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study help
mathematics
college algebra
College Algebra 11th Edition Michael Sullivan, Michael Sullivan III - Solutions
A fruit drink is made by mixing juices. Such a drink with 50% juice is to be mixed with a drink that is 30% juice to obtain 200 L of a drink that is 45% juice. How much of each should be used? 50% Juice 30% Juice Mixture Liters of Drink X y Percent Liters of (as a Pure Juice decimal) 0.50 0.30 0.45
How many liters each of 8% and 20% hydrogen peroxide should be mixed together to obtain 8 L of 12.5% solution?
Solve each system. 4x - 8y = -7 4y + z = 7 -8x + 2 = −4 -4
A total of $3000 is invested, part at 2% simple interest and part at 4%. If the total annual return from the two investments is $100, how much is invested at each rate? Principal Rate (in dollars) (as a decimal) X y 3000 0.02 0.04 XXXXXX Interest (in dollars) 0.02x 0.04y 100
Solve each system. If a system is inconsistent or has dependent equations, say so. 2xy + 3z = 0 5x + y z = 0 -2x + 3y + 4z = 0
Solve each system. -5x + 2y + z = 5 -3x - 2y 2 = 3 -x+6y= 1
An investor will invest a total of $15,000 in two accounts, one paying 4% annual simple interest and the other 3%. If he wants to earn $550 annual interest, how much should he invest at each rate? Principal Rate (in dollars) (as a decimal) X y 15,000 0.04 0.03 Interest (in dollars)
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. 3x-4y = -22 -3x + y = 0
Solve each system. 0 = N 15/00 + -7 || 1 2- N 1100 1 तलि बलि + - -5 + X = 2. Nim -Tin min बॉल -
Solve each inequality. 2x + 3 > 5 or x 1 ≤ 6
Noemi sells real estate. On three recent sales, she made 10% commission, 6% commission, and 5% commission. Her total commissions on these sales were $17,000, and she sold property worth $280,000. If the 5% sale amounted to the sum of the other two, what were the three sales prices?
Point A has coordinates (-2, 6) and point B has coordinates (4, -2).What is the standard form of the equation of line AB?
Solve each system by graphing. 2x+3y = -6 x-3y = -3
In the great baseball year of 1961, Yankee teammates Mickey Mantle, Roger Maris, and Yogi Berra combined for 137 home runs. Mantle hit 7 fewer than Maris, and Maris hit 39 more than Berra. What were the home run totals for each player?
Solve each problem. Graph the line having slope 2/3 and passing through the point (-1, -3).
Two days at Busch Gardens (Tampa Bay) and 3 days at Universal Studios Florida (Orlando) cost $510, while 4 days at Busch Gardens and 2 days at Universal Studios cost $580. (Prices are based on single-day admissions.) What was the cost per day for each park?
A regulation National Hockey League ice rink has perimeter 570 ft. The length of the rink is 30 ft longer than twice the width. What are the dimensions of an NHL ice rink?
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. 4x + y = 6 y = 2x
Solve each system. 6.2x 1.4y+2.4z = -1.80 - 3.1x + 2.8y 0.2z = 5.68 9.3x8.4y4.8z = -34.20
A plane flies 560 mi in 1.75 hr traveling with the wind. The return trip later against the same wind takes the plane 2 hr. Find the rate of the plane and the speed of the wind. Let x = the rate of the plane and y = the speed of the wind. With Wind Against Wind t d r x+y 1.75 2
A jar contains only pennies, nickels, and dimes. The number of dimes is one more than the number of nickels, and the number of pennies is six more than the number of nickels. How many of each denomination are in the jar, if the total value is $4.80?
