Solve the equation, using the quadratic formula. If the equation has no real solution, so state. 5x2 - 4x = -2
> (a) Determine whether the parabola will open upward or downward. (b) Find the equation of the axis of symmetry. (c) Find the vertex. (d) Find the y-intercept. (e) Find the x-intercepts if they exist. (f) Sketch the graph. (g) Find the domain and range of
> O. Selling Chocolates Ryan sells chocolate on the Internet. His monthly profit, p, in dollars, can be estimated by p = 15n - 300, where n is the number of dozens of chocolates he sells in a month. (a) Graph p = 15n - 300, for n ( 60. (b) From the graph,
> (a) Determine whether the parabola will open upward or downward. (b) Find the equation of the axis of symmetry. (c) Find the vertex. (d) Find the y-intercept. (e) Find the x-intercepts if they exist. (f) Sketch the graph. (g) Find the domain and range of
> Factor the trinomial. 3x2 - 7x + 2
> (a) Determine whether the parabola will open upward or downward. (b) Find the equation of the axis of symmetry. (c) Find the vertex. (d) Find the y-intercept. (e) Find the x-intercepts if they exist. (f) Sketch the graph. (g) Find the domain and range of
> The radius of a balloon and its volume Use your intuition to determine whether the variation between the indicated quantities is direct or inverse.
> For what value of b will the line joining the points P and Q be parallel to the indicated axis? P(-6, 2b + 3), Q(7, -12); x-axis
> (a) Determine whether the parabola will open upward or downward. (b) Find the equation of the axis of symmetry. (c) Find the vertex. (d) Find the y-intercept. (e) Find the x-intercepts if they exist. (f) Sketch the graph. (g) Find the domain and range of
> x2 + 2x - 48 Factor the trinomial.
> (a) Determine whether the parabola will open upward or downward. (b) Find the equation of the axis of symmetry. (c) Find the vertex. (d) Find the y-intercept. (e) Find the x-intercepts if they exist. (f) Sketch the graph. (g) Find the domain and range of
> For what value of b will the line joining the points P and Q be parallel to the indicated axis? P (4, 7), Q (b, -20; y-axis
> Graph the function by using the slope and y-intercept. /
> x2 + 4x – 32 Factor the trinomial.
> Graph the function by using the slope and y-intercept. f (x) = 2x + 5
> Points A, B, and C are three vertices of a parallelogram with sides parallel to the x-axis. Plot the three points. Determine the coordinates of the fourth point, D, to complete the parallelogram. Note: There are two possible answers for point D. A (-2, 2
> Graph the function by using the slope and y-intercept. f (x) = 2x + 1
> Determine the area of the triangle.
> x2 – 64 Factor the trinomial.
> Evaluate the function for the given value of x. f (x) = -3x2 - 6x + 10, x = -2
> Points A, B, and C are three vertices of a rectangle. Plot the three points. (a) Determine the coordinates of the fourth point, D, to complete the rectangle. (b) Determine the area of the rectangle; use A = lw. A(-4, 2), B(7, 2), C(7, 8)
> f (x) = 3x2 + 2x - 5, x = -4 Evaluate the function for the given value of x.
> x2 - x - 30 Factor the trinomial.
> f (x) = -2x2 + 3x - 1, x = 3 Evaluate the function for the given value of x.
> Determine the equation of the graph.
> f (x) = x2 - 5, x = 7 Evaluate the function for the given value of x.
> x2 - 5x – 6 Factor the trinomial.
> Speed of Light Light travels at about 186,000 miles per second through space. The distance, d, in miles that light travels in t seconds can be determined by the function d(t) = 186,000t. (a) Light reaches the moon from Earth in about 1.3 sec. Determine t
> The time required to fill a pool with a hose and the volume of water coming from the hose Use your intuition to determine whether the variation between the indicated quantities is direct or inverse.
> Determine the equation of the graph.
> f(x) = 8x + 2, x = -2 Evaluate the function for the given value of x.
> Are indicated on the graph in Fig. 6.22.Write the coordinates of the indicated point.
> Appreciation of a House A house initially cost $150,000. The value, V, of the house after n years if it appreciates at a constant rate of 4% per year can be determined by the function V = f(n) = +150,000(1.04)n. (a) Determine f(8) and explain its meaning
> Graph the equation using the slope and y-intercept, as in Examples 6 and 7. 3x + 4y - 8 = 0
> Evaluate the function for the given value of x. f (x) = 4x - 1, x = 2
> Are indicated on the graph in Fig. 6.22.Write the coordinates of the indicated point.
