Exam 2: Equations and Inequalities

Solve the problem. -A computer company uses the linear model $y = - 45 x + 34,030$ to predict the decline in sales of a computer after it has been on the market more than one year. If $\mathrm { x }$ is the number of months after the first year and $y$ is the number of computers sold during that month, how many computers will be sold 2 months after the first year?

(Multiple Choice)

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Question 481

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $3 , - 9$

(Multiple Choice)

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Question 482

Solve the rational inequality. Write the solution set in interval notation. - $\frac { - 3 } { - 7 x - 5 } > 0$

(Multiple Choice)

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Question 483

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 4 ] { x ^ { 2 } - 13 } = 1$

(Multiple Choice)

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Question 484

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 2 x + 5 } - \sqrt { x - 2 } = 3$

(Multiple Choice)

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Question 485

Solve the equation. - $\frac { x - 6 } { 5 } = \frac { x + 3 } { 7 }$

(Multiple Choice)

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Question 486

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { 4 x ^ { 2 } - 7 x - 3 } = \sqrt [ 3 ] { 4 x ^ { 2 } + 10 x - 1 }$

(Multiple Choice)

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Question 487

Decide what values of the variable cannot possibly be solutions for the equation. - $( x + 10 ) ^ { 2 / 5 } = ( 49 x ) ^ { 1 / 5 }$

(Multiple Choice)

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Question 488

Decide what values of the variable cannot possibly be solutions for the equation. - $( 2 x + 3 ) ^ { 1 / 2 } + ( 4 - x ) ^ { 1 / 2 } = 4$

(Multiple Choice)

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Question 489

Solve the inequality. Write the solution set in interval notation. - $| 2 - 3 x | \leq 11$

(Multiple Choice)

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Question 490

Solve the problem. -A square lawn has an area of 882 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle?

(Multiple Choice)

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Question 491

Solve the equation by the zero-factor property. - $4 x ^ { 2 } - 3 x - 7 = 0$

(Multiple Choice)

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Question 492

Solve and graph the inequality. Give answer in interval notation. - $- 6 ( 2 x - 2 ) < - 18 x - 18$

(Multiple Choice)

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Question 493

Solve the problem. -A rock falls from a tower that is 464 feet high. As it is falling, its height is given by the formula $h = 464 - 16 t ^ { 2 }$ How many seconds (in tenths) will it take for the rock to hit the ground (h = 0)?

(Multiple Choice)

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Question 494

Solve the inequality. Write the solution set in interval notation. - $\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| > 0$

(Multiple Choice)

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Question 495

Write the number as the product of a real number and i. - $\sqrt { - 13 }$

(Multiple Choice)

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Question 496

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $3 , - 9$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { - 3 } { - 7 x - 5 } > 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 4 ] { x ^ { 2 } - 13 } = 1$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 2 x + 5 } - \sqrt { x - 2 } = 3$

Solve the equation. - $\frac { x - 6 } { 5 } = \frac { x + 3 } { 7 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { 4 x ^ { 2 } - 7 x - 3 } = \sqrt [ 3 ] { 4 x ^ { 2 } + 10 x - 1 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $( x + 10 ) ^ { 2 / 5 } = ( 49 x ) ^ { 1 / 5 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $( 2 x + 3 ) ^ { 1 / 2 } + ( 4 - x ) ^ { 1 / 2 } = 4$

Solve the inequality. Write the solution set in interval notation. - $| 2 - 3 x | \leq 11$

Solve the problem. -A square lawn has an area of 882 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle?

Solve the equation by the zero-factor property. - $4 x ^ { 2 } - 3 x - 7 = 0$

Solve and graph the inequality. Give answer in interval notation. - $- 6 ( 2 x - 2 ) < - 18 x - 18$

Solve the problem. -A rock falls from a tower that is 464 feet high. As it is falling, its height is given by the formula $h = 464 - 16 t ^ { 2 }$ How many seconds (in tenths) will it take for the rock to hit the ground (h = 0)?