On the basis of average total costs per day for business travel to New York City and Washington, DC (which include a hotel room, car rental, and three meals), 2 days in New York and 3 days in Washington cost $2484, while 4 days in New York and 2 days in Washington cost $3120. What was the average
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. 2x - y = 6 y = 5x
Two angles of a triangle have the same measure. The measure of the third angle is 4° less than twice the measure of each of the equal angles. Find the measures of the three angles. xº (2x-4) ot
Solve each system. 2x - 3y + 2z = -1 x + 2y + 2 = 17 z 2y - 2 = 7
Tickets to a production of A Midsummer Night’s Dream at Broward College cost $5 for general admission or $4 with a student ID. If 184 people paid to see a performance and $812 was collected, how many of each type of ticket were sold?
In the 2016 Summer Olympics in Rio de Janeiro, Japan earned 9 fewer gold medals than bronze. The number of silver medals earned was 34 less than twice the number of bronze medals. Japan earned a total of 41 medals. How many of each kind of medal did Japan earn?
In Problems 5–16, write a general formula to describe each variation. V varies directly with x³; V = 367 when x = 3
In Problems 5–16, write a general formula to describe each variation. v varies directly with t; v = 16 when t = 2
In Problems 5–16, write a general formula to describe each variation. A varies directly with x²; A = 47 when x = 2
In Problems 5–16, write a general formula to describe each variation. y varies inversely with Vx; y = 4 when x = 9
The equation of a circle can be changed from general form to standard from by doing which of the following? (a) Completing the squares (b) Solving for x (c) Solving for y (d) Squaring both sides
If a line slants downward from left to right, then which of the following describes its slope? (a) Positive.(b) Zero.(c) Negative.(d) Undefined.
True or False The center of the circle (x + 3)2 + (y - 2)2 = 13 is (3, -2).
In Problems 5–16, write a general formula to describe each variation. y varies directly with x; y = 2 when x = 10
Multiple Choice Choose the best description for the model y = kx/z, if k is a nonzero constant.(a) Y varies directly with x and z. (b) Y is inversely proportional to x and z. (c) Y varies directly with x and inversely with z. (d) Y is directly proportion to z and inversely
The x-intercepts of the graph of an equation are those x-values for which __________.
Which equation represents a joint variation model? (a) y = 5x 5 (c) y = X (b) y = x² + z² 5xz (d) y W
True or False The equation 3x + 4y = 6 is written in general form.
For the line 2x + 3y = 6, the x-intercept is _____ and the y-intercept is _____.
If x and y are two quantities, then y is directly proportional to x if there is a nonzero number k for which ______ .
Choose the formula for finding the slope m of a nonvertical line that contains the two distinct points (x1, y1) and (x2, y2). (a) m = (c) m = Y2X₂ yi - X1 X2X1 - Y2Y1 X₁y₁ (b) m = Y₁Y2 (d) m = y2-X1 X2Y1 Y2Y1 X2 - X1 X₁ X₂ X1 # x₂
In Problems 5–16, write a general formula to describe each variation. z varies directly with the sum of the squares of x and y; z = 26 when x = 5 and y = 12
In Problems 5–16, write a general formula to describe each variation. F varies inversely with d²; F = 10 when d = 5
Choose the correct statement about the graph of the line y = -3. (a) The graph is vertical with x-intercept -3. (b) The graph is horizontal with y-intercept -3. (c) The graph is vertical with y-intercept -3. (d) The graph is horizontal with x-intercept -3.
