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mathematics
college algebra
Intermediate Algebra 13th Edition Margaret Lial, John Hornsby, Terry McGinnis - Solutions
In Problems 49 and 50, graph each system of inequalities. Jy ≤ x² [xy ≤ 4
In Problems 46–48, graph each system of inequalities. State whether the graph is bounded or unbounded, and label the corner points. x ≥ 0 y = 0 y ≤ 8 x + 2y = 2 2x +
In Problems 49 and 50, graph each system of inequalities. [x² + y² ≤ 16 [(x + y = 2
In Problems 69–80, find the sum of each sequence. 40 Σκ k=1
In Problems 69–80, find the sum of each sequence. 24 Σ(-k) k=1
In Problems 69–80, find the sum of each sequence. 50 Σ8 k=1
In Problems 69–80, find the sum of each sequence. 20 Σ (5k + 3) k=1
In Problems 69–80, find the sum of each sequence. 60 Σ (24) k=10
In Problems 69–80, find the sum of each sequence. 16 Σ (k2 + 4) k=1
In Problems 44 and 45 graph each inequality. y ≤ x2
In Problems 69–80, find the sum of each sequence. 40 Σ(-3k) k=8
In Problems 69–80, find the sum of each sequence. 20 Σκ k=5
In Problems 69–80, find the sum of each sequence. 14 Σ (k2 – 4) k=0
In Problems 69–80, find the sum of each sequence. 24 Σκ k=4
A highly reflective mirror reflects 95% of the light that falls on it. In a light box having walls made of the mirror, the light reflects back-and-forth between the mirrors. (a) If the original intensity of the light is I0 before it falls on a mirror, write the nth term of the sequence that
Problems 105–111 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.If $2500 is invested at 3% compounded monthly, find the amount that results after a period of 2 years.
Problems 105–111 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Multiply: (3x - 2)3
Problems 105–111 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Find an equation of the parabola with vertex (-3, 4) and focus (1, 4).
Problems 105–111 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Find the horizontal asymptote, if one exists, of f(x) 9x 3x² - 2x - 1
Which elements of each set are (a) Natural numbers, (b) Whole numbers, (c) Integers,(d) Rational numbers, (e) Irrational numbers, (f) Real numbers? 3 13 40 {-8, -V5, -0.6, 0, 2, V3, m, 5, 12, 17, 20 - 4
Simplify each expression.a + a
Multiply or divide as indicated. Write answers in lowest terms as needed. 4 5 6 7
Match each statement in Column I with the appropriate property in Column II. Answers may be used more than once. I (a) 6+ (-6) = 0 (b) −2+(3+6)=(−2+ 3) + 6 (c) 5x + 15x = (5 +15)x (d) 13 0 0 . (e) −9+0= -9 (f) 4.1 = 4 (g) (a + b) + c = (b + a) + c II A. Distributive property B. Inverse
Evaluate each expression. (0.3) ³
Simplify each expression. - (2d-f)
Multiply or divide as indicated. Write answers in lowest terms as needed. 5 2 97
Simplify each expression. -(3m-n)
Evaluate each expression. (0.1) 3
Multiply or divide as indicated. Write answers in lowest terms as needed. 2 15 3100 8
Evaluate each expression. 5 3
Find each sum or difference.-6 - 5
Determine whether each statement is true or false. If it is false, tell why.Every integer is a whole number.
Find each sum or difference.-8 - 17
Determine whether each statement is true or false. If it is false, tell why.Every natural number is an integer.
A father opened a savings account for his daughter on her first birthday, depositing $1000. Each year on her birthday he deposits another $1000, making the last deposit on her 21st birthday. If the account pays 1.5% interest compounded annually, how much is in the account at the end of the day on
Evaluate S6 for each arithmetic sequence. an 1 2 +7
Find the indicated term of each binomial expansion. 8 (x + ²) ²: 2 seventh term
Evaluate S6 for each arithmetic sequence. an || 2 -=n+6 3
Find the sum of the first six terms of the arithmetic sequence with a1 = 8 and d = 2.
Find the sum of the geometric series 15 − 6 + 1/2/2 - 24 5 25 +
Use the remainder theorem to evaluate ƒ(k). f(x) = -x³-5x² - 4x - 2; k = -4
Use the remainder theorem to evaluate ƒ(k). f(x) = x³ + 3x²-x+ 5; k= −1
Find the indicated term of each binomial expansion. 15 (a+b)"; 3 ; eighth term
Use the remainder theorem to evaluate ƒ(k). f(x) = x³ + 5x² 3x + 4; k= 3
Use the remainder theorem to evaluate ƒ(k). f(x) = 2x³ 4x² + 5x-33; k= 3
Write each series using summation notation.3 + 4 + 5 + 6 + 7
A teacher puts $1000 in a retirement account at the end of each quarter (1/4 of a year) for 15 yr. If the account pays 2.2% annual interest compounded quarterly, how much will be in the account at that time?
Use the remainder theorem to evaluate ƒ(k). f(x) = x³ 3x² + 4x - 4; k = 2
Find each sum or difference. 19+ (-13)
Write each fraction in lowest terms. 132 77
Perform the indicated operations. -2[3 (1-2) + 2] √9(-3) - (-2)
Write each expression using exponents. (0.8) (0.8)
We can show a connection between dividing one polynomial by another and factoring the first polynomial. Let ƒ(x) = 2x2 + 5x - 12. Work Exercises in order.Use the conclusion reached in Exercise 45 to decide whether x - 3 is a factor of g(x) = 3x3 - 4x2 - 17x + 6. If so, factor g(x) completely.Data
Simplify each expression.6a + 5a
Use set-builder notation to describe each set.{11, 12, 13, 14}
List the elements in each set.{y|y is an integer greater than 8}
Determine whether each statement is true or false. If it is false, correct the statement so that it is true.The product of 5 positive factors and 5 negative factors is positive.
