Question 1

Solve the system of equations. $\left( \begin{array} { l } 
3 x - y = 8 \
6 x - 2 y = - 1
\end{array} \right)$

Accepted Answer

To solve the system of equations

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Question 2

The sum of the present ages of Eric and his father is 59 years. In 11 years, his father will be twice as old as Eric will be at that time. Find their present ages.

Accepted Answer

A)  Eric is 14 and his father is 45 years old 
B)  Eric is 16 and his father is 43 years old 
C)  Eric is 15 and his father is 44 years old 
D)  Eric is 16 and his father is 45 years old 
E)  Eric is 13 and his father is 46 years old 
A)  Eric is 14 and his father is 45 years old 
B)  Eric is 16 and his father is 43 years old 
C)  Eric is 15 and his father is 44 years old 
D)  Eric is 16 and his father is 45 years old 
E)  Eric is 13 and his father is 46 years old

Question 3

Solve the equation. $\frac { 2 x - 1 } { 4 } + \frac { 3 x + 2 } { 12 } = \frac { 5 } { 8 }$

Accepted Answer

A)  $\left\{ \frac { 17 } { 18 } \right\}$ 
B)  $\left\{ \frac { 18 } { 17 } \right\}$ 
C)  $\left\{ - \frac { 18 } { 17 } \right\}$ 
D)  $\left\{ - \frac { 17 } { 18 } \right\}$ 
E)  $\varnothing$ 
A)  $\left\{ \frac { 17 } { 18 } \right\}$ 
B)  $\left\{ \frac { 18 } { 17 } \right\}$ 
C)  $\left\{ - \frac { 18 } { 17 } \right\}$ 
D)  $\left\{ - \frac { 17 } { 18 } \right\}$ 
E)  $\varnothing$

Question 4

A person s intelligence quotient ( I ) is found by dividing mental age ( M ), as indicated by standard tests, by chronological age ( C ) and then multiplying this ratio by 100. The formula $I = \frac { 100 \mathrm { M } } { \mathrm { C } }$ can be used. If the I range of a group of 16-year-olds is given by $68 \leq I \leq 189$ , find the range of the mental age of this group. Please enter your answer in interval notation.

Accepted Answer

The answer of A person s intelligence quotient ( I...

Question 5

Multiplying both sides of an inequality by a negative number reverses the inequality symbol.

Accepted Answer

A) True 
 B)False

Question 6

Solve the inequality and express the solution set using interval notation. $17 ( x + 4 ) - 3 ( x - 8 ) < 0$

Accepted Answer

The answer of Solve the inequality and express the solution...

Question 7

Candace had scores of 96, 83, 93, and 86 on her first four exams of the semester. What score must she obtain on the fifth exam to have an average of 89.4 or better for the five exams? Please enter your answer as an inequality. Use " x " for decision variable.

Accepted Answer

The answer of Candace had scores of 96, 83, 93,...

Question 8

Solve the inequality. | x | < 8 Please enter your answer in interval notation.

Accepted Answer

The answer of Solve the inequality. | x | <...

Question 9

Perform the indicated divisions of polynomials by monomials. Match each of the expressions with the corresponding polynomial to obtain a true statement.
-$3 s ^ { 7 } - 8 s - 11$

Accepted Answer

A)  $\frac { 21 s ^ { 8 } - 56 s ^ { 2 } - 77 s } { 7 s }$ 
B)  $\frac { - 21 s ^ { 9 } + 56 s ^ { 3 } - 77 s ^ { 2 } } { - 7 s }$ 
C)  $\frac { 21 s ^ { 8 } - 56 s ^ { 2 } + 77 s } { - s }$ 
D)  $\frac { 21 s q - 56 s ^ { 2 } q ^ { 2 } - 77 s ^ { 8 } q ^ { 9 } } { - s q }$ 
E)  $\frac { - 21 s ^ { 8 } q ^ { 8 } + 56 s ^ { 9 } q ^ { 8 } - 77 s ^ { 8 } q ^ { 9 } } { 7 s q }$ 
A)  $\frac { 21 s ^ { 8 } - 56 s ^ { 2 } - 77 s } { 7 s }$ 
B)  $\frac { - 21 s ^ { 9 } + 56 s ^ { 3 } - 77 s ^ { 2 } } { - 7 s }$ 
C)  $\frac { 21 s ^ { 8 } - 56 s ^ { 2 } + 77 s } { - s }$ 
D)  $\frac { 21 s q - 56 s ^ { 2 } q ^ { 2 } - 77 s ^ { 8 } q ^ { 9 } } { - s q }$ 
E)  $\frac { - 21 s ^ { 8 } q ^ { 8 } + 56 s ^ { 9 } q ^ { 8 } - 77 s ^ { 8 } q ^ { 9 } } { 7 s q }$