To test whether the graph of an equation is symmetric with respect to the origin, replace __________ in the equation and simplify. If an equivalent equation results, then the graph is symmetric with respect to the origin. (a) x by -x (c) x by -x and y by-y (b) y by-y (d) x by -y and y by -x
In Problems 5–16, write a general formula to describe each variation. T varies directly with the cube root of x and the square of d; T 18 when x = 8 and d = 3
In Problems 13–18, determine which of the given points are on the graph of the equation. Equation: y = x - √x Points: (0, 0); (1, 1); (2,4)
In Problems 13–24, write the standard form of the equation and the general form of the equation of each circle of radius r and center (h, k). Graph each circle. r = 2; (h, k) = (0,0)
In Problems 5–16, write a general formula to describe each variation. M varies directly with the square of d and inversely with the square root of x; M = 24 when x = 9 and d = 4
In Problems 15 and 16, plot each point in the xy-plane. State which quadrant or on what coordinate axis each point lies. (a) A = (-3,2) (b) B= (6,0) (c) C = (-2,-2) (d) D = (6,5) (e) E= (0, -3) F (6,-3) (f)
In Problems 5–16, write a general formula to describe each variation. The square of T varies directly with the cube of a and inversely with the square of d; T = 2 when a = 2 and d = 4
In Problems 13–24, write the standard form of the equation and the general form of the equation of each circle of radius r and center (h, k). Graph each circle.r = 3; (h, k) = (1,0)
In Problems 19–32, find the distance d between the points P1 and P2. P₁ = (2,-3); P₂ = (4,2)
The velocity v of a falling object is directly proportional to the time t of the fall. If, after 2 seconds, the velocity of the object is 64 feet per second, what will its velocity be after 3 seconds?
In Problems 25–32, graph the line that contains the point P and has slope m. P= (1, 2); m = 3
In Problems 19–32, find the distance d between the points P1 and P2. P₁ = (-7,3); P₂ = (4,0)
In Problems 19–32, find the distance d between the points P1 and P2. P₁ = (-1,0); P₂ = (2,4)
In Problems 13–24, write the standard form of the equation and the general form of the equation of each circle of radius r and center (h, k). Graph each circle. r = 2√5; (h, k) = (-3,2)
In Problems 13–24, write the standard form of the equation and the general form of the equation of each circle of radius r and center (h, k). Graph each circle. r = V13; (h, k) = (5, -1)
The distance s that an object falls is directly proportional to the square of the time t of the fall. If an object falls 16 feet in 1 second, how far will it fall in 3 seconds? How long will it take an object to fall 64 feet?
In Problems 19–32, find the distance d between the points P1 and P2. P₁ = (3,-4); P₂ = (5,4)
In Problems 17–24, plot each pair of points and determine the slope of the line containing the points. Graph the line. (-3,-1); (2, -1)
In Problems 19–32, find the distance d between the points P1 and P2. YA 2-P, = (2, 1) P = (0, 0) -2 -1 2 x
In Problems 19–32, find the distance d between the points P1 and P2. P₂=(-2,2) -2 YA 2 -1 P₁ = (1, 1) 2 X
The monthly payment p on a mortgage varies directly with the amount borrowed B. If the monthly payment on a 15-year mortgage is $8.99 for every $1000 borrowed, find a linear equation that relates the monthly payment p to the amount borrowed B for a mortgage with these terms. Then find the monthly
In Problems 17–24, plot each pair of points and determine the slope of the line containing the points. Graph the line. (-1,1); (2,3)
In Problems 17–22, write an equation that relates the quantities.The force F (in newtons) of attraction between two bodies varies jointly with their masses m and M (in kilograms) and inversely with the square of the distance d (in meters) between them. The constant of proportionality is G = 6.67
In Problems 5–16, write a general formula to describe each variation. The cube of z varies directly with the sum of the squares of x and y; z = 2 when x = 9 and y = 4
In Problems 17–22, write an equation that relates the quantities.The perimeter p of a rectangle varies jointly with the sum of the lengths of its sides l and w. The constant of proportionality is 2.
In Problems 17–22, write an equation that relates the quantities.The volume V of a sphere varies directly with the cube of its radius r. The constant of proportionality is 4π/3.
