Student: Assignment: Summer Assignment ­ Part Date: 1. · PDF fileAssignment: Summer...

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1. 2. Student: _____________________ Date: _____________________ Assignment: Summer Assignment Part 1 of 9 Algebra Essentials On the real number line, label the points with coordinates , , , , , , and . 0 3 −3 9 2 − 4.5 7 4 1.25 Label the point with coordinate . 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 Label the point with coordinate . 3 -5 -4 -3 -2 -1 0 1 2 3 4 5 Label the point with coordinate . −3 -5 -4 -3 -2 -1 0 1 2 3 4 5 Label the point with coordinate . 9 2 -5 -4 -3 -2 -1 0 1 2 3 4 5 Label the point with coordinate . − 4.5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Label the point with coordinate . 7 4 -5 -4 -3 -2 -1 0 1 2 3 4 5 Label the point with coordinate . 1.25 -5 -4 -3 -2 -1 0 1 2 3 4 5 Graph the numbers x on the real number line. x ≥−7 Choose the graph that illustrates the inequality on the real number line. A. -12 -6 0 6 12 B. -12 -6 0 6 12 C. -12 -6 0 6 12 D. -12 -6 0 6 12

Transcript of Student: Assignment: Summer Assignment ­ Part Date: 1. · PDF fileAssignment: Summer...

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Student: _____________________ Date: _____________________

Assignment: Summer Assignment ­ Part1 of 9 ­ Algebra Essentials

On the real number line, label the points with coordinates , , , , , , and .0 3 − 392

− 4.574

1.25

Label the point with coordinate . 0

-5 -4 -3 -2 -1 0 1 2 3 4 5

Label the point with coordinate . 3

-5 -4 -3 -2 -1 0 1 2 3 4 5

Label the point with coordinate . − 3

-5 -4 -3 -2 -1 0 1 2 3 4 5

Label the point with coordinate . 92

-5 -4 -3 -2 -1 0 1 2 3 4 5

Label the point with coordinate . − 4.5

-5 -4 -3 -2 -1 0 1 2 3 4 5

Label the point with coordinate . 74

-5 -4 -3 -2 -1 0 1 2 3 4 5

Label the point with coordinate . 1.25

-5 -4 -3 -2 -1 0 1 2 3 4 5

Graph the numbers x on the real number line.

x ≥ − 7

Choose the graph that illustrates the inequality on the real number line.

A.

-12 -6 0 6 12

B.

-12 -6 0 6 12

C.

-12 -6 0 6 12

D.

-12 -6 0 6 12

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Graph the numbers x on the real number line.

x > − 2

Choose the correct graph below.

A.

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

-2

B.

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

-2

C.

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

-2

D.

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

-2

Use the given real number line to compute the distance d(C,E).

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

A B C D E

(Type an integer or a simplified fraction.)d(C,E) =

Determine which of the value(s), if any, must be excluded from the domain of the variable in the expression .x2 − 1x

x = 3 x = 1 x = 0 x = − 1

Select all that apply.

x = 3x = 1x = 0x = − 1None

Determine which of the value(s), if any, must be excluded from the domain of the variable in the expression .x

x2 − 1

x 0= x = − 1 x = 4 x     =1

Select all that apply.

x 0 =x = − 1x = 4x = 1None

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Determine the domain of the variable x in the given expression.

9x − 10

Choose the correct domain below.

A. x | x ≠ − 10B. x | x ≠ 10C. x | x ≠ 0D. The domain is all real numbers.

Simplify the given expression.

( − 3)2

=( − 3)2

Simplify the expression.

2z35

2z35=

(Simplify your answer. Type your answer using exponential notation.)

Simplify the given expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0.

x y2 − 2 2

x y =2 − 2 2

(Simplify your answer. Use integers or fractions for any numbers in the expression.)

Simplify the given expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0.

2x − 7

7y − 2

− 2

(Simplify your answer. Use positive exponents only.)=2x − 7

7y − 2

− 2

Find the value of the expression if x and y .= 7 = − 5

x2 + y2

x2 + y2 = (Simplify your answer. Type an exact answer, using radicals as needed.)

Find the value of the expression if x and y .= 3 = − 2

xy

(Simplify your answer.)xy =

14.