Question 10

Solve the system of equations. $\left( \begin{array} { l } 
3 x - y = 6 \
6 x - 2 y = - 2
\end{array} \right)$

Accepted Answer

A)  $( 3 , - 3 )$ 
B)  $( 3,3 )$ 
C)  $( 1,3 )$ 
D)  $( 1 , - 3 )$ 
E)  no solution 
A)  $( 3 , - 3 )$ 
B)  $( 3,3 )$ 
C)  $( 1,3 )$ 
D)  $( 1 , - 3 )$ 
E)  no solution

Question 11

Solve the equation using factoring techniques. x 2 + 6 x + 5 = 0

Accepted Answer

A)  x = 1, x = 5 
B)  x = -1, x = -5 
C)  x = 1, x = -5 
A)  x = 1, x = 5 
B)  x = -1, x = -5 
C)  x = 1, x = -5

Question 12

Solve the compound inequality. Express the solution sets in interval notation. $2 x + 7  1$

Accepted Answer

A)  $( - \infty , - 4 ] \cup [ - 3 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 3 ) \cup ( - 4 , \infty )$ 
D)  $( - \infty , - 4 ) \cup ( - 3 , \infty )$ 
E)  $( - \infty , - 3 ] \cup [ - 4 , \infty )$ 
A)  $( - \infty , - 4 ] \cup [ - 3 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 3 ) \cup ( - 4 , \infty )$ 
D)  $( - \infty , - 4 ) \cup ( - 3 , \infty )$ 
E)  $( - \infty , - 3 ] \cup [ - 4 , \infty )$

Question 13

Find the quotient and remainder for the division problem. $\left( 3 x ^ { 3 } + 10 x ^ { 2 } - 5 x - 1 \right) \div \left( x ^ { 2 } + 4 x \right)$ $\text { Q :}$ __________ $\mathrm { R } :$ __________

Accepted Answer

The answer of Find the quotient and remainder for the...

Question 14

Find the indicated product. Assume the variable that appears as exponent represents positive integer. $\left( 2 x ^ { n } + 5 \right) \left( 3 x ^ { n } - 7 \right)$

Accepted Answer

The answer of Find the indicated product. Assume the variable...

Question 15

Find the quotient. $\frac { 24 x ^ { 6 } y ^ { 5 } } { - 6 x ^ { 2 } y ^ { 3 } }$

Accepted Answer

The answer of Find the quotient. \(\frac { 24 x...

Question 16

Factor the polynomial completely. Indicate if it is not factorable using integers. $( a + 1 ) ^ { 2 } - b ^ { 2 }$

Accepted Answer

The answer of Factor the polynomial completely. Indicate if it...

Question 17

Solve the inequality. $\left| \frac { x - 2 } { 5 } \right| < 6$

Accepted Answer

A)  $( - 28,2 ) \cup ( 2,32 )$ 
B)  $( - 28,32 )$ 
C)  $( - \infty , 28 ) \cup ( 32 , \infty )$ 
D)  $\phi$ 
A)  $( - 28,2 ) \cup ( 2,32 )$ 
B)  $( - 28,32 )$ 
C)  $( - \infty , 28 ) \cup ( 32 , \infty )$ 
D)  $\phi$

Question 18

Solve the inequality and express the solution set using interval notation. $x \geq 3.3 + 0.45 x$

Accepted Answer

The answer of Solve the inequality and express the solution...

Question 19

The absolute value of a negative number is a positive number.

