Find all real solutions. 3y 2 = 4 - y 4

A) y = - 3, 4, 1 B) y = - 4, - 1 C) y = 1, - 1 D) y = 3, 1 E) y = 3, - 4 A) y = - 3, 4, 1 B) y = - 4, - 1 C) y = 1, - 1 D) y = 3, 1 E) y = 3, - 4

Find all real solutions. x 4 + x 2 - 4 = 0

A) $x = \sqrt { \frac { - 1 + \sqrt { 17 } } { 2 } }$ B) $x = \sqrt { \frac { 1 - \sqrt { 13 } } { 2 } }$ C) $x = \pm \sqrt { \frac { 1 - \sqrt { 13 } } { 2 } }$ D) $x = \pm \sqrt { \frac { - 1 \pm \sqrt { 17 } } { 2 } }$ E) $x = \pm \sqrt { \frac { - 1 + \sqrt { 17 } } { 2 } }$ A) $x = \sqrt { \frac { - 1 + \sqrt { 17 } } { 2 } }$ B) $x = \sqrt { \frac { 1 - \sqrt { 13 } } { 2 } }$ C) $x = \pm \sqrt { \frac { 1 - \sqrt { 13 } } { 2 } }$ D) $x = \pm \sqrt { \frac { - 1 \pm \sqrt { 17 } } { 2 } }$ E) $x = \pm \sqrt { \frac { - 1 + \sqrt { 17 } } { 2 } }$

Exam 2: Equations and Inequalities

Find a quadratic equation with the roots of $r _ { 1 } = 1 - \sqrt { 2 } \text { and } r _ { 2 } = 1 + \sqrt { 2 }$ . Write the answer in the form $a x ^ { 2 } + b x + c = 0$ where a, b, and c are integers and $a = 1$ .

Free

(Multiple Choice)

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Question 1

Correct Answer:

Verified

C

Solve. Express your answer using interval notation. $\frac { 2 x + 1 } { 2 } - \frac { x - 4 } { 4 } < x + \frac { 1 } { 2 }$

Free

(Multiple Choice)

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Question 2

Correct Answer:

Verified

D

Solve the equation. $x ^ { 2 } + 6 x - 4 = 0$

Free

(Multiple Choice)

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Question 3

Correct Answer:

Verified

A

Find all real solutions. 3y² = 4 - y⁴

(Multiple Choice)

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Question 4

Solve the equation. $5 y ^ { 2 } - 5 y - 2 = 0$

(Multiple Choice)

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Question 5

Find all real solutions. $t ^ { \frac { 3 } { 2 } } = 125$

(Multiple Choice)

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Question 6

Solve. Express your answer using interval notation. $3 - x \leq 5$

(Multiple Choice)

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Question 7

Solve the inequality. Express your answer in interval form. $\frac { 2 - x } { 3 - 4 x } \geq 0$

(Multiple Choice)

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Question 8

Solve the equation. $81 s ^ { 2 } + 18 s + 1 = 0$

(Multiple Choice)

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Question 9

Find all real solutions. x⁴ + x² - 4 = 0

(Multiple Choice)

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Question 10

Solve. Express your answer using interval notation. $3.99 \leq \frac { x } { 3 } - 1 \leq 3.999$

(Multiple Choice)

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Question 11

A ball is thrown straight upward. Suppose that the height of the ball at time t is given by the formula h = - 18t² + 126t, where h is in feet and t is in seconds, with t = 0 corresponding to the instant that the ball is first tossed. At what time(s) does the ball reach a height of 108 ft?

(Multiple Choice)

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Question 12

Data from the Apollo 11 moon mission in July Error in evaluating expression: helpvar2 showed temperature readings on the lunar surface varying over the interval $- 185 ^ { \circ } \leq C \leq 111 ^ { \circ }$ on the Celsius scale. What is the corresponding interval on the Fahrenheit scale? (Round the numbers you obtain to the nearest integers.) Express your answer using interval notation.