15.

Find the value of the expression if x . What is the value if x ?3x − 3x + 3x − 33 2 = 2 = 1

If x , then . (Simplify your answer.)= 2 3x − 3x + 3x − 33 2 =

If x , then . (Simplify your answer.)= 1 3x − 3x + 3x − 33 2 =

Use a calculator to evaluate the given expression. Round your answer to three decimal places.

(7.8) − 2

(Round to three decimal places as needed.)(7.8) ≈− 2

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Student: _____________________ Date: _____________________

Assignment: Summer Assignment ­ Part2 of 9 ­ Geometry Essentials

(1)

Complete the sentence below.

The formula for the circumference C of a circle of radius r is _______.

The formula for the circumference C of a circle of radius r is (1)

C = πr .43

2

C = πr .2

C = 2πr.

C = 4πr .2

C = πr.

Decide whether the following statement is true or false.

The triangle with sides of length 9, 12, and 15 is a right triangle.

Choose the correct answer below.

TrueFalse

Determine whether the statement below is true or false.

The triangles shown are similar.

Choose the correct answer below.

TrueFalse

The lengths of the legs of a right triangle are given. Find the hypotenuse.

a = 10, b = 24

The length of the hypotenuse, c, is .

The lengths of the legs of a right triangle are given. Find the hypotenuse.

a = 24, b = 45

The length of the hypotenuse, c, is .

100° 100°

25°25°

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11.

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse.

, , 18 24 30

Is the triangle a right triangle?

NoYes

What is the length of the hypotenuse?

The triangle is not a right triangle.

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse.

, , 5 7 11

Select the correct choice below and fill in any answer boxes in your choice.

A. It is a right triangle. The hypotenuse is the side that is of length .

B. It is not a right triangle.

The lengths of the sides of a triangle are given. Determine if it is a right triangle. If it is, identify the hypotenuse.

15, 36, 39

Select the correct choice below and fill in any answer boxes in your choice.

A. It is a right triangle. The hypotenuse is the side that is of length .

B. It is not a right triangle.

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse.

, , 8 6 5

Select the correct choice below and fill in any answer boxes in your choice.

A. It is a right triangle. The hypotenuse is the side that is of length .

B. It is not a right triangle.

Find the area A of a triangle with height inches and base inches.5 2

square inchesA =

Find the area A and circumference C of a circle of radius meters.9

square metersA = (Type an exact answer in terms of .)π

metersC = (Type an exact answer in terms of .)π

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Find the area of the shaded region.

The area of the shaded region is square units. (Type an exact answer, using as needed.)π

Find the area of the shaded region.

8

8

The exact area is square units.A = (Type an exact answer, using as needed.)π

Given a pair of similar triangles, find the missing length x and the missing angles A, B, and C.

The missing length x is .

The measure of the angle A is .°

The measure of the angle B is .°

The measure of the angle C is .°

A Norman window consists of a rectangle surmounted by a semicircle. Find the area of the Norman window shown to the right. How much wood frame is needed to enclose the window? 11'

4'

The area of the window is .A = ft2

(Round to the nearest hundredth as needed.)

The amount of wood frame needed to enclose the window is ft. (Round to the nearest hundredth as needed.)

12

12

63°90°

27°

1

4 12

x

A

B

C

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Student: _____________________ Date: _____________________

Assignment: Summer Assignment ­ Part3 of 9 ­ Polynomials

Complete the sentence below.

The polynomial is of degree _______. The leading coefficient is _______.2x − 3x + 12x − 25 4 3

The polynomial is of degree . The leading coefficient is .2x − 3x + 12x − 25 4 3

(Type an integers or decimals.)

Find the following product using the special product formulas.

_________.x2 − 4 x2 + 4 =

.x2 − 4 x2 + 4 = (Simplify your answer.)

Complete the sentence below.

(x a)( ) _______− x + ax + a2 2 =

(x a)( ) (Simplify your answer.)− x + ax + a2 2 =

Tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial.

8x3

Select the correct choice below and, if necessary, fill in the answer boxes within your choice.

A. The expression is a monomial. The variable(s) is/are , the coefficient is , and the degree of the monomial is .

(Use a comma to separate answers as needed.)B. The expression is not a monomial.

Tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not.

− 9x + 7x3 2

Is the given expression a monomial? Select the correct choice below and fill in any answer boxes in your choice.

A. The given expression is a monomial. The variable(s) of the monomial is/are . The coefficient of the monomial is . The degree of the monomial is . (Use a comma to separate answers as needed.)

B. The given expression is not a monomial. It has a coefficient that is negative.C. The given expression is not a monomial. It has at least one term with an exponent that is greater

than one.D. The given expression is not a monomial. It has more than one term.

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7.

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Tell whether the given expression is a polynomial. If it is, give its degree.

5x − 59

Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. The given expression is a polynomial. Its degree is .

B. The expression is not a polynomial.

Tell whether the given expression is a polynomial. If it is, give its degree.

5x −85

x9

Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. The given expression is a polynomial. Its degree is .

B. The expression is not a polynomial.

Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not.

y2 + 5

y4 − 6

Therefore, is the given expression a polynomial?

A. The given expression is a polynomial.B. The given expression is not a polynomial, because there is only one monomial term.C. The given expression is not a polynomial, because the polynomial in the denominator has degree

greater than 0.

What is the degree of ? Select the correct choice below and fill in the answer box within your choice if necessary.y2 + 5

y4 − 6

A.

B. The expression is not a polynomial.

as indicated. Express your answer as a single polynomial in standard form.Add

x + 9x + 9 + (5x − 6)2

x + 9x + 9 + (5x − 6)2 =

as indicated. Express your answer as a single polynomial in standard form.Subtract

5 x + x − 3 − 2 2x − 2x3 2 3 2

5 x + x − 3 − 2 2x − 2x3 2 3 2 =

11.

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Multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form.

(3x + 3)(x + 3)

(3x + 3)(x + 3) =

Multiply the polynomials using a special product formula. Express your answer as a single polynomial in standard form.

(5x − 4)2

(5x − 4)2 =

Find the quotient and the remainder. Check your work by verifying that .(Quotient)(Divisor) + Remainder = Dividend

divided by 7x − 7x + x + 53 2 x2

The quotient is , and the remainder is .

For the given expression, find the quotient and the remainder.  Check your work by verifying that (Quotient)(Divisor) Remainder Dividend.+ =

divided by 8x − 8x + 3x + 64 2 x + 82

Quotient:

Remainder:

For the given expression, find the quotient and the remainder. Check your work by verifying that (Quotient )(Divisor ) Remainder Dividend.+ =

divided by 6x − 6x + 4x + 25 2 3x − 13

Quotient:

Remainder:

Factor completely the given polynomial.  

3− 3x2

Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. 3 − 3x2 =

B. The polynomial is prime.

Factor the given polynomial completely. If the polynomial cannot be factored, say that it is prime.

x + 10x + 212

Select the correct choice below and fill in any answer boxes within your choice.

A. x + 10x + 212 =

B. The polynomial is prime.

18.

19.

20.

Factor the given polynomial completely. If the polynomial cannot be factored, say that it is prime.

x − 7x + 42

Select the correct choice below and fill in any answer boxes within your choice.

A. x − 7x + 42 =

B. The polynomial is prime.

Factor completely the given polynomial.

5x + 5x + 502

Select the correct choice below and fill in any answer boxes within your choice.

A. 5x + 5x + 502 =

B. The polynomial is prime.

Factor the given polynomial completely. If the polynomial cannot be factored, say that it is prime.

9x + 27x − 902

Select the correct choice below and fill in any answer boxes within your choice.

A. 9x + 27x − 902 =

B. The polynomial is prime.

15. 2x2

− 4x + 4x + 22

16. A. 3 − 3x2 = 3(1 − x)(1 + x)

17. A. x + 10x + 212 = (x + 7)(x + 3)

18. B. The polynomial is prime.

19. A. 5x + 5x + 502 = 5 x + x + 102

20. A. 9x + 27x − 902 = 9(x + 5)(x − 2)

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Student: _____________________ Date: _____________________

Assignment: Summer Assignment ­ Part4 of 9 ­ Synthetic Division

(1) the quotient and the remainder the divisor and the dividend

the dividend and the remainder the quotient and the divisor

the divisor and the remainder the quotient and the dividend

(2) dividend. quotient. remainder. divisor .

