Question 1

Perform the multiplication and simplify. $\frac { q ^ { 2 } - 1 } { 5 q ^ { 2 } - 34 q + 45 } \mathbf { g } \frac { q - 5 } { q ^ { 2 } - 9 q + 8 }$

Accepted Answer

A)  $\frac { q - 1 } { ( 5 q - 9 ) ( q - 8 ) } , \quad q \neq - 1 , q \neq 5$ 
B)  $\frac { q + 1 } { ( 5 q - 9 ) ( q - 8 ) } , \quad q \neq 1 , q \neq 5$ 
C)  $\frac { q - 1 } { ( 5 q - 9 ) ( q + 8 ) } , \quad q \neq 1 , q \neq 5$ 
D)  $\frac { q + 1 } { ( 5 q - 9 ) ( q + 8 ) } , \quad q \neq 1 , q \neq 5$ 
E)  $- \frac { q + 1 } { ( 5 q + 9 ) ( q - 8 ) } , \quad q \neq - 1 , q \neq 5$ 
A)  $\frac { q - 1 } { ( 5 q - 9 ) ( q - 8 ) } , \quad q \neq - 1 , q \neq 5$ 
B)  $\frac { q + 1 } { ( 5 q - 9 ) ( q - 8 ) } , \quad q \neq 1 , q \neq 5$ 
C)  $\frac { q - 1 } { ( 5 q - 9 ) ( q + 8 ) } , \quad q \neq 1 , q \neq 5$ 
D)  $\frac { q + 1 } { ( 5 q - 9 ) ( q + 8 ) } , \quad q \neq 1 , q \neq 5$ 
E)  $- \frac { q + 1 } { ( 5 q + 9 ) ( q - 8 ) } , \quad q \neq - 1 , q \neq 5$

Question 2

The lowest recorded January temperature for a city is $- 15 ^ { \circ } \mathrm { F }$ and the highest recorded temperature is $68 ^ { \circ } F.$ Find the distance between the numbers to determine the range of temperatures for January.

Accepted Answer

A)  $- 30 ^ { \circ } \mathrm { F }$ 
B)  $- 83 ^ { \circ } \mathrm { F }$ 
C)  $- 53 ^ { \circ } \mathrm { F }$ 
D)  $- 15 ^ { \circ } \mathrm { F }$ 
E)  $83 ^ { \circ } F$ 
A)  $- 30 ^ { \circ } \mathrm { F }$ 
B)  $- 83 ^ { \circ } \mathrm { F }$ 
C)  $- 53 ^ { \circ } \mathrm { F }$ 
D)  $- 15 ^ { \circ } \mathrm { F }$ 
E)  $83 ^ { \circ } F$

Question 3

Simplify the expression. $\left( \frac { 4 } { v } \right) ^ { 2 } \left( \frac { 2 } { v } \right) ^ { 3 }$

Accepted Answer

A)  $\frac { 48 } { v ^ { 5 } }$ 
B)  $\frac { 128 } { v ^ { 5 } }$ 
C)  $\frac { 128 } { v ^ { 6 } }$ 
D)  $\frac { 48 } { v ^ { 6 } }$ 
E)  $\frac { 24 } { v ^ { 6 } }$ 
A)  $\frac { 48 } { v ^ { 5 } }$ 
B)  $\frac { 128 } { v ^ { 5 } }$ 
C)  $\frac { 128 } { v ^ { 6 } }$ 
D)  $\frac { 48 } { v ^ { 6 } }$ 
E)  $\frac { 24 } { v ^ { 6 } }$

Question 4

Write the number in scientific notation. One minute is about 0.000099 week.

