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mathematics
college algebra
Intermediate Algebra 13th Edition Margaret Lial, John Hornsby, Terry McGinnis - Solutions
Solve each system. If the system is inconsistent or has dependent equations, say so. y2z = 0 y + z = 0 z = 0 x + 3x = 4x + 2y
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. y = -4x 8x + 2y = 4
In the triangle below, x is 10 less than y and 20 less than z. Write a system of equations and find the measures of the three angles. bol N
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. -2x + 3y = -16 2x - 5y = 24
Solve each system. If the system is inconsistent or has dependent equations, say so. = 2x + 3y - z = 0 x - 4y + 2z = 0 3x-5y - z = 0
Solve each system. If the system is inconsistent or has dependent equations, say so. X- x - 2y + 1 2 = 4 3 3x - 6у + бу + z = 12 -6x + 12y - 2z = -3
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. 6x + 5y = -7 11y = 1 -6x
Solve each system. If the system is inconsistent or has dependent equations, say so. 4x + y 1 4" x + 1 2x + 2y 2z = 3 3 1 2 4 -2 = 2 = 1
In a certain triangle, the measure of the second angle is 10° greater than three times the first. The third angle measure is equal to the sum of the measures of the other two. Find the measures of the three angles.
The perimeter of a triangle is 70 cm. The longest side is 4 cm less than the sum of the other two sides. Twice the shortest side is 9 cm less than the longest side. Find the length of each side of the triangle. y N X
The measure of the largest angle of a triangle is 12° less than the sum of the measures of the other two. The smallest angle measures 58° less than the largest. Find the measures of the angles.
Extend the method of this section to solve each system. Express the solution in the form (x, y, z, w). y + z = x + 2x + y2 + x - 2y + 3z + w = 18 - x - y + 2 + 2w = 8 w = 5 w = 3
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. 11 2x-5y = 3x + y = 8
Extend the method of this section to solve each system. Express the solution in the form (x, y, z, w). 3x + y2 + 2w = 9 x + y + 2z w = 10 xyz + 3w = -2 -x+y= 2 + w = -6 -
The perimeter of a triangle is 56 in. The longest side measures 4 in. less than the sum of the other two sides. Three times the shortest side is 4 in. more than the longest side. Find the lengths of the three sides. Perimeter = 56 in.
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. -2x + 3y = 1 - 4x + y = -3
In the 2016 Summer Olympics, host Brazil earned 1 more gold medal than silver. The number of silver medals that Brazil earned was the same as the number of its bronze medals. Brazil earned a total of 19 medals. How many of each kind of medal did Brazil earn? C
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. 4x + 3y = 1 3x + 2y = 2
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. 3x +4y=-6 5x +3y=1
Extend the method of this section to solve each system. Express the solution in the form (x, y, z, w). 3x + y 2 + w = −3 -3 2x + 4y + z w = -7 -2x + 3y - 5z + w = 3 5x + 4y5z + 2w = -7
Extend the method of this section to solve each system. Express the solution in the form (x, y, z, w). x - 3y +72+ w = 11 2x + 4y +62 - 3w = -3 3x + 2y + 2 + 2w = 19 4x + y 3z + w = 22 -
In 2017, the average Facebook user in the United States spent 693 more minutes per month using Facebook than the average Instagram user spent using Instagram. The average Instagram user spent 36 fewer minutes per month using Instagram than the average Snapchat user spent using Snapchat. The total
Tickets for a Harlem Globetrotters show cost $30 for upper level, $51 for center court, or $76 for floor seats. Nine times as many upper level tickets were sold as floor tickets, and the number of upper level tickets sold was 55 more than the sum of the number of center court tickets and floor
A circle has an equation of the following form.It is a fact from geometry that given three noncollinear points—that is, points that do not all lie on the same straight line—there will be a circle that contains them. For example, the points (4, 2), (-5, -2), and (0, 3) lie on the circle whose
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. 7x + 2y = 6 -14x - 4y = -12 ||
A circle has an equation of the following form.It is a fact from geometry that given three noncollinear points—that is, points that do not all lie on the same straight line—there will be a circle that contains them. For example, the points (4, 2), (-5, -2), and (0, 3) lie on the circle whose
A circle has an equation of the following form.It is a fact from geometry that given three noncollinear points—that is, points that do not all lie on the same straight line—there will be a circle that contains them. For example, the points (4, 2), (-5, -2), and (0, 3) lie on the circle whose
A circle has an equation of the following form.It is a fact from geometry that given three noncollinear points—that is, points that do not all lie on the same straight line—there will be a circle that contains them. For example, the points (4, 2), (-5, -2), and (0, 3) lie on the circle whose
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. 3x +3y = 0 4x + 2y = 3
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. 8x + 4y = 0 4x - 2y = 2
A wholesaler supplies college t-shirts to three college bookstores: A, B, and C. The wholesaler recently shipped a total of 800 t-shirts to the three bookstores. Twice as many t-shirts were shipped to bookstore B as to bookstore A, and the number shipped to bookstore C was 40 less than the sum of
An office supply store sells three models of computer desks: A, B, and C. In one month, the store sold a total of 85 computer desks. The number of model B desks was five more than the number of model C desks. The number of model A desks was four more than twice the number of model C desks. How many
A plant food is to be made from three chemicals. The mix must include 60% of the first and second chemicals. The second and third chemicals must be in the ratio of 4 to 3 by weight. How much of each chemical is needed to make 750 kg of the plant food?
