Exam 2: Equations and Inequalities

Decide what values of the variable cannot possibly be solutions for the equation. -A water tank can be filled in 6 minutes and emptied in 8 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?

(Multiple Choice)

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Question 121

Solve for y. -Sophia borrowed $13,671 at 6% simple interest for 3 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 3 months? Round answers to the nearest cent if Necessary.

(Multiple Choice)

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Question 122

Solve the problem. -A bookcase is to be constructed as shown in the figure below. The height of the bookcase is 2 feet longer than the length of a shelf. If 22 feet of lumber is available for the entire unit (including the shelves, but NOT the back Of the bookcase), find the length and height of the unit.

(Multiple Choice)

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Question 123

Solve the equation by completing the square. - $2 x ^ { 2 } + 7 x + 3 = 0$

(Multiple Choice)

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Question 124

The cost of producing $t$ units is $C = 3 t ^ { 2 } + 9 t$ , and the revenue generated from sales is $R = 4 t ^ { 2 } + t$ . Determine the number of units to be sold in order to generate a profit.

(Multiple Choice)

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Question 125

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { x + 3 } = 8$

(Multiple Choice)

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Question 126

The outside of a picture frame has a length which is 3 cm more than width. The area enclosed by the outside of the picture frame is 154 square cm. Find the width of the outside of the picture frame.

(Multiple Choice)

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Question 127

Simplify the power of i. -¡56

(Multiple Choice)

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Question 128

Write the number as the product of a real number and i. - $\sqrt { - 49 }$

(Multiple Choice)

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Question 129

The area of a square is numerically 4 less than the perimeter. Find the length of the side, if the side is greater than 1.

(Multiple Choice)

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Question 130

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $t ^ { 2 } + 2 t + 1 = 0$

(Multiple Choice)

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Question 131

Solve the inequality. Write the solution set in interval notation. - $( x + 6 ) ( x + 1 ) ( x - 9 ) < 0$

(Multiple Choice)

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Question 132

Solve for the indicated variable. - $A = 2 \pi a ^ { 2 }$ , for $a$

(Multiple Choice)

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Question 133

Find the product. Write the answer in standard form. - $( 6 + 8 i ) ( 6 - 8 i )$

(Multiple Choice)

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Question 134

Decide what values of the variable cannot possibly be solutions for the equation. - $4 x = \sqrt { 1 - 6 x }$

(Multiple Choice)

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Question 135

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 16 } { x + 2 } = 1 + \frac { 2 } { x - 4 }$

(Multiple Choice)

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Question 136

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

(Multiple Choice)

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Question 137

Find the quotient. Write the answer in standard form. - $\frac { 6 + 5 i } { 3 + 4 i }$

(Multiple Choice)

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Question 138

Write the number in standard form a + bi. - $\frac { 4 + \sqrt { - 80 } } { 2 }$

(Multiple Choice)

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Question 139

Solve the equation by the zero-factor property. - $2 x ^ { 2 } - 3 x - 5 = 0$

(Multiple Choice)

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Question 140

Decide what values of the variable cannot possibly be solutions for the equation. -A water tank can be filled in 6 minutes and emptied in 8 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?

Solve for y. -Sophia borrowed $13,671 at 6% simple interest for 3 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 3 months? Round answers to the nearest cent if Necessary.

Solve the equation by completing the square. - $2 x ^ { 2 } + 7 x + 3 = 0$

The cost of producing $t$ units is $C = 3 t ^ { 2 } + 9 t$ , and the revenue generated from sales is $R = 4 t ^ { 2 } + t$ . Determine the number of units to be sold in order to generate a profit.

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { x + 3 } = 8$

The outside of a picture frame has a length which is 3 cm more than width. The area enclosed by the outside of the picture frame is 154 square cm. Find the width of the outside of the picture frame.

Simplify the power of i. -¡56

Write the number as the product of a real number and i. - $\sqrt { - 49 }$

The area of a square is numerically 4 less than the perimeter. Find the length of the side, if the side is greater than 1.