Complete the sentence below.

To check division, the expression that is being divided, the dividend, should equal the product of the _______ plus the _______.

To check division, the expression that is being divided, the dividend, should equal the product of (1) plus

the (2)

Determine whether the statement below is true or false.

In using synthetic division, the divisor is always a polynomial of degree 1, whose leading coefficient is 1.

Choose the correct answer below.

FalseTrue

Decide whether the following statement is true or false.

means .− 2 5 4 3 1

− 10 12 − 30

5 − 6 15 − 29

5x3 + 4x2 + 3x + 1x + 2

= 5x − 6x + 15 +2 − 29x + 2

Choose the correct answer below.

FalseTrue

Use synthetic division to find the quotient and remainder when is divided by .2x + 4x − 9x + 53 2 x − 3

Quotient:

Remainder:

Use synthetic division to find the quotient and remainder when is divided by .x − 5x + x5 3 x + 4

Quotient:

Remainder:

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Use synthetic division to find the quotient and remainder when

  is divided by 9x − 8x + 6x + 66 4 2 x − 2

Quotient:

Remainder:

Use synthetic division to find the quotient and remainder when

is divided by x − 325 x − 2

Quotient:

Remainder:

Use synthetic division to determine whether x c is a factor of the given polynomial.−

;   4x − 20x − 9x + 604 3 x − 5

Is a factor of the given polynomial?x − 5

NoYes

Use synthetic division to determine whether is a factor of .x + 2 6x + 53x + 406 3

Is a factor of the given polynomial?x + 2

NoYes

Use synthetic division to determine whether x c is a factor of the given polynomial.−

;   5x − 45x + 3x − 276 4 2 x + 3

Is a factor of the given polynomial?x + 3

NoYes

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Student: _____________________ Date: _____________________

Assignment: Summer Assignment ­ Part5 of 9 ­ Rational Expressions

(1) lowest terms. factored form. quotient form.

Complete the sentence below.

When the numerator and denominator of a rational expression contain no common factors (except 1 and 1), the rational expression is in _______.

When the numerator and denominator of a rational expression contain no common factors (except 1 and 1), the rational

expression is in (1)

(1) least common method. least complex multiple. least complex method. least common multiple.

Complete the sentence below.

LCM is an abbreviation for _________.

LCM is an abbreviation for (1)

Determine whether the statement below is true or false.

The rational expression is reduced to lowest terms.3x3 − 5xx + 1

Choose the correct answer below.

TrueFalse

Reduce the rational expression to lowest terms.

x2 − 4x5x − 20

x2 − 4x5x − 20

=

(Simplify your answer. Use integers or fractions for any numbers in the expression.)

5.

6.

7.

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9.

Reduce the rational expression to lowest terms.

40x

25x2 − 5x

40x

25x2 − 5x=

(Simplify your answer. Use integers or fractions for any numbers in the expression.)

Reduce the given rational expression to lowest terms.

y2 − 9

5y2 − 10y − 15

=y2 − 9

5y2 − 10y − 15 (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Perform the indicated operation and simplify the result. Leave your answer in factored form.

•10x2

x2 − 4

x3 − 8

2x

•10x2

x2 − 4

x3 − 8

2x=

(Simplify your answer. Type your answer in factored form. Use integers or fractions for any numbers in the expression.)

Perform the indicated operation and simplify the result. Leave your answer in factored form.

3 − x3 + x

7x

x2 − 9

3 − x3 + x

7x

x2 − 9

=

(Simplify your answer. Type your answer in factored form. Use integers or fractions for any numbers in the expression.)

Perform the indicated operation and simplify the result. Leave your answer in factored form.

−x2

6x − 54

6x − 5

− =x2

6x − 54

6x − 5 (Simplify your answer. Type your answer in factored form. Use integers or fractions for any numbers in the expression.)

10. Perform the indicated operation and simplify the result. Leave your answer in factored form.

+x

x2 − 49

4

x

+ =x

x2 − 49

4

x (Simplify your answer. Type your answer in factored form. Use integers or fractions for any numbers in the expression.)