A circle has an equation of the following form.It is a fact from geometry that given three noncollinear points—that is, points that do not all lie on the same straight line—there will be a circle that contains them. For example, the points (4, 2), (-5, -2), and (0, 3) lie on the circle whose
A circle has an equation of the following form.It is a fact from geometry that given three noncollinear points—that is, points that do not all lie on the same straight line—there will be a circle that contains them. For example, the points (4, 2), (-5, -2), and (0, 3) lie on the circle whose
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. 5x-5y=3 x - y = 12
The National Hockey League uses a point system to determine team standings. A team is awarded 2 points for a win (W), 0 points for a loss in regulation play (L), and 1 point for an overtime loss (OTL). Use this information to solve each problem.During the 2016–2017 NHL regular season, the Anaheim
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. 2x - 3y = 7 -4x+6y= 14
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. x + y = 2x - 2y = 0 0
The National Hockey League uses a point system to determine team standings. A team is awarded 2 points for a win (W), 0 points for a loss in regulation play (L), and 1 point for an overtime loss (OTL). Use this information to solve each problem.During the same NHL regular season, the Los Angeles
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. 3 la ala 2x + y = 3 -x + 1 3 3 = 1 =
There are three kinds of bait boxes—those containing fish, those containing bugs, and those containing worms. Although the bait boxes look alike, each kind has a different weight. Use the information in FIGURE A to write a system of three equations, and solve it to determine the weight of each
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. + 3x + 3y = 0 -2x - y = 0
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. X =x + 1 तितकि || 2 || = 2 00/ 8 5 5
How many ounces of 5% hydrochloric acid, 20% hydrochloric acid, and water must be combined to obtain 10 oz of solution that is 8.5% hydrochloric acid if the amount of water used must equal the total amount of the other two solutions?
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. 1 =x + 1 य 3 1 5 x + 2y 2 || = 49 18 4 3
Solve each system using the method of your choice. 3x + y = -7 x-y=-5
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. 10 1 있 + 입 입 ן alulo
To minimize the amount of work required, determine whether to use the substitution or the elimination method to solve each system. Explain. Do not actually solve. (a) 3x + y = −7 x - y = -5 (b) 6x - y = 5 y = 11x (c) 3x - 2y = 0 9x + 8y = 7
Solve each system using the method of your choice. 6x - y = 5 y=11x
Solve each system using the method of your choice. 3x-2y = 0 9x + 8y = 7
Explain why System A would be more difficult to solve by substitution than System B. System A: 3x + 7y = 19 8x - 5y = 4 System B: x + 7y = 8 3x - 2y = 4
Solve each system using the method of your choice. 3x-5y = 7 2x + 3y = 30
Solve each system using the method of your choice. 2x +3y=10 -3x + y = 18
Solve each system using the method of your choice. x + y = 10 2x - y = 5
Solve each system using the method of your choice. y = y = 1 5 x + 1 3 5*- - 3
Solve each system using the method of your choice. 0.2x + 0.5y = 6 0.4x + y = 9
Solve each system using the method of your choice. 7x - 8y = 0 2x + 5y = 0
Solve each system using the method of your choice. 1 2 4 4x - y = -2 1 -X 1 1 8 ||
Solve each system using the method of your choice. 0.3x + 0.2y = 0.4 0.5x + 0.4y = 0.7
Solve each system using the method of your choice. 1 + -x 6 3 1 -x + 1 4 1 드 = 8 = 12
Write the equations of each system in slope-intercept form, and use the results to determine how many solutions the system has. Do not actually solve. 2x = -3y + 1 6x = -9y + 3
Write the equations of each system in slope-intercept form, and use the results to determine how many solutions the system has. Do not actually solve. 3x + 7y = 4 6x + 14y = 3
Answer each question using the graphs provided.The figure shows graphs that represent supply and demand for a certain brand of low-fat frozen yogurt at various prices per half-gallon (in dollars).(a) At what price does supply equal demand?(b) For how many half-gallons does supply equal demand?(c)
Answer each question using the graphs provided.Sharon compared the monthly payments she would incur for two types of mortgages: fixed rate and variable rate. Her observations led to the following graphs.(a) For which years would the monthly payment be more for the fixed-rate mortgage than for the
Write the equations of each system in slope-intercept form, and use the results to determine how many solutions the system has. Do not actually solve. -x + 2y = 8 4x8y = 1
The graph shows college student enrollment (in thousands) for three states from 2011 through 2016.(a) During what years did the number of college students enrolled in Colorado exceed that for Utah?(b) Between what two consecutive years did Utah first have the highest enrollment?(c) In what year