(Multiple Choice)

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Question 13

Use the graph to solve the inequality. $x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12 \geq 0$ $Use the graph to solve the inequality. x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12 \geq 0$

(Multiple Choice)

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Question 14

Solve the inequality. Express your answer in interval form. $( 7 x - 1 ) ^ { 7 } ( 7 x - 3 ) ^ { 9 } ( 7 x - 6 ) > 0$

(Multiple Choice)

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Question 15

Solve the equation. $2 y ^ { 2 } - 3 y - 3 = 0$

(Multiple Choice)

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Question 16

Solve. Express your answer using interval notation. $- 7 \leq 2 x + 3 \leq 13$

(Multiple Choice)

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Question 17

Solve. Express your answer using interval notation. $\left| \frac { 2 - 5 x } { 2 } \right| > 2$

(Multiple Choice)

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Question 18

Solve. Express your answer using interval notation. $- 1 \leq x - 5 \leq 0$

(Multiple Choice)

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Question 19

Solve the inequality. Express your answer in interval form. $( x - 4 ) ( x + 2 ) ( x + 9 ) \geq 0$

(Multiple Choice)

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Question 20

Find a quadratic equation with the roots of $r _ { 1 } = 1 - \sqrt { 2 } \text { and } r _ { 2 } = 1 + \sqrt { 2 }$ . Write the answer in the form $a x ^ { 2 } + b x + c = 0$ where a, b, and c are integers and $a = 1$ .

Solve. Express your answer using interval notation. $\frac { 2 x + 1 } { 2 } - \frac { x - 4 } { 4 } < x + \frac { 1 } { 2 }$

Solve the equation. $x ^ { 2 } + 6 x - 4 = 0$

Find all real solutions. 3y² = 4 - y⁴

Solve the equation. $5 y ^ { 2 } - 5 y - 2 = 0$

Find all real solutions. $t ^ { \frac { 3 } { 2 } } = 125$

Solve. Express your answer using interval notation. $3 - x \leq 5$

Solve the inequality. Express your answer in interval form. $\frac { 2 - x } { 3 - 4 x } \geq 0$

Solve the equation. $81 s ^ { 2 } + 18 s + 1 = 0$

Find all real solutions. x⁴ + x² - 4 = 0

Solve. Express your answer using interval notation. $3.99 \leq \frac { x } { 3 } - 1 \leq 3.999$

A ball is thrown straight upward. Suppose that the height of the ball at time t is given by the formula h = - 18t² + 126t, where h is in feet and t is in seconds, with t = 0 corresponding to the instant that the ball is first tossed. At what time(s) does the ball reach a height of 108 ft?

Use the graph to solve the inequality. $x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12 \geq 0$ $Use the graph to solve the inequality. x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12 \geq 0$

Solve the inequality. Express your answer in interval form. $( 7 x - 1 ) ^ { 7 } ( 7 x - 3 ) ^ { 9 } ( 7 x - 6 ) > 0$

Solve the equation. $2 y ^ { 2 } - 3 y - 3 = 0$

Solve. Express your answer using interval notation. $- 7 \leq 2 x + 3 \leq 13$

Solve. Express your answer using interval notation. $\left| \frac { 2 - 5 x } { 2 } \right| > 2$

Solve. Express your answer using interval notation. $- 1 \leq x - 5 \leq 0$

Solve the inequality. Express your answer in interval form. $( x - 4 ) ( x + 2 ) ( x + 9 ) \geq 0$

Fundamentals

Functions

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Exam 2: Equations and Inequalities

Find a quadratic equation with the roots of r1=1−2 and r2=1+2r _ { 1 } = 1 - \sqrt { 2 } \text { and } r _ { 2 } = 1 + \sqrt { 2 }r1​=1−2​ and r2​=1+2​ . Write the answer in the form ax2+bx+c=0a x ^ { 2 } + b x + c = 0ax2+bx+c=0 where a, b, and c are integers and a=1a = 1a=1 .

Solve. Express your answer using interval notation. 2x+12−x−44<x+12\frac { 2 x + 1 } { 2 } - \frac { x - 4 } { 4 } < x + \frac { 1 } { 2 }22x+1​−4x−4​<x+21​

Solve the equation. x2+6x−4=0x ^ { 2 } + 6 x - 4 = 0x2+6x−4=0

Find all real solutions. 3y 2 = 4 - y 4

Solve the equation. 5y2−5y−2=05 y ^ { 2 } - 5 y - 2 = 05y2−5y−2=0

Find all real solutions. t32=125t ^ { \frac { 3 } { 2 } } = 125t23​=125

Solve. Express your answer using interval notation. 3−x≤53 - x \leq 53−x≤5

Solve the inequality. Express your answer in interval form. 2−x3−4x≥0\frac { 2 - x } { 3 - 4 x } \geq 03−4x2−x​≥0