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Student: _____________________ Date: _____________________

Assignment: Summer Assignment ­ Part6 of 9 ­ Solving Equations

Factor.

x − 8x − 482

x − 8x − 482 =

Solve the following equation.

(x − 4)(4x + 5) = 0

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution set is . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

B. There is no solution.

Determine whether the following statement is true or false.

The solution of the equation 3x 8 0 is .− =38

Choose the correct answer below.

TrueFalse

Find the value of the variable that satisfies the equation. Check your solution. Answers that are not integers may be left in fractional form or decimal form.

8x − 2 = 14

x =

Solve the equation.

x13

=415

The solution set is . (Type an integer or a simplified fraction.)

Solve the equation.

( x) (x )5 1 + 2 = 9 − 4

Select the correct choice below and fill in any answer boxes in your choice.

A. The solution set is . (Simplify your answer.)

B. There is no solution.

7.

8.

9.

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12.

Solve the equation.

+14y

6y= 4

Select the correct choice below and fill in any answer boxes in your choice.

A. The solution set is . (Simplify your answer.)

B. There is no solution.

Solve the equation.

(x + 7)(x − 1) = (x + 1)2

Select the correct choice below and fill in any answer boxes in your choice.

A. The solution set is . (Simplify your answer.)

B. There is no solution.

Solve the equation.

x = 16x2

x = (Use a comma to separate answers as needed.)

Solve the equation.

32x − 5

=2

x + 4

Select the correct choice below and fill in any answer boxes in your choice.

A. The solution set is . (Simplify your answer.)

B. There is no solution.

Solve the equation by factoring.

+ =11(x − 2)x − 3

2x

− 2x(x − 3)

What is the solution set?

   (Use a comma to separate answers as needed.)

Solve the equation by the square root method.

(x − 3) = 362

What is the solution set?  

(Use a comma to separate answers as needed.)

13.

14.

15.

Solve the quadratic equation by completing the square.

x + 6x = − 52

What is the solution set?

    (Use a comma to separate answers as needed.)

Find the real solutions, if any, of the following equation. Use the quadratic formula.

0x − 4x − 12 =

Select the correct choice below and, if necessary, fill in the answer box to complete your answer.

A. The solution set is . (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.)

B. The solution is not a real number.

Find the real solutions, if any, using the quadratic formula.

2x − 9x + 10 = 02

Select the correct choice below and fill in any answer boxes in your choice.

A. The solution set is . (Simplify your answer. Use a comma to separate answers as needed.)

B. The solution is not a real number.

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Student: _____________________ Date: _____________________

Assignment: Summer Assignment ­ Part7 of 9 ­ Complex Numbers and QuadraticEquations

Verify whether the following sentence is true or false.

The square of a complex number is sometimes negative.

Choose the correct answer below.

FalseTrue

Write the expression in the standard form .a + b i

( − 2 + i )( − 2 − i )

(Simplify your answer.)( − 2 + i )( − 2 − i ) =

(1) real imaginary

(2) real imaginary

(3) imaginary unit. complex unit.

Fill in the blanks.

In the complex number 5+2 , the number 5 is called the ________ part, the number 2 is called the__________ part, and the number is called the_______ .

i

i

In the complex number , the number 5 is called the (1) part, the number 2 is called the

(2) part, and the number is called the (3)

5 + 2 i

i

State whether the following statement is true or false.

The conjugate of is .2 + 5 i − 2 − 5 i

Choose the correct answer below.

FalseTrue

State whether the following statement is true or false.

All real numbers are complex numbers.

Choose the correct answer below.

TrueFalse

Write the expression in the standard form .a + b i

(3 − 6 i ) + (9 + 3 i )

   (Simplify your answer.)(3 − 6 i ) + (9 + 3 i ) =

7.

8.

9.

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14.

Write the expression in the standard form .a + b i

(6 − 7 i ) − (5 + 9 i )

(Simplify your answer.)(6 − 7 i ) − (5 + 9 i ) =

Multiply.

( i )9 6 − 2

( i ) = 9 6 − 2 (Type your answer in the form a+bi.)

Multiply.