> The radicand in the quadratic formula, b2 - 4ac, is called the discriminates. How many real number solutions will the quadratic equation have if the discriminant is (a) greater than 0, (b) equal to 0, or (c) less than zero? Explain your answer.
> Graph the equation using the slope and y-intercept, as in Examples 6 and 7. 3x + 2y = 6
> Determine whether the set of ordered pairs is a function. {(4, 2), (4, -3), (4, 5)}
> Determine the area of the triangle.
> Fill in the blanks with an appropriate word, phrase, or symbol(s). 2. The sum of the areas of the surfaces of a three-dimensional figure is called the figure’s _____________ area. 4. A polyhedron whose bases are congruent polygons and whose sides are pa
> Plot all the points on the same axes. (4.5, 3.5)
> Height of a Rocket A model rocket is launched from a hill 80 feet above sea level. The launch site is next to the ocean, and the rocket wil fall into the ocean. The rocket’s height, h, above sea level can be determined by the equation h = -16t 2 + 64t +
> Graph the equation using the slope and y-intercept, as in Examples 6 and 7.
> Determine whether the set of ordered pairs is a function. {(-1, 2), (-1, 4), (-1, 6),(-1, 9)}
> Graph the equation, using the x- and y-intercepts, as in Example 4. x - y = 3
> Gardner and Walkway CJ’s garden is surrounded by a uniform-width walkway. The garden and walkway together cover an area of 320 square feet. If the dimensions of the garden are 12 feet by 16 feet, determine the width of the walkway.
> Graph the equation using the slope and y-intercept, as in Examples 6 and 7. y = 3x - 1
> Determine whether the set of ordered pairs is a function. {(-4, 2), (1, 5), (3, -7), (5, 6)}
> Graph the equation, using the x- and y-intercepts, as in Example 4. x - y = 4
> (2). The ordered pair or ordered pairs that satisfy all equations in a system of equations is called the _________ to the system of equations. (4). A system of equations that has at least one solution is called a(n) _______ system of equations. (6). If t
> Graph the equation using the slope and y-intercept, as in Examples 6 and 7. y = -x – 2
> Determine whether the graph represents a function. If it does represent a function, give its domain and range.
> Graph the equation by plotting points, as in Example 3.
> Solve the equation, using the quadratic formula. If the equation has no real solution, so state. 4x2 + 7x - 1 = 0
> Determine the slope of the line through the given points. If the slope is undefined, so state. (2, 1) and (-5, -9)
> Determine whether the graph represents a function. If it does represent a function, give its domain and range.
> Graph the equation by plotting points, as in Example 3. 3y = 2x – 3
> Hourly Temperature The following graph indicates the hourly temperature, in degrees Fahrenheit, in Rochester, New York, from 10 a.m. through 8 p.m. on Monday, September 8, 2014. The function t1x2 = -0.48x2 + 5.0x + 64.38 can be used to estimate the hourl
> Determine the slope of the line through the given points. If the slope is undefined, so state. (2, 6) and (2, -3)
> Determine whether the graph represents a function. If it does represent a function, give its domain and range.
> Fill in the blanks with an appropriate word, phrase, or symbol(s). 2. Since clock 12 arithmetic, under the operation of addition, contains only the elements 51, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 126, the mathematical system is ______ . 4. In clock 12 arith
> Graph the equation by plotting points, as in Example 3. y - 4x = 8
> When solving a system of linear equations by the substitution method, a student obtained the equation 0 = 0 and gave the solution as 10, 02. What is the student’s error?
> Determine the slope of the line through the given points. If the slope is undefined, so state. (-3, -5) and (-1, -2)
> Determine whether the graph represents a function. If it does represent a function, give its domain and range.
> Graph the equation by plotting points, as in Example 3. y = -2x + 3
> Construct a system of two linear equations that has no solution. Explain how you know the system has no solution.
> Determine the slope of the line through the given points. If the slope is undefined, so state. (-2, 6) and (-4, 9)
> 2x2 - 4x + 5 = 0 Solve the equation, using the quadratic formula. If the equation has no real solution, so state.
> Graph the equation by plotting points, as in Example 3. y = x – 2
> Develop a system of linear equations that has 16, 52 as its solution. Explain how you developed your system of equations.
> (2). A binary operation is an operation or rule that can be performed on exactly two elements of a set, with the result being a(n) ______ element. (4). A specific example illustrating that a property is not true is called a(n) _______ . (6). Since the pr
> Determine the slope of the line through the given points. If the slope is undefined, so state. (4, 3) and (3, 4)
> Solve the equation, using the quadratic formula. If the equation has no real solution, so state. x2 = -8x + 15
> Graph the equation and state the slope of the line if the