In Problems 19–32, find the distance d between the points P1 and P2. P₁ = (-4,-3); P₂ = (6,2)
In Problems 25–32, graph the line that contains the point P and has slope m. P = (2, 4); m = 3 4
The elongation E of a spring balance varies directly with the applied weight W (see the figure). If E = 3 when W = 20, find E when W = 15. 00 3 W TEI
In Problems 19–32, find the distance d between the points P1 and P2. P₁ = (5,-2); P₂ = (6,1)
The rate of vibration of a string under constant tension varies inversely with the length of the string. If a string is 48 inches long and vibrates 256 times per second, what is the length of a string that vibrates 576 times per second?
In Problems 31–40, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis; (b) the y-axis; (c) the origin. (4, -2)
In Problems 33–38, a point on a line and its slope are given. Find the point-slope form of the equation of the line. P = (1,3); m = 2/5
In Problems 33–38, a point on a line and its slope are given. Find the point-slope form of the equation of the line. P = (2,4); m = 3 4
In Problems 33–38, a point on a line and its slope are given. Find the point-slope form of the equation of the line. P = (-1,3); m = 0
The weight of an object above the surface of Earth varies inversely with the square of the distance from the center of Earth. If Maria weighs 125 pounds when she is on the surface of Earth (3960 miles from the center), determine Maria’s weight when she is at the top of Denali (3.8 miles from the
The weight of a body above the surface of Earth varies inversely with the square of the distance from the center of Earth. If a certain body weighs 55 pounds when it is 3960 miles from the center of Earth, how much will it weigh when it is 3965 miles from the center?
The intensity I of light (measured in foot-candles) varies inversely with the square of the distance from the bulb. Suppose that the intensity of a 100-watt light bulb at a distance of 2 meters is 0.075 foot-candle. Determine the intensity of the bulb at a distance of 5 meters.
The force exerted by the wind on a plane surface varies directly with the area of the surface and the square of the velocity of the wind. If the force on an area of 20 square feet is 11 pounds when the wind velocity is 22 miles per hour, find the force on a surface area of 47.125 square feet
In Problems 33–38, a point on a line and its slope are given. Find the point-slope form of the equation of the line. P = (2,−4); m = 0
The volume V of a right circular cylinder varies directly with the square of its radius r and its height h. The constant of proportionality is π. See the figure. Write an equation for V. r ㅈ h
In Problems 41–52, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, the origin or none of these. -3 у 3 -3 3X
In Problems 19–32, find the distance d between the points P1 and P2. P₁ = (-0.2, 0.3); P₂ = (2.3, 1.1)
In Problems 25–32, graph the line that contains the point P and has slope m. P = (-1,3); m = 0
In Problems 19–30, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. 9x² + 4y 36
At the corner Shell station, the revenue R varies directly with the number g of gallons of gasoline sold. If the revenue is $34.08 when the number of gallons sold is 12, find a linear equation that relates revenue R to the number g of gallons of gasoline sold. Then find the revenue R when the
In Problems 19–32, find the distance d between the points P1 and P2. P₁ (1.2, 2.3); P₂ = (-0.3, 1.1)
In Problems 25–32, graph the line that contains the point P and has slope m. P = (2, 4); m = 0
In Problems 19–30, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. 4x² + y = 4
In Problems 31–40, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis; (b) the y-axis; (c) the origin. (3,4)
In Problems 25–32, graph the line that contains the point P and has slope m. P= (0, 3); slope undefined
The cost C of roasted almonds varies directly with the number A of pounds of almonds purchased. If the cost is $23.75 when the number of pounds of roasted almonds purchased is 5, find a linear equation that relates the cost C to the number A of pounds of almonds purchased. Then find the cost C when
In Problems 25–32, graph the line that contains the point P and has slope m. P= (-2, 0); slope undefined
Suppose that the demand D for candy at the movie theater is inversely related to the price p. (a) When the price of candy is $2.75 per bag, the theater sells 156 bags of candy. Express the demand for candy in terms of its price. (b) Determine the number of bags of candy that will be sold
In Problems 19–32, find the distance d between the points P1 and P2. P₁ = (a, a); P₂= (0,0)
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