Accepted Answer

A) 0.99 F1F1F1S1F1F1F10 10-4 
B) 99 F1F1F1S1F1F1F10 10-6 
C) 9.9 F1F1F1S1F1F1F10 10-5 
D) 9.9 F1F1F1S1F1F1F10 10-6 
E) 0.000099 F1F1F1S1F1F1F10 10-5 
A) 0.99 F1F1F1S1F1F1F10 10-4 
B) 99 F1F1F1S1F1F1F10 10-6 
C) 9.9 F1F1F1S1F1F1F10 10-5 
D) 9.9 F1F1F1S1F1F1F10 10-6 
E) 0.000099 F1F1F1S1F1F1F10 10-5

Question 5

Place the correct symbol (, or =) between the pair of real numbers. $- | 3 |$ $- | - 3 |$

Accepted Answer

A)  $- | 3 |  - | - 3 |$ 
C)  $- | 3 | = - | - 3 |$ 
A)  $- | 3 |  - | - 3 |$ 
C)  $- | 3 | = - | - 3 |$

Question 6

Simplify the expression. $6 z ^ { 6 } \left( 4 z ^ { 8 } \right) ^ { 3 }$

Accepted Answer

A)  $72 z ^ { 17 }$ 
B)  $384 z ^ { 17 }$ 
C)  $384 z ^ { 30 }$ 
D)  $24 z ^ { 30 }$ 
E)  $72 z ^ { 30 }$ 
A)  $72 z ^ { 17 }$ 
B)  $384 z ^ { 17 }$ 
C)  $384 z ^ { 30 }$ 
D)  $24 z ^ { 30 }$ 
E)  $72 z ^ { 30 }$

Question 7

Completely factor the expression below. $3 u + 7 u ^ { 2 } + 21 + u ^ { 3 }$

Accepted Answer

A)  $( u + 7 ) \left( 3 - u ^ { 2 } \right)$ 
B)  $( u + 7 ) \left( 3 + u ^ { 2 } \right)$ 
C)  $\left( u ^ { 2 } - 7 \right) ( 3 + u )$ 
D)  $\left( u ^ { 2 } - 7 \right) ( 3 - u )$ 
E)  $\left( u ^ { 2 } + 7 \right) ( 3 - u )$ 
A)  $( u + 7 ) \left( 3 - u ^ { 2 } \right)$ 
B)  $( u + 7 ) \left( 3 + u ^ { 2 } \right)$ 
C)  $\left( u ^ { 2 } - 7 \right) ( 3 + u )$ 
D)  $\left( u ^ { 2 } - 7 \right) ( 3 - u )$ 
E)  $\left( u ^ { 2 } + 7 \right) ( 3 - u )$

Question 8

Determine which numbers in the set are irrational numbers. $1.222 \ldots , \frac { \sqrt { 5 } } { 2 } , 0 , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 9.090990999 \ldots , 5 \pi$

Accepted Answer

A)  $\frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 5 \pi$ 
B)  $\frac { \sqrt { 5 } } { 2 } , 0 , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 5 \pi$ 
C)  $\frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , 9.090990999 \ldots , 5 \pi$ 
D)  $1.222 \ldots , \frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 9.090990999 \ldots , 5 \pi$ 
E)  $\frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , 5 \pi$ 
A)  $\frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 5 \pi$ 
B)  $\frac { \sqrt { 5 } } { 2 } , 0 , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 5 \pi$ 
C)  $\frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , 9.090990999 \ldots , 5 \pi$ 
D)  $1.222 \ldots , \frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 9.090990999 \ldots , 5 \pi$ 
E)  $\frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , 5 \pi$

Question 9

Evaluate the expression for the given value of x. $- x ^ { 4 }$ x = -2

Accepted Answer

A) 8 
B)  $\frac { 1 } { 16 }$ 
C)  $- \frac { 1 } { 16 }$ 
D) -16 
E) 16 
A) 8 
B)  $\frac { 1 } { 16 }$ 
C)  $- \frac { 1 } { 16 }$ 
D) -16 
E) 16

Question 10

Rewrite the expression with positive exponents and simplify. $\left( 3 p ^ { - 3 } \right) ^ { 4 } \left( - 3 p ^ { - 2 } \right) ^ { - 1 }$