Solve the equation. 81s2+18s+1=081 s ^ { 2 } + 18 s + 1 = 081s2+18s+1=0

Find all real solutions. x 4 + x 2 - 4 = 0

Solve. Express your answer using interval notation. 3.99≤x3−1≤3.9993.99 \leq \frac { x } { 3 } - 1 \leq 3.9993.99≤3x​−1≤3.999

A ball is thrown straight upward. Suppose that the height of the ball at time t is given by the formula h = - 18t 2 + 126t, where h is in feet and t is in seconds, with t = 0 corresponding to the instant that the ball is first tossed. At what time(s) does the ball reach a height of 108 ft?

Use the graph to solve the inequality. x3−3x2−4x+12≥0x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12 \geq 0x3−3x2−4x+12≥0

Solve the inequality. Express your answer in interval form. (7x−1)7(7x−3)9(7x−6)>0( 7 x - 1 ) ^ { 7 } ( 7 x - 3 ) ^ { 9 } ( 7 x - 6 ) > 0(7x−1)7(7x−3)9(7x−6)>0

Solve the equation. 2y2−3y−3=02 y ^ { 2 } - 3 y - 3 = 02y2−3y−3=0

Solve. Express your answer using interval notation. −7≤2x+3≤13- 7 \leq 2 x + 3 \leq 13−7≤2x+3≤13

Solve. Express your answer using interval notation. ∣2−5x2∣>2\left| \frac { 2 - 5 x } { 2 } \right| > 2​22−5x​​>2

Solve. Express your answer using interval notation. −1≤x−5≤0- 1 \leq x - 5 \leq 0−1≤x−5≤0

Solve the inequality. Express your answer in interval form. (x−4)(x+2)(x+9)≥0( x - 4 ) ( x + 2 ) ( x + 9 ) \geq 0(x−4)(x+2)(x+9)≥0

Fundamentals

Functions

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Find a quadratic equation with the roots of $r _ { 1 } = 1 - \sqrt { 2 } \text { and } r _ { 2 } = 1 + \sqrt { 2 }$ . Write the answer in the form $a x ^ { 2 } + b x + c = 0$ where a, b, and c are integers and $a = 1$ .

Solve. Express your answer using interval notation. $\frac { 2 x + 1 } { 2 } - \frac { x - 4 } { 4 } < x + \frac { 1 } { 2 }$

Solve the equation. $x ^ { 2 } + 6 x - 4 = 0$

Find all real solutions. 3y² = 4 - y⁴

Solve the equation. $5 y ^ { 2 } - 5 y - 2 = 0$

Find all real solutions. $t ^ { \frac { 3 } { 2 } } = 125$

Solve. Express your answer using interval notation. $3 - x \leq 5$

Solve the inequality. Express your answer in interval form. $\frac { 2 - x } { 3 - 4 x } \geq 0$

Solve the equation. $81 s ^ { 2 } + 18 s + 1 = 0$

Find all real solutions. x⁴ + x² - 4 = 0

Solve. Express your answer using interval notation. $3.99 \leq \frac { x } { 3 } - 1 \leq 3.999$

A ball is thrown straight upward. Suppose that the height of the ball at time t is given by the formula h = - 18t² + 126t, where h is in feet and t is in seconds, with t = 0 corresponding to the instant that the ball is first tossed. At what time(s) does the ball reach a height of 108 ft?

Use the graph to solve the inequality. $x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12 \geq 0$ $Use the graph to solve the inequality. x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12 \geq 0$

Solve the inequality. Express your answer in interval form. $( 7 x - 1 ) ^ { 7 } ( 7 x - 3 ) ^ { 9 } ( 7 x - 6 ) > 0$

Solve the equation. $2 y ^ { 2 } - 3 y - 3 = 0$

Solve. Express your answer using interval notation. $- 7 \leq 2 x + 3 \leq 13$

Solve. Express your answer using interval notation. $\left| \frac { 2 - 5 x } { 2 } \right| > 2$

Solve. Express your answer using interval notation. $- 1 \leq x - 5 \leq 0$

Solve the inequality. Express your answer in interval form. $( x - 4 ) ( x + 2 ) ( x + 9 ) \geq 0$