Accepted Answer

A) True 
 B)False

Question 20

Solve the inequality. $| x - 4 | \geq 6$

Accepted Answer

A)  $-$ 10, 2 
B)  $( - \infty , - 2 ] \cup [ 10 , \infty )$ 
C)  $[ 4,6 ]$ 
D)  $\phi$ 
A)  $-$ 10, 2 
B)  $( - \infty , - 2 ] \cup [ 10 , \infty )$ 
C)  $[ 4,6 ]$ 
D)  $\phi$

Solve the system of equations. $\left( \begin{array} { l } 3 x - y = 8 \\6 x - 2 y = - 1\end{array} \right)$

The sum of the present ages of Eric and his father is 59 years. In 11 years, his father will be twice as old as Eric will be at that time. Find their present ages.

Solve the equation. $\frac { 2 x - 1 } { 4 } + \frac { 3 x + 2 } { 12 } = \frac { 5 } { 8 }$

Multiplying both sides of an inequality by a negative number reverses the inequality symbol.

Solve the inequality and express the solution set using interval notation. $17 ( x + 4 ) - 3 ( x - 8 ) < 0$

Candace had scores of 96, 83, 93, and 86 on her first four exams of the semester. What score must she obtain on the fifth exam to have an average of 89.4 or better for the five exams? Please enter your answer as an inequality. Use " x " for decision variable.

Solve the inequality. | x | < 8 Please enter your answer in interval notation.

Perform the indicated divisions of polynomials by monomials. Match each of the expressions with the corresponding polynomial to obtain a true statement. - $3 s ^ { 7 } - 8 s - 11$

Solve the system of equations. $\left( \begin{array} { l } 3 x - y = 6 \\6 x - 2 y = - 2\end{array} \right)$

Solve the equation using factoring techniques. x ² + 6 x + 5 = 0

Solve the compound inequality. Express the solution sets in interval notation. $2 x + 7 < - 1 \text { or } 2 x + 7 > 1$

Find the quotient and remainder for the division problem. $\left( 3 x ^ { 3 } + 10 x ^ { 2 } - 5 x - 1 \right) \div \left( x ^ { 2 } + 4 x \right)$ $\text { Q :}$ $\mathrm { R } :$

Find the indicated product. Assume the variable that appears as exponent represents positive integer. $\left( 2 x ^ { n } + 5 \right) \left( 3 x ^ { n } - 7 \right)$

Find the quotient. $\frac { 24 x ^ { 6 } y ^ { 5 } } { - 6 x ^ { 2 } y ^ { 3 } }$

Factor the polynomial completely. Indicate if it is not factorable using integers. $( a + 1 ) ^ { 2 } - b ^ { 2 }$

Solve the inequality. $\left| \frac { x - 2 } { 5 } \right| < 6$

Solve the inequality and express the solution set using interval notation. $x \geq 3.3 + 0.45 x$

The absolute value of a negative number is a positive number.

Solve the inequality. $| x - 4 | \geq 6$

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 8: A Transition From Elementary Algebra to Intermediate Algebra

Solve the system of equations. (3x−y=86x−2y=−1)\left( \begin{array} { l } 3 x - y = 8 \\6 x - 2 y = - 1\end{array} \right)(3x−y=86x−2y=−1​)

The sum of the present ages of Eric and his father is 59 years. In 11 years, his father will be twice as old as Eric will be at that time. Find their present ages.

Solve the equation. 2x−14+3x+212=58\frac { 2 x - 1 } { 4 } + \frac { 3 x + 2 } { 12 } = \frac { 5 } { 8 }42x−1​+123x+2​=85​

Multiplying both sides of an inequality by a negative number reverses the inequality symbol.

Solve the inequality and express the solution set using interval notation. 17(x+4)−3(x−8)<017 ( x + 4 ) - 3 ( x - 8 ) < 017(x+4)−3(x−8)<0

Candace had scores of 96, 83, 93, and 86 on her first four exams of the semester. What score must she obtain on the fifth exam to have an average of 89.4 or better for the five exams? Please enter your answer as an inequality. Use " x " for decision variable.