Accepted Answer

A)  $\frac { 1 } { 15 p ^ { 10 } }$ 
B)  $\frac { 15 } { p ^ { 10 } }$ 
C)  $\frac { 36 } { p ^ { 10 } }$ 
D)  $- \frac { 27 } { p ^ { 10 } }$ 
E)  $- \frac { 1 } { 27 p ^ { 10 } }$ 
A)  $\frac { 1 } { 15 p ^ { 10 } }$ 
B)  $\frac { 15 } { p ^ { 10 } }$ 
C)  $\frac { 36 } { p ^ { 10 } }$ 
D)  $- \frac { 27 } { p ^ { 10 } }$ 
E)  $- \frac { 1 } { 27 p ^ { 10 } }$

Question 11

Find the area of the shaded region in the figure. Write your result as a polynomial in standard form.

Accepted Answer

A) 7x2 + 17x 
B) 7x2 + 23x 
C) 9x2 + 17x 
D) 9x2 + 23x 
E) 8x2 + 18x 
A) 7x2 + 17x 
B) 7x2 + 23x 
C) 9x2 + 17x 
D) 9x2 + 23x 
E) 8x2 + 18x

Question 12

The length L of the hypotenuse of a right triangle is $L = \sqrt { x ^ { 2 } + y ^ { 2 } }$ where x and y are the lengths of the other two sides. Find the length of the hypotenuse when the other sides measure 1 unit and $\frac { 4 } { 3 }$ units.

Accepted Answer

A) 1 unit 
B)  $\frac { \sqrt { 7 } } { 2 }$ units 
C)  $\frac { 25 } { 9 }$ units 
D)  $\frac { \sqrt { 7 } } { 3 }$ units 
E)  $\frac { 5 } { 3 }$ units 
A) 1 unit 
B)  $\frac { \sqrt { 7 } } { 2 }$ units 
C)  $\frac { 25 } { 9 }$ units 
D)  $\frac { \sqrt { 7 } } { 3 }$ units 
E)  $\frac { 5 } { 3 }$ units

Question 13

Simplify the complex fraction. $\frac { ( x - 6 ) } { \left( \frac { x } { 6 } - \frac { 6 } { x } \right) }$

Accepted Answer

A)  $\frac { 6 x } { x + 6 } , \quad x \neq 6 , x \neq 0$ 
B)  $\frac { 6 x } { x + 6 } , \quad x \neq - 6$ 
C)  $\frac { 6 x } { x - 6 } , x \neq 6$ 
D)  $\frac { 6 x } { x - 6 } , \quad x \neq - 6$ 
E)  $\frac { x + 6 } { 6 x } , \quad x \neq 0$ 
A)  $\frac { 6 x } { x + 6 } , \quad x \neq 6 , x \neq 0$ 
B)  $\frac { 6 x } { x + 6 } , \quad x \neq - 6$ 
C)  $\frac { 6 x } { x - 6 } , x \neq 6$ 
D)  $\frac { 6 x } { x - 6 } , \quad x \neq - 6$ 
E)  $\frac { x + 6 } { 6 x } , \quad x \neq 0$

Question 14

Evaluate the expression without using a calculator. $4 ^ { - 3 / 2 }$

Accepted Answer

A) -8 
B) 4 
C) -4 
D)  $\frac { 1 } { 8 }$ 
E)  $- \frac { 1 } { 8 }$ 
A) -8 
B) 4 
C) -4 
D)  $\frac { 1 } { 8 }$ 
E)  $- \frac { 1 } { 8 }$

Question 15

A rectangular room has a floor space of $\left( x ^ { 2 } + 5 x + 6 \right)$ square feet. If the width of the room is $( x + 2 )$ feet, what is the length?