Write the equations of each system in slope-intercept form, and use the results to determine how many solutions the system has. Do not actually solve. 5x = -2y + 1 10x = 4y + 2
The following systems can be solved by elimination. One way to do this is to letSubstitute, solve for p and q, and then find x and y. p = = and q = . X y
The following systems can be solved by elimination. One way to do this is to letSubstitute, solve for p and q, and then find x and y. p = = and q = . X y
The following systems can be solved by elimination. One way to do this is to letSubstitute, solve for p and q, and then find x and y. p = = and q = . X y
The graph shows numbers of nuclear weapons possessed by the United States and USSR/ Russia from 1950 through 2017.(a) In what year were the numbers of nuclear weapons approximately equal?(b) Approximately how many nuclear weapons did each country possess in that year?(c) Express the point of
Make up a system of the following form, where a, b, c, d, e, and f are consecutive integers. Solve the system. ax + by = c dx + ey = f
Solve by any method. Assume that a and b represent nonzero constants. ax + by = c ax-2by 2by = c
Solve by any method. Assume that a and b represent nonzero constants. ax + by = 2 - ax + 2by = 1
Solve by any method. Assume that a and b represent nonzero constants. 2ax - y = 3 y = 5ax
Solve by any method. Assume that a and b represent nonzero constants. Зах + 2y = 1 -ax + y = 2 +
Determine whether each statement is true or false. If false, correct the righthand side of the statement. (ab)² = ab²
Match each description in Column I with the correct polynomial in Column II. Choices in Column II may be used once, more than once, or not at all. I (a) Monomial of degree 2 (b) Trinomial of degree 5 (c) Polynomial with leading coefficient 1 (d) Binomial in descending powers (e) Term with degree
In scientific notation, a number is written with a decimal point (before / after) the first nonzero digit and multiplied by a ________ of 10. A number written in scientific notation is expressed in the form__________ ×__________ , where 1 ≤ |a| < 10 and n is an integer.
Work each problem involving polynomial functions and function notation.A polynomial function is a function defined by a ________ in (one / two / three) variable(s), consisting of one or more (factors / terms) and usually written in descending ________ of the variable.
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. x - 4y = 2 4x 16y=8
Three kinds of tickets are available for a rock concert: “up close,” “in the middle,” and “far out.” “Up close” tickets cost $10 more than “in the middle” tickets. “In the middle” tickets cost $10 more than “far out” tickets. Twice the cost of an “up close” ticket is
Solve each system. 5.5x2.5y + 1.62 = 11.83 2.2x + 5.0y 0.12 = -5.97 - 3.3x - 7.5y + 3.2z = 21.25
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. -x - 4y = -14 y = 2x - 1
A survey measured public recognition of some popular contemporary advertising slogans. Complete the results shown in the table if 2500 people were surveyed.Point A has coordinates (-2, 6) and point B has coordinates (4, -2). Percent Recognition (nearest tenth of a percent) Slogan (product or
Solve each system. 2xy + 32 = 6 3z x + 2y 2y + 2 = 8 z = 1
For Valentine’s Day, Ms. Sweet will mix some $6-per-lb nuts with some $3-per-lb chocolate candy to obtain 100 lb of mix, which she will sell at $3.90 per lb. How many pounds of each should she use? Nuts Chocolate Mixture Number of Pounds X y 100 Price per Pound (in dollars) Value (in dollars)
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. -3x - 5y = -17 y = 4x + 8
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. 4x - 5y = -11 x + 2y = 7
How many gallons each of 25% alcohol and 35% alcohol should be mixed to obtain 20 gal of 32% alcohol? Gallons of Solution X y 20 Percent (as a decimal) 25% = 0.25 35% = 0.35 32% Gallons of Pure Alcohol
Solve each system. 4x + 2y 32 = 6 x - 4y + z 2 -x + = -4 2z = 2
The sum of the measures of the angles of any triangle is 180°. The largest angle measures 10° less than the sum of the other two. The measure of the middle-sized angle is the average of the other two. Find the measures of the three angles. Do xº
How many liters each of 15% acid and 33% acid should be mixed to obtain 120 L of 21% acid? Liters of Solution X y 120 Percent (as a decimal) 15% = 0.15 33% = 21% Liters of Pure Acid
Solve each system. 2x + 3y 4z = 4 x 6y + z = -16 -x + 32 = 8
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. 3x - y = 10 2x + 5y = 1
A party mix is made by adding nuts that sell for $2.50 per kg to a cereal mixture that sells for $1 per kg. How much of each should be added to obtain 30 kg of a mix that will sell for $1.70 per kg? Nuts Cereal Mixture Number of Kilograms X y Price per Kilogram (in
Solve each system. 2x + y = 6 зу - 2z = -4 3x-5z = = -1
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. 2x - y = 5x - 2y = 4 8
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. 3x + 2y = 6 4x + y = 3
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