes the solutions to this quadratic​ equation? a)There must be two nonreal solutions. b) There must be two real solutions. c) There must be exactly one real solution. d) There will be no solutions to this quadratic equation.

b) There must be two real solutions.

If u is an algebraic expression and c is a real number such that c>0, then the inequality |u|>c is equivalent to... a) u<-c or u<c b) u<-c or u>c c)u>-c or u>c d) -c<u<c

b) u<-c or u>c

Which of the following equations is not a disguised quadratic​ equation? a) 2x^4-11x^2+12=0 b)x^5-x^3-6=0 c)x^2/3-9x^1/3+8=0 d)3x^-2-5x^-1-2=0

b)x^5-x^3-6=0

Are you gonna dab on dem haters and get straight hundreds?????

DAB DAB DAB

Which of the following best describes the zero product​ property? a) If two nonzero factors are multiplied​ together, then the product must also be nonzero. b) The product of zero and another factor is always zero. c) If two factors multiplied together are equal to​ zero, then at least one of the factors must be zero. d) If the product of two factors is equal to​ zero, then both factors must be equal to zero.

c) If two factors multiplied together are equal to​ zero, then at least one of the factors must be zero.

Which of the following statements describes the absolute value of a number a​? a) The positive value of a negative number a can be represented by the absolute value of a number a. b) Given |a|​, a is always positive. c) The distance from the number a to 0 on a number line can be represented by the absolute value of a number a. d) The opposite value of a number a can be represented by the absolute value of a number a.

c) The distance from the number a to 0 on a number line can be represented by the absolute value of a number a.

Which of the following statements is not true concerning the equation x^2-c=0 for c>0? a) A quadratic equation in this form can always be solved by factoring. b) A quadratic equation in this form can always be solved using the square root property. c) This equation is not considered to be a quadratic equation because it is not of the form ax^2+bx+c=0 d) The​ left-hand side of this equation is called a difference of two squares.

c) This equation is not considered to be a quadratic equation because it is not of the form ax^2+bx+c=0

Which of the following is typically not one of the three ways to describe the solutions to a linear​ inequality? a) Write the solution in​ set-builder notation. b) Write the solution in interval notation. c) Write the solution in inequality form. d) Graph the solution on a number line.

c) Write the solution in inequality form.

Which of the following statements is​ true? a) The solution to an absolute value equation is always positive. b) The solution to an absolute value equation must always be greater than or equal to zero. c) Every absolute value equation has two solutions. d) It is possible for an absolute value equation to have no solution.

d) It is possible for an absolute value equation to have no solution.

If u is an algebraic expression and c is a real number such that c>0​, then the equation |u|=c is equivalent to... a) -c<u<c b) -u=c c) u=-c d) u=-c or u=c

d) u=-c or u=c