Accepted Answer

A)  $( x - 3 )$ feet 
B)  $( x + 3 )$ feet 
C)  $( 3 x + 1 )$ feet 
D)  $( 3 x - 1 )$ feet 
E)  $( x - 2 )$ feet 
A)  $( x - 3 )$ feet 
B)  $( x + 3 )$ feet 
C)  $( 3 x + 1 )$ feet 
D)  $( 3 x - 1 )$ feet 
E)  $( x - 2 )$ feet

Question 16

Identify the rule of algebra illustrated by the statement. -9r - 3r = (-9 - 3)r

Accepted Answer

A) associative property of addition 
B) commutative property of addition 
C) associative property of multiplication 
D) commutative property of multiplication 
E) distributive property 
A) associative property of addition 
B) commutative property of addition 
C) associative property of multiplication 
D) commutative property of multiplication 
E) distributive property

Question 17

Evaluate the expression for the given value of x. expression: $\frac { x + 4 } { x - 4 }$ value: x = -4

Accepted Answer

A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C) 0 
D) not possible since numerator is 0 
E) not possible since denominator is 0 
A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C) 0 
D) not possible since numerator is 0 
E) not possible since denominator is 0

Question 18

Evaluate $\frac { p ^ { 2 } + q ^ { 2 } } { p + q }$ when $p = - 12$ and $q = 9 .$

Accepted Answer

A) -3 
B) 9 
C) 441 
D) -75 
E) -147 
A) -3 
B) 9 
C) 441 
D) -75 
E) -147

Question 19

Perform the operation and write the result in standard form. $\left( 8 x ^ { 4 } - 6 \right) - \left( 5 x ^ { 4 } - 4 x - 9 \right)$

Accepted Answer

A)  $3 x ^ { 4 } - 4 x - 15$ 
B)  $3 x ^ { 4 } + 4 x + 3$ 
C)  $3 x ^ { 8 } + 4 x + 3$ 
D)  $3 x ^ { 8 } - 4 x - 15$ 
E)  $13 x ^ { 8 } - 4 x - 15$ 
A)  $3 x ^ { 4 } - 4 x - 15$ 
B)  $3 x ^ { 4 } + 4 x + 3$ 
C)  $3 x ^ { 8 } + 4 x + 3$ 
D)  $3 x ^ { 8 } - 4 x - 15$ 
E)  $13 x ^ { 8 } - 4 x - 15$

Question 20

The quality control inspector for a tire factory is testing the rim diameter of various tires. A tire is rejected if its rim diameter varies too much from its expected measure. The diameter should not differ by more than 0.1 inch or by more than $0.1 \%$ of the expected diameter measure. Find the widest range of allowable values for the actual diameter if the expected diameter is 14.000 inches. Round to the nearest thousandth.

Accepted Answer

A) between 13.900 inches and 14.014 inches 
B) between 13.986 inches and 14.100 inches 
C) between 13.986 inches and 14.014 inches 
D) between 13.900 inches and 14.000 inches 
E) between 13.900 inches and 14.100 inches 
A) between 13.900 inches and 14.014 inches 
B) between 13.986 inches and 14.100 inches 
C) between 13.986 inches and 14.014 inches 
D) between 13.900 inches and 14.000 inches 
E) between 13.900 inches and 14.100 inches

Perform the multiplication and simplify. $\frac { q ^ { 2 } - 1 } { 5 q ^ { 2 } - 34 q + 45 } \mathbf { g } \frac { q - 5 } { q ^ { 2 } - 9 q + 8 }$

The lowest recorded January temperature for a city is $- 15 ^ { \circ } \mathrm { F }$ and the highest recorded temperature is $68 ^ { \circ } F.$ Find the distance between the numbers to determine the range of temperatures for January.

Simplify the expression. $\left( \frac { 4 } { v } \right) ^ { 2 } \left( \frac { 2 } { v } \right) ^ { 3 }$

Write the number in scientific notation. One minute is about 0.000099 week.

