Question 1

Solve the inequality.  (3x−2) (4x+9) ≥0( 3 x - 2 )  ( 4 x + 9 )  \geq 0(3x−2) (4x+9) ≥0

Accepted Answer

A)    (−∞,−2]∪[3,∞) ( - \infty , - 2 ] \cup [ 3 , \infty ) (−∞,−2]∪[3,∞)  
B)    (−∞,2) ∪(3,∞) ( - \infty , 2 )  \cup ( 3 , \infty ) (−∞,2) ∪(3,∞)  
C)    (−∞,−94]∪[23,∞) \left( - \infty , - \frac { 9 } { 4 } \right] \cup \left[ \frac { 2 } { 3 } , \infty \right) (−∞,−49​]∪[32​,∞) D) All of the above
E) A) and C)

Question 2

Solve the quadratic equation. $14 n ^ { 2 } = 36$

Accepted Answer

The answer of Solve the quadratic equation. \(14 n ^...

Question 3

Use the quadratic formula to solve the quadratic equation. 20 y 2 $-$ 181 y + 399 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

Accepted Answer

The answer of Use the quadratic formula to solve the...

Question 4

Find two numbers such that their sum is 8 and their product is 7. Please enter your answer as two numbers, separated by a comma.

Accepted Answer

1, 7

Question 5

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution.
- x=−5,x=7x = - 5 , x = 7x=−5,x=7

Accepted Answer

A)    x2−2x−35=0x ^ { 2 } - 2 x - 35 = 0x2−2x−35=0  
B)    x2−2x−63=0x ^ { 2 } - 2 x - 63 = 0x2−2x−63=0  
C)    x2−2x−8=0x ^ { 2 } - 2 x - 8 = 0x2−2x−8=0D) None of the above
E) A) and B)

Question 6

Add or subtract as indicated. ( $-$ 3 $-$ 9 i ) + (4 $-$ 6 i )

Accepted Answer

The answer of Add or subtract as indicated. ( $-$...

Question 7

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. y 2  −-−  6 y  −-−  27 = 0

Accepted Answer

A)   two real solutions
B)   one real solution with a multiplicity of two
C)   two nonreal complex solutions D) All of the above
E) A) and B) A

Question 8

Solve the quadratic equation using the method that seems most appropriate to you. $x ^ { 2 } - 4 x - 19 = 0$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the quadratic equation using the method...

Question 9

A perfect-square trinomial is the product of the square of a binomial.

Accepted Answer

A) True 
 B)False

Question 10

Use the quadratic formula to solve the quadratic equation. x 2 + 4 x $-$ 21 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

Accepted Answer

The answer of Use the quadratic formula to solve the...

Question 11

The length of a rectangular floor is 8 meter less than twice its width. If a diagonal of the rectangle is 20 meters, find the length and width of the floor.

Accepted Answer

A)   width is 11 m, length is 17 m
B)   width is 10 m, length is 15 m
C)   width is 24 m, length is 32 m
D)   width is 12 m, length is 16 m
E)   width is 14 m, length is 18 mF) B) and C)
G) A) and C)

Question 12

Use the method of completing the square to solve the quadratic equation. 3 x 2 + 5 x  −-−  1 = 0

Accepted Answer

A)    x=5+372,x=−5−372x = \frac { 5 + \sqrt { 37 } } { 2 } , x = \frac { - 5 - \sqrt { 37 } } { 2 }x=25+37c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,x=2−5−37c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    x=−5+376,x=−5−376x = \frac { - 5 + \sqrt { 37 } } { 6 } , x = \frac { - 5 - \sqrt { 37 } } { 6 }x=6−5+37c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,x=6−5−37c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    x=−5+372,x=5+372x = \frac { - 5 + \sqrt { 37 } } { 2 } , x = \frac { 5 + \sqrt { 37 } } { 2 }x=2−5+37c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,x=25+37c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​D) B) and C)
E) None of the above B

Question 13

Solve the inequality. ( x + 4 )( x $-$ 2 ) 0 Please enter your answer in interval notation.

Accepted Answer

The answer of Solve the inequality. ( x + 4...

Question 14

For this problem a and b represent the lengths of the legs of a right triangle, and c represents the length of the hypotenuse. Find c if a = 16 centimeters and b = 24 centimeters. Express the answer in simplest radical form.

Accepted Answer

The answer of For this problem a and b represent...

Question 15

Use the method of completing the square to solve the quadratic equation. x 2 + 6 x $-$ 6 = 0 Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Use the method of completing the square...

Question 16

Write $\sqrt { - 3 } \sqrt { - 81 }$ in terms of i , perform the indicated operations, and simplify.

Accepted Answer

The answer of Write \(\sqrt { - 3 } \sqrt...

Question 17

Solve each quadratic equation using the method that seems most appropriate. 2( x + 1 )  2 + 1 = 15

Accepted Answer

A)    x=1+7,x=1−7x = 1 + \sqrt { 7 } , x = 1 - \sqrt { 7 }x=1+7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​,x=1−7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    x=−1+7,x=−1−7x = - 1 + \sqrt { 7 } , x = - 1 - \sqrt { 7 }x=−1+7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​,x=−1−7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    x=1+7,x=−1+7x = 1 + \sqrt { 7 } , x = - 1 + \sqrt { 7 }x=1+7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​,x=−1+7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​D) A) and C)
E) A) and B)

Question 18

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. $x ^ { 2 } - 5 x - 50 = 0$

Accepted Answer

The answer of Use the discriminant to determine whether the...