Complete each statement.Like terms are terms with the _______ variables raised to the _______ powers.
List the elements in each set.{p|p is an integer less than 3}
Suppose that a nonlinear system is composed of equations whose graphs are those described, and the number of points of intersection of the two graphs is as given. Make a sketch satisfying these conditions. A parabola and a hyperbola; two points
We have seen that the center of an ellipse may be shifted away from the origin. The same process applies to hyperbolas. For example, the hyperbolahas the same graph asbut it is centered at (-5, 2), as shown at the right. Graph each hyperbola with center shifted away from the origin. (x +
We have seen that the center of an ellipse may be shifted away from the origin. The same process applies to hyperbolas. For example, the hyperbolahas the same graph asbut it is centered at (-5, 2), as shown at the right. Graph each hyperbola with center shifted away from the origin. (x +
Answer each question, and give a short explanation.How many points are there on the graph of (x-4)² + (y - 1)² =-1?
Solve each problem. See FIGURE 16 and use the fact that c2 = a2 - b2, where a2 > b2. Round answers to the nearest tenth.The orbit of Mars is an ellipse with the sun at one focus. For x and y in millions of miles, the equation of the orbit is(a) Find the greatest distance (apogee) from Mars to
Graph. f(x) = -3x + 5
Graph each system of inequalities. y < x² y> -2 x + y -6
We can show a connection between dividing one polynomial by another and factoring the first polynomial. Let ƒ(x) = 2x2 + 5x - 12. Work Exercises in order.Solve ƒ(x) = 0.
Graph each step function. f(x) = [x + 2]
Solve each system. 3x²2y² = 12 x² + 4y² = 18
Solve each system using the elimination method or a combination of the elimination and substitution methods. 5x² = 20 - 5y² 2y² = 2 x² -
Which fraction is not equal to 5/9? A. 15 27 B. 30 54 C. 40 74 D. 55 99
Complete the table of fraction, decimal, and percent equivalents. Fraction in Lowest Terms Decimal 1.5 Percent
Write each fraction in lowest terms. 8 16
Graphon a number line. 5 {-3.0.75, 3, 5, 6.3}
Complete each statement and give an example.The difference of two negative numbers is negative if _____________ .
Based on the discussions of ellipses in the previous section and of hyperbolas in this section, match each equation with its graph. A. C. 19: 0 3 X X B. D. -3-0 X
Write each fraction in lowest terms. 4 " 12
Fill in each blank with the appropriate response. The graph of the solution set of the system y > x2 + 1 x² x2 + v2 9 y 1 4
LetSimplify the elements of A as necessary, and then list those elements of A that belong to the specified set.Whole numbers A = {-V6, -1, -0.5, 0, 3, V25, 7.5, 244, V-4}.
Perform the indicated operations. 7-42+2(6) + (-4)²
Determine whether each statement is true or false. If it is false, correct the statement so that it is true.The product of 10 positive factors and 10 negative factors is positive.
Complete each statement.The associative property is used to change the _______ of three terms or factors.
Without actually plotting points, match each function defined by the absolute value expression with its graph. A. C. ⠀⠀⠀ ⠀⠀⠀⠀ .......... ⠀⠀ ..... . LULL... a .... 2. ........ ...... : X B. D. -02 X
List the elements in each set.{z|z is an integer less than or equal to 4}
Graph. 4y > 3x - 12 x2 < 16 - y2
Write each expression using exponents. (-4)(-4)(-4)(-4)
Graph. f(x)=√9-x²
Determine whether each statement is true or false. If it is false, correct the statement so that it is true.In the exponential expression -25, the base is -2.
Complete each statement.When simplifying an expression, only _______ terms can be combined.
Complete each statement and give an example.The quotient formed by any nonzero number divided by 0 is _____________ , and the quotient formed by 0 divided by any nonzero number is _____________ .
Graph each system of inequalities. y = -x² y≥x-3 y≤ -1 x < 1
List the elements in each set.{a|a is an even integer greater than 8}
Solve each problem. See FIGURE 16 and use the fact that c2 = a2 - b2, where a2 > b2. Round answers to the nearest tenth.The orbit of Venus around the sun (one of the foci) is an ellipse with equationwhere x and y are measured in millions of miles.(a) Find the greatest distance (apogee) between
Use the remainder theorem to decide whether the given number is a solution of the equation. x³ 2x² 3x + 10 = 0; x = -2 -
Fill in each blank with the correct response.The value of the sum 3 Σ (i + 2) is . i=1
Use the remainder theorem to decide whether the given number is a solution of the equation. x4 + 2x³ 3x² + 8x = 8; x = -2 -
Use the remainder theorem to decide whether the given number is a solution of the equation. x4x36x² + 5x = -10; x = -2
Use the remainder theorem to decide whether the given number is a solution of the equation. 3x³ + 2x²2x + 11 = 0; x = -2
Evaluate S6 for each arithmetic sequence.an = 3n - 8
We can show a connection between dividing one polynomial by another and factoring the first polynomial. Let ƒ(x) = 2x2 + 5x - 12. Work Exercises in order.Factor ƒ(x).
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