Place the correct symbol (<, >, or =) between the pair of real numbers. $- | 3 |$ $- | - 3 |$

Simplify the expression. $6 z ^ { 6 } \left( 4 z ^ { 8 } \right) ^ { 3 }$

Completely factor the expression below. $3 u + 7 u ^ { 2 } + 21 + u ^ { 3 }$

Determine which numbers in the set are irrational numbers. $1.222 \ldots , \frac { \sqrt { 5 } } { 2 } , 0 , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 9.090990999 \ldots , 5 \pi$

Evaluate the expression for the given value of x. $- x ^ { 4 }$ x = -2

Rewrite the expression with positive exponents and simplify. $\left( 3 p ^ { - 3 } \right) ^ { 4 } \left( - 3 p ^ { - 2 } \right) ^ { - 1 }$

Find the area of the shaded region in the figure. Write your result as a polynomial in standard form.

The length L of the hypotenuse of a right triangle is $L = \sqrt { x ^ { 2 } + y ^ { 2 } }$ where x and y are the lengths of the other two sides. Find the length of the hypotenuse when the other sides measure 1 unit and $\frac { 4 } { 3 }$ units.

Simplify the complex fraction. $\frac { ( x - 6 ) } { \left( \frac { x } { 6 } - \frac { 6 } { x } \right) }$

Evaluate the expression without using a calculator. $4 ^ { - 3 / 2 }$

A rectangular room has a floor space of $\left( x ^ { 2 } + 5 x + 6 \right)$ square feet. If the width of the room is $( x + 2 )$ feet, what is the length?

Identify the rule of algebra illustrated by the statement. -9r - 3r = (-9 - 3)r

Evaluate the expression for the given value of x. expression: $\frac { x + 4 } { x - 4 }$ value: x = -4

Evaluate $\frac { p ^ { 2 } + q ^ { 2 } } { p + q }$ when $p = - 12$ and $q = 9 .$

Perform the operation and write the result in standard form. $\left( 8 x ^ { 4 } - 6 \right) - \left( 5 x ^ { 4 } - 4 x - 9 \right)$

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Exam 1: Fundamental Concepts of Algebra

Perform the multiplication and simplify. q2−15q2−34q+45gq−5q2−9q+8\frac { q ^ { 2 } - 1 } { 5 q ^ { 2 } - 34 q + 45 } \mathbf { g } \frac { q - 5 } { q ^ { 2 } - 9 q + 8 }5q2−34q+45q2−1​gq2−9q+8q−5​

The lowest recorded January temperature for a city is −15∘F- 15 ^ { \circ } \mathrm { F }−15∘F and the highest recorded temperature is 68∘F.68 ^ { \circ } F.68∘F. Find the distance between the numbers to determine the range of temperatures for January.

Simplify the expression. (4v)2(2v)3\left( \frac { 4 } { v } \right) ^ { 2 } \left( \frac { 2 } { v } \right) ^ { 3 }(v4​)2(v2​)3

Write the number in scientific notation. One minute is about 0.000099 week.

Place the correct symbol (<, >, or =) between the pair of real numbers. −∣3∣- | 3 |−∣3∣ −∣−3∣- | - 3 |−∣−3∣

Simplify the expression. 6z6(4z8)36 z ^ { 6 } \left( 4 z ^ { 8 } \right) ^ { 3 }6z6(4z8)3

Completely factor the expression below. 3u+7u2+21+u33 u + 7 u ^ { 2 } + 21 + u ^ { 3 }3u+7u2+21+u3

Determine which numbers in the set are irrational numbers. 1.222…,52,0,−14π3,64,9.090990999…,5π1.222 \ldots , \frac { \sqrt { 5 } } { 2 } , 0 , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 9.090990999 \ldots , 5 \pi1.222…,25​​,0,−314π​,64​,9.090990999…,5π

Evaluate the expression for the given value of x. −x4- x ^ { 4 }−x4 x = -2

Rewrite the expression with positive exponents and simplify. (3p−3)4(−3p−2)−1\left( 3 p ^ { - 3 } \right) ^ { 4 } \left( - 3 p ^ { - 2 } \right) ^ { - 1 }(3p−3)4(−3p−2)−1

Find the area of the shaded region in the figure. Write your result as a polynomial in standard form.