Solve the inequality. Write the solution set in interval notation. - $\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| > 0$

Write the number as the product of a real number and i. - $\sqrt { - 13 }$

Review of Basic Concepts

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 2: Equations and Inequalities

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - 3,−93 , - 93,−9

Solve the rational inequality. Write the solution set in interval notation. - −3−7x−5>0\frac { - 3 } { - 7 x - 5 } > 0−7x−5−3​>0

Decide what values of the variable cannot possibly be solutions for the equation. - x2−134=1\sqrt [ 4 ] { x ^ { 2 } - 13 } = 14x2−13​=1

Decide what values of the variable cannot possibly be solutions for the equation. - 2x+5−x−2=3\sqrt { 2 x + 5 } - \sqrt { x - 2 } = 32x+5​−x−2​=3

Solve the equation. - x−65=x+37\frac { x - 6 } { 5 } = \frac { x + 3 } { 7 }5x−6​=7x+3​

Decide what values of the variable cannot possibly be solutions for the equation. - 4x2−7x−33=4x2+10x−13\sqrt [ 3 ] { 4 x ^ { 2 } - 7 x - 3 } = \sqrt [ 3 ] { 4 x ^ { 2 } + 10 x - 1 }34x2−7x−3​=34x2+10x−1​

Decide what values of the variable cannot possibly be solutions for the equation. - (x+10)2/5=(49x)1/5( x + 10 ) ^ { 2 / 5 } = ( 49 x ) ^ { 1 / 5 }(x+10)2/5=(49x)1/5

Decide what values of the variable cannot possibly be solutions for the equation. - (2x+3)1/2+(4−x)1/2=4( 2 x + 3 ) ^ { 1 / 2 } + ( 4 - x ) ^ { 1 / 2 } = 4(2x+3)1/2+(4−x)1/2=4

Solve the inequality. Write the solution set in interval notation. - ∣2−3x∣≤11| 2 - 3 x | \leq 11∣2−3x∣≤11

Solve the problem. -A square lawn has an area of 882 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle?

Solve the equation by the zero-factor property. - 4x2−3x−7=04 x ^ { 2 } - 3 x - 7 = 04x2−3x−7=0

Solve and graph the inequality. Give answer in interval notation. - −6(2x−2)<−18x−18- 6 ( 2 x - 2 ) < - 18 x - 18−6(2x−2)<−18x−18

Solve the problem. -A rock falls from a tower that is 464 feet high. As it is falling, its height is given by the formula h=464−16t2h = 464 - 16 t ^ { 2 }h=464−16t2 How many seconds (in tenths) will it take for the rock to hit the ground (h = 0)?

Solve the inequality. Write the solution set in interval notation. - ∣x4+6x2+9∣>0\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| > 0​x4+6x2+9​>0

Write the number as the product of a real number and i. - −13\sqrt { - 13 }−13​

Review of Basic Concepts

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $3 , - 9$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { - 3 } { - 7 x - 5 } > 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 4 ] { x ^ { 2 } - 13 } = 1$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 2 x + 5 } - \sqrt { x - 2 } = 3$

Solve the equation. - $\frac { x - 6 } { 5 } = \frac { x + 3 } { 7 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { 4 x ^ { 2 } - 7 x - 3 } = \sqrt [ 3 ] { 4 x ^ { 2 } + 10 x - 1 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $( x + 10 ) ^ { 2 / 5 } = ( 49 x ) ^ { 1 / 5 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $( 2 x + 3 ) ^ { 1 / 2 } + ( 4 - x ) ^ { 1 / 2 } = 4$

Solve the inequality. Write the solution set in interval notation. - $| 2 - 3 x | \leq 11$

Solve the equation by the zero-factor property. - $4 x ^ { 2 } - 3 x - 7 = 0$

Solve and graph the inequality. Give answer in interval notation. - $- 6 ( 2 x - 2 ) < - 18 x - 18$

Solve the problem. -A rock falls from a tower that is 464 feet high. As it is falling, its height is given by the formula $h = 464 - 16 t ^ { 2 }$ How many seconds (in tenths) will it take for the rock to hit the ground (h = 0)?

Solve the inequality. Write the solution set in interval notation. - $\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| > 0$

Write the number as the product of a real number and i. - $\sqrt { - 13 }$