Solve the inequality. | x | < 8 Please enter your answer in interval notation.

Perform the indicated divisions of polynomials by monomials. Match each of the expressions with the corresponding polynomial to obtain a true statement. - 3s7−8s−113 s ^ { 7 } - 8 s - 113s7−8s−11

Solve the system of equations. (3x−y=66x−2y=−2)\left( \begin{array} { l } 3 x - y = 6 \\6 x - 2 y = - 2\end{array} \right)(3x−y=66x−2y=−2​)

Solve the equation using factoring techniques. x 2 + 6 x + 5 = 0

Solve the compound inequality. Express the solution sets in interval notation. 2x+7<−1 or 2x+7>12 x + 7 < - 1 \text { or } 2 x + 7 > 12x+7<−1 or 2x+7>1

Find the quotient and remainder for the division problem. (3x3+10x2−5x−1)÷(x2+4x)\left( 3 x ^ { 3 } + 10 x ^ { 2 } - 5 x - 1 \right) \div \left( x ^ { 2 } + 4 x \right)(3x3+10x2−5x−1)÷(x2+4x) Q :\text { Q :} Q : __________ R:\mathrm { R } :R: __________

Find the indicated product. Assume the variable that appears as exponent represents positive integer. (2xn+5)(3xn−7)\left( 2 x ^ { n } + 5 \right) \left( 3 x ^ { n } - 7 \right)(2xn+5)(3xn−7)

Find the quotient. 24x6y5−6x2y3\frac { 24 x ^ { 6 } y ^ { 5 } } { - 6 x ^ { 2 } y ^ { 3 } }−6x2y324x6y5​

Factor the polynomial completely. Indicate if it is not factorable using integers. (a+1)2−b2( a + 1 ) ^ { 2 } - b ^ { 2 }(a+1)2−b2

Solve the inequality. ∣x−25∣<6\left| \frac { x - 2 } { 5 } \right| < 6​5x−2​​<6

Solve the inequality and express the solution set using interval notation. x≥3.3+0.45xx \geq 3.3 + 0.45 xx≥3.3+0.45x

The absolute value of a negative number is a positive number.

Solve the inequality. ∣x−4∣≥6| x - 4 | \geq 6∣x−4∣≥6

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Solve the system of equations. $\left( \begin{array} { l } 3 x - y = 8 \\6 x - 2 y = - 1\end{array} \right)$

Solve the equation. $\frac { 2 x - 1 } { 4 } + \frac { 3 x + 2 } { 12 } = \frac { 5 } { 8 }$

Solve the inequality and express the solution set using interval notation. $17 ( x + 4 ) - 3 ( x - 8 ) < 0$

Perform the indicated divisions of polynomials by monomials. Match each of the expressions with the corresponding polynomial to obtain a true statement. - $3 s ^ { 7 } - 8 s - 11$

Solve the system of equations. $\left( \begin{array} { l } 3 x - y = 6 \\6 x - 2 y = - 2\end{array} \right)$

Solve the equation using factoring techniques. x ² + 6 x + 5 = 0

Solve the compound inequality. Express the solution sets in interval notation. $2 x + 7 < - 1 \text { or } 2 x + 7 > 1$

Find the quotient and remainder for the division problem. $\left( 3 x ^ { 3 } + 10 x ^ { 2 } - 5 x - 1 \right) \div \left( x ^ { 2 } + 4 x \right)$ $\text { Q :}$ $\mathrm { R } :$

Find the indicated product. Assume the variable that appears as exponent represents positive integer. $\left( 2 x ^ { n } + 5 \right) \left( 3 x ^ { n } - 7 \right)$

Find the quotient. $\frac { 24 x ^ { 6 } y ^ { 5 } } { - 6 x ^ { 2 } y ^ { 3 } }$

Factor the polynomial completely. Indicate if it is not factorable using integers. $( a + 1 ) ^ { 2 } - b ^ { 2 }$

Solve the inequality. $\left| \frac { x - 2 } { 5 } \right| < 6$

Solve the inequality and express the solution set using interval notation. $x \geq 3.3 + 0.45 x$

Solve the inequality. $| x - 4 | \geq 6$