The length L of the hypotenuse of a right triangle is L=x2+y2L = \sqrt { x ^ { 2 } + y ^ { 2 } }L=x2+y2​ where x and y are the lengths of the other two sides. Find the length of the hypotenuse when the other sides measure 1 unit and 43\frac { 4 } { 3 }34​ units.

Simplify the complex fraction. (x−6)(x6−6x)\frac { ( x - 6 ) } { \left( \frac { x } { 6 } - \frac { 6 } { x } \right) }(6x​−x6​)(x−6)​

Evaluate the expression without using a calculator. 4−3/24 ^ { - 3 / 2 }4−3/2

A rectangular room has a floor space of (x2+5x+6)\left( x ^ { 2 } + 5 x + 6 \right)(x2+5x+6) square feet. If the width of the room is (x+2)( x + 2 )(x+2) feet, what is the length?

Identify the rule of algebra illustrated by the statement. -9r - 3r = (-9 - 3)r

Evaluate the expression for the given value of x. expression: x+4x−4\frac { x + 4 } { x - 4 }x−4x+4​ value: x = -4

Evaluate p2+q2p+q\frac { p ^ { 2 } + q ^ { 2 } } { p + q }p+qp2+q2​ when p=−12p = - 12p=−12 and q=9.q = 9 .q=9.

Perform the operation and write the result in standard form. (8x4−6)−(5x4−4x−9)\left( 8 x ^ { 4 } - 6 \right) - \left( 5 x ^ { 4 } - 4 x - 9 \right)(8x4−6)−(5x4−4x−9)

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

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Filters

Perform the multiplication and simplify. $\frac { q ^ { 2 } - 1 } { 5 q ^ { 2 } - 34 q + 45 } \mathbf { g } \frac { q - 5 } { q ^ { 2 } - 9 q + 8 }$

The lowest recorded January temperature for a city is $- 15 ^ { \circ } \mathrm { F }$ and the highest recorded temperature is $68 ^ { \circ } F.$ Find the distance between the numbers to determine the range of temperatures for January.

Simplify the expression. $\left( \frac { 4 } { v } \right) ^ { 2 } \left( \frac { 2 } { v } \right) ^ { 3 }$

Place the correct symbol (<, >, or =) between the pair of real numbers. $- | 3 |$ $- | - 3 |$

Simplify the expression. $6 z ^ { 6 } \left( 4 z ^ { 8 } \right) ^ { 3 }$

Completely factor the expression below. $3 u + 7 u ^ { 2 } + 21 + u ^ { 3 }$

Determine which numbers in the set are irrational numbers. $1.222 \ldots , \frac { \sqrt { 5 } } { 2 } , 0 , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 9.090990999 \ldots , 5 \pi$

Evaluate the expression for the given value of x. $- x ^ { 4 }$ x = -2

Rewrite the expression with positive exponents and simplify. $\left( 3 p ^ { - 3 } \right) ^ { 4 } \left( - 3 p ^ { - 2 } \right) ^ { - 1 }$

The length L of the hypotenuse of a right triangle is $L = \sqrt { x ^ { 2 } + y ^ { 2 } }$ where x and y are the lengths of the other two sides. Find the length of the hypotenuse when the other sides measure 1 unit and $\frac { 4 } { 3 }$ units.

Simplify the complex fraction. $\frac { ( x - 6 ) } { \left( \frac { x } { 6 } - \frac { 6 } { x } \right) }$

Evaluate the expression without using a calculator. $4 ^ { - 3 / 2 }$

A rectangular room has a floor space of $\left( x ^ { 2 } + 5 x + 6 \right)$ square feet. If the width of the room is $( x + 2 )$ feet, what is the length?

Evaluate the expression for the given value of x. expression: $\frac { x + 4 } { x - 4 }$ value: x = -4

Evaluate $\frac { p ^ { 2 } + q ^ { 2 } } { p + q }$ when $p = - 12$ and $q = 9 .$

Perform the operation and write the result in standard form. $\left( 8 x ^ { 4 } - 6 \right) - \left( 5 x ^ { 4 } - 4 x - 9 \right)$