Question 19

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution.
- x=−2,x=4x = - 2 , x = 4x=−2,x=4

Accepted Answer

A)    x2−2x−35=0x ^ { 2 } - 2 x - 35 = 0x2−2x−35=0  
B)    x2−2x−63=0x ^ { 2 } - 2 x - 63 = 0x2−2x−63=0  
C)    x2−2x−8=0x ^ { 2 } - 2 x - 8 = 0x2−2x−8=0D) B) and C)
E) A) and C)

Question 20

Find the quotient $\frac { - 2 + 16 i } { - 1 + i }$ and express the answer in the standard form of a complex number.

Accepted Answer

The answer of Find the quotient \(\frac { - 2...

Exam 11: Quadratic Equations and Inequalities

Solve the inequality. (3x−2) (4x+9) ≥0( 3 x - 2 ) ( 4 x + 9 ) \geq 0(3x−2) (4x+9) ≥0

Correct AnswerverifiedShow Answer

Solve the quadratic equation. 14n2=3614 n ^ { 2 } = 3614n2=36

Correct AnswerverifiedShow Answer

Use the quadratic formula to solve the quadratic equation. 20 y 2 −-− 181 y + 399 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

Correct AnswerverifiedShow Answer

Find two numbers such that their sum is 8 and their product is 7. Please enter your answer as two numbers, separated by a comma.

Correct Answerverified1, 7

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution. - x=−5,x=7x = - 5 , x = 7x=−5,x=7

Correct AnswerverifiedShow Answer

Add or subtract as indicated. ( −-− 3 −-− 9 i ) + (4 −-− 6 i )

Correct AnswerverifiedShow Answer

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. y 2 −-− 6 y −-− 27 = 0

Correct AnswerverifiedA

Solve the quadratic equation using the method that seems most appropriate to you. x2−4x−19=0x ^ { 2 } - 4 x - 19 = 0x2−4x−19=0 Please enter your answer as two numbers, separated by a comma.

Correct AnswerverifiedShow Answer

A perfect-square trinomial is the product of the square of a binomial.

Correct AnswerverifiedShow Answer

Use the quadratic formula to solve the quadratic equation. x 2 + 4 x −-− 21 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

Correct AnswerverifiedShow Answer

The length of a rectangular floor is 8 meter less than twice its width. If a diagonal of the rectangle is 20 meters, find the length and width of the floor.

Correct AnswerverifiedShow Answer

Use the method of completing the square to solve the quadratic equation. 3 x 2 + 5 x −-− 1 = 0

Correct AnswerverifiedB

Solve the inequality. ( x + 4 )( x −-− 2 ) 0 Please enter your answer in interval notation.

Correct AnswerverifiedShow Answer

For this problem a and b represent the lengths of the legs of a right triangle, and c represents the length of the hypotenuse. Find c if a = 16 centimeters and b = 24 centimeters. Express the answer in simplest radical form.

Correct AnswerverifiedShow Answer

Use the method of completing the square to solve the quadratic equation. x 2 + 6 x −-− 6 = 0 Please enter your answer as two numbers, separated by a comma.

Correct AnswerverifiedShow Answer

Write −3−81\sqrt { - 3 } \sqrt { - 81 }−3​−81​ in terms of i , perform the indicated operations, and simplify.

Correct AnswerverifiedShow Answer

Solve each quadratic equation using the method that seems most appropriate. 2( x + 1 ) 2 + 1 = 15

Correct AnswerverifiedShow Answer

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. x2−5x−50=0x ^ { 2 } - 5 x - 50 = 0x2−5x−50=0

Correct AnswerverifiedShow Answer

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution. - x=−2,x=4x = - 2 , x = 4x=−2,x=4

Correct AnswerverifiedShow Answer

Find the quotient −2+16i−1+i\frac { - 2 + 16 i } { - 1 + i }−1+i−2+16i​ and express the answer in the standard form of a complex number.

Correct AnswerverifiedShow Answer

Solve the inequality. $( 3 x - 2 ) ( 4 x + 9 ) \geq 0$

Correct Answer
verified

Solve the quadratic equation. $14 n ^ { 2 } = 36$

Correct Answer
verified

Use the quadratic formula to solve the quadratic equation. 20 y 2 $-$ 181 y + 399 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

Correct Answer
verified

Correct Answer
verified
1, 7

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution. - $x = - 5 , x = 7$

Correct Answer
verified

Add or subtract as indicated. ( $-$ 3 $-$ 9 i ) + (4 $-$ 6 i )

Correct Answer
verified

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. y 2 $-$ 6 y $-$ 27 = 0

Correct Answer
verified
A

Solve the quadratic equation using the method that seems most appropriate to you. $x ^ { 2 } - 4 x - 19 = 0$ Please enter your answer as two numbers, separated by a comma.

Correct Answer
verified

Correct Answer
verified

Use the quadratic formula to solve the quadratic equation. x 2 + 4 x $-$ 21 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

Correct Answer
verified

Correct Answer
verified

Use the method of completing the square to solve the quadratic equation. 3 x 2 + 5 x $-$ 1 = 0

Correct Answer
verified
B

Solve the inequality. ( x + 4 )( x $-$ 2 ) 0 Please enter your answer in interval notation.

Correct Answer
verified

Correct Answer
verified

Use the method of completing the square to solve the quadratic equation. x 2 + 6 x $-$ 6 = 0 Please enter your answer as two numbers, separated by a comma.

Correct Answer
verified

Write $\sqrt { - 3 } \sqrt { - 81 }$ in terms of i , perform the indicated operations, and simplify.

Correct Answer
verified

Solve each quadratic equation using the method that seems most appropriate. 2( x + 1 ) ² + 1 = 15

Correct Answer
verified

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. $x ^ { 2 } - 5 x - 50 = 0$

Correct Answer
verified

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution. - $x = - 2 , x = 4$

Correct Answer
verified

Find the quotient $\frac { - 2 + 16 i } { - 1 + i }$ and express the answer in the standard form of a complex number.

Correct Answer
verified