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $t ^ { 2 } + 2 t + 1 = 0$

Solve the inequality. Write the solution set in interval notation. - $( x + 6 ) ( x + 1 ) ( x - 9 ) < 0$

Solve for the indicated variable. - $A = 2 \pi a ^ { 2 }$ , for $a$

Find the product. Write the answer in standard form. - $( 6 + 8 i ) ( 6 - 8 i )$

Decide what values of the variable cannot possibly be solutions for the equation. - $4 x = \sqrt { 1 - 6 x }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 16 } { x + 2 } = 1 + \frac { 2 } { x - 4 }$

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

Find the quotient. Write the answer in standard form. - $\frac { 6 + 5 i } { 3 + 4 i }$

Write the number in standard form a + bi. - $\frac { 4 + \sqrt { - 80 } } { 2 }$

Solve the equation by the zero-factor property. - $2 x ^ { 2 } - 3 x - 5 = 0$

Review of Basic Concepts

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 2: Equations and Inequalities

Decide what values of the variable cannot possibly be solutions for the equation. -A water tank can be filled in 6 minutes and emptied in 8 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?

Solve for y. -Sophia borrowed $13,671 at 6% simple interest for 3 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 3 months? Round answers to the nearest cent if Necessary.

Solve the equation by completing the square. - 2x2+7x+3=02 x ^ { 2 } + 7 x + 3 = 02x2+7x+3=0

The cost of producing ttt units is C=3t2+9tC = 3 t ^ { 2 } + 9 tC=3t2+9t , and the revenue generated from sales is R=4t2+tR = 4 t ^ { 2 } + tR=4t2+t . Determine the number of units to be sold in order to generate a profit.

Decide what values of the variable cannot possibly be solutions for the equation. - x+33=8\sqrt [ 3 ] { x + 3 } = 83x+3​=8

The outside of a picture frame has a length which is 3 cm more than width. The area enclosed by the outside of the picture frame is 154 square cm. Find the width of the outside of the picture frame.

Simplify the power of i. -¡56

Write the number as the product of a real number and i. - −49\sqrt { - 49 }−49​

The area of a square is numerically 4 less than the perimeter. Find the length of the side, if the side is greater than 1.

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - t2+2t+1=0t ^ { 2 } + 2 t + 1 = 0t2+2t+1=0

Solve the inequality. Write the solution set in interval notation. - (x+6)(x+1)(x−9)<0( x + 6 ) ( x + 1 ) ( x - 9 ) < 0(x+6)(x+1)(x−9)<0

Solve for the indicated variable. - A=2πa2A = 2 \pi a ^ { 2 }A=2πa2 , for aaa

Find the product. Write the answer in standard form. - (6+8i)(6−8i)( 6 + 8 i ) ( 6 - 8 i )(6+8i)(6−8i)

Decide what values of the variable cannot possibly be solutions for the equation. - 4x=1−6x4 x = \sqrt { 1 - 6 x }4x=1−6x​

Decide what values of the variable cannot possibly be solutions for the equation. - 16x+2=1+2x−4\frac { 16 } { x + 2 } = 1 + \frac { 2 } { x - 4 }x+216​=1+x−42​

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

Find the quotient. Write the answer in standard form. - 6+5i3+4i\frac { 6 + 5 i } { 3 + 4 i }3+4i6+5i​

Write the number in standard form a + bi. - 4+−802\frac { 4 + \sqrt { - 80 } } { 2 }24+−80​​

Solve the equation by the zero-factor property. - 2x2−3x−5=02 x ^ { 2 } - 3 x - 5 = 02x2−3x−5=0

Review of Basic Concepts

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Solve the equation by completing the square. - $2 x ^ { 2 } + 7 x + 3 = 0$

The cost of producing $t$ units is $C = 3 t ^ { 2 } + 9 t$ , and the revenue generated from sales is $R = 4 t ^ { 2 } + t$ . Determine the number of units to be sold in order to generate a profit.

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { x + 3 } = 8$

Write the number as the product of a real number and i. - $\sqrt { - 49 }$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $t ^ { 2 } + 2 t + 1 = 0$

Solve the inequality. Write the solution set in interval notation. - $( x + 6 ) ( x + 1 ) ( x - 9 ) < 0$

Solve for the indicated variable. - $A = 2 \pi a ^ { 2 }$ , for $a$

Find the product. Write the answer in standard form. - $( 6 + 8 i ) ( 6 - 8 i )$

Decide what values of the variable cannot possibly be solutions for the equation. - $4 x = \sqrt { 1 - 6 x }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 16 } { x + 2 } = 1 + \frac { 2 } { x - 4 }$

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

Find the quotient. Write the answer in standard form. - $\frac { 6 + 5 i } { 3 + 4 i }$

Write the number in standard form a + bi. - $\frac { 4 + \sqrt { - 80 } } { 2 }$

Solve the equation by the zero-factor property. - $2 x ^ { 2 } - 3 x - 5 = 0$