3 i (6 − 2 i )

3 i (6 − 2 i ) = (Type your answer in the form . Use integers or fractions for any numbers in the expression.)a + b i

Write the expression in the standard form .a + b i

(5 − 2 i )(5 + i )

(Simplify your answer.)(5 − 2 i )(5 + i ) =

Solve the equation in the complex number system.

x + 4 = 02

The solution set is . (Simplify your answer. Use a comma to separate answers as needed.)

Solve the equation by factoring.

x − 49 = 02

What is the solution set?  

   (Use a comma to separate answers as needed.)

Solve the equation in the complex number system.

x − 6x + 90 = 02

The solution set is .   (Use a comma to separate answers as needed.)

Solve the equation in the complex number system.

x − 4x + 5 = 02

What is the solution set?  

(Use a comma to separate answers as needed.)

15. Solve the equation in the complex number system.

049x − 14x + 22 =

What is the solution set?

A. 17, 27

B. 17

i , −17

i

C. 17+17

i , 27−17

i

D. 17+17

i , 17−17

i

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Student: _____________________ Date: _____________________

Assignment: Summer Assignment ­ Part8 of 9 ­ Interval Notation and SolvingInequalities

(1) mathematical expression. mathematical modeling.

Fill in the blank.

The process of using variables to represent unknown quantities and then finding relationships that involve these variables is referred to as ____________.

The process of using variables to represent unknown quantities and then finding relationships that involve these variables is

referred to as (1)

Graph the inequality on a number line, and write the inequality in interval notation.

x ≥ − 10

Choose the graph that illustrates the inequality on the real number line.

A.

-12 -6 0 6 12

B.

-12 -6 0 6 12

C.

-12 -6 0 6 12

D.

-12 -6 0 6 12

Use interval notation to express the inequality.  

(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

(1) negative positive

If each side of an inequality is multiplied by a(n) __________ number, then the sense of the inequality symbol is reversed.

If each side of an inequality is multiplied by a(n) (1) number, then the sense of the inequality symbol is reversed.

(1) closed interval, open interval,

A(n) ___________, denoted , consists of all real numbers x for which .[ ]a,b a ≤ x ≤ b

A(n) (1) denoted , consists of all real numbers x for which .[ ]a,b a ≤ x ≤ b

5.

6.

7.

Express the graph shown in color using interval notation. Also express the graph as an inequality involving x.

  -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Choose the correct interval notation below that is represented by the graph.

A. [ − 9, 8)B. [ − 9, 8]C. ( − 8, 9]D. , − 9 8

Choose the correct inequality below that is represented by the graph.

A. x− 9 ≤ ≤ 8B. x− 9 < ≤ 8C. x− 9 ≤ < 8D. x− 9 < < 8

Write the given inequality using interval notation, and illustrate the inequality using the real number line.

4 ≤ x ≤ 8

Use interval notation to express the inequality. What is the resulting interval?

Choose the graph that illustrates the inequality on the real number line.

A.

-2 -1 0 1 2 3 4 5 6 7 8 9 10

B.

-2 -1 0 1 2 3 4 5 6 7 8 9 10

C.

-2 -1 0 1 2 3 4 5 6 7 8 9 10

D.

-2 -1 0 1 2 3 4 5 6 7 8 9 10

Write the inequality using interval notation and illustrate the inequality using the real number line.

− 5 ≤ x < 7

Choose the correct interval notation below that represents the inequality.

A. ( , ]− 5 7B. ( , )− 5 7C. [ , )− 5 7D. [ , ]− 5 7

Choose the correct real number line below that represents the inequality.

A.

-10 -8 -6 -4 -2 0 2 4 6 8 10

-5 7 B.

-10 -8 -6 -4 -2 0 2 4 6 8 10

-5 7

C.

-10 -8 -6 -4 -2 0 2 4 6 8 10

-5 7 D.

-10 -8 -6 -4 -2 0 2 4 6 8 10

-5 7

8.

9.

10.

11.

Write the inequality using interval notation and illustrate the inequality using the real number line.

x ≥ 8

Choose the correct interval notation below that represents the inequality.

A. [ , )8∞

B. ( , ]8∞

C. [ , ]8∞

D. ( , )8∞

Choose the correct real number line below that represents the inequality.

A.

-10 -8 -6 -4 -2 0 2 4 6 8 10

8 B.

-10 -8 -6 -4 -2 0 2 4 6 8 10

8

C.

-10 -8 -6 -4 -2 0 2 4 6 8 10

8 D.

-10 -8 -6 -4 -2 0 2 4 6 8 10

8

Write the given interval as an inequality involving x, and illustrate the interval using the real number line.

[6, 9]

Use an inequality involving x to to express the interval. What is the resulting inequality?

Choose the graph that illustrates the interval on the real number line.

A.

-2 -1 0 1 2 3 4 5 6 7 8 9 10

B.

-2 -1 0 1 2 3 4 5 6 7 8 9 10

C.

-2 -1 0 1 2 3 4 5 6 7 8 9 10

D.

-2 -1 0 1 2 3 4 5 6 7 8 9 10

Fill in the blank with the correct inequality symbol.

If then ___ .x < 12, x − 12 0

If then .x < 12, x − 12 0

Fill in the blank with the correct inequality symbol.

If then ___ .x ≤ − 7, 3x − 21

If then .x ≤ − 7, 3x − 21

12.

13.

Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set.

19 − 3x ≤ 10

Choose the correct answer below that is the solution set to the inequality.

A. x|x or , )≥ − 3 [ − 3∞

B. x|x or , )≥ − 9 [ − 9∞

C. x|x or , )≤ 3 (3∞

D. x|x or ,≥ 3 [3∞)

Choose the correct graph below that is the solution set to the inequality.

A.-9 -6 -3 0 3 6 9

B.-18 -15 -12 -9 -6 -3 0

C.-9 -6 -3 0 3 6 9

D.-9 -6 -3 0 3 6 9

Solve the following inequality. Graph the solution set.

7x − 6 > 29

The solution is . (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Choose the graph of the inequality below.

A.-12 -9 -6 -3 0 3 6 9 12

B.-12 -9 -6 -3 0 3 6 9 12

C.-12 -9 -6 -3 0 3 6 9 12

D.-12 -9 -6 -3 0 3 6 9 12

14.

15.

Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set.

≤ <14

x + 17

75

Choose the correct answer below that is the solution set to the inequality.

A. or x|34≤ x <

445

,34

445

B. or x|34≥ x >

445

,34

445

C. or x|34≤ x <

445

,34

445

D. or x|34≥ x >

445

,34

445

Choose the correct graph below that is the solution set to the inequality.

A.

0 3 6 9

B.

-9 -6 -3 0

C.

0 3 6 9

D.

0 3 6 9

Solve the inequality.

0 < <2x

89

What is the solution?  

(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

1.

2.

3.

4.

5.

6.

Student: _____________________ Date: _____________________

Assignment: Summer Assignment ­ Part9 of 9 ­ Rational Exponents

Graph the inequality on a number line, and write the inequality in interval notation.

x ≥ − 10

Choose the graph that illustrates the inequality on the real number line.

A.

-12 -6 0 6 12

B.

-12 -6 0 6 12

C.

-12 -6 0 6 12

D.

-12 -6 0 6 12

Use interval notation to express the inequality.  

(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Evaluate and .( )− 2 2 − 22

(Type an integer or a decimal.)( )− 2 2 =

(Type an integer or a decimal.)− 22 =

Evaluate and .100 ( )− 10 2

(Type an integer or a decimal.)100 =

(Type an integer or a decimal.)( )− 10 2 =

Decide whether the following statement is true or false.

= − 24 ( − 2)4

Choose the correct answer below.

TrueFalse

Simplify the given expression.

3 − 125

3 − 125 =

Simplify the expression.

7 3 42

(Type an exact answer, using radicals as needed.)7 3 42=

7.

8.

9.

10.

Simplify the given expression.

− + 445 125

− + 445 125 = (Type an exact answer, using radicals as needed.)

Simplify the given expression.

+ 3 − 16 6

(Type an exact answer, using radicals as needed.)+ 3 − 16 6 =

Simplify the given expression. Assume that all variables are positive.

x − 3 2

x − 3 2 = (Type an exact answer, using radicals as needed.)

Rationalize the denominator of the expression.

− 10

13

− 10

13=

(Type a simplified fraction. Type an exact answer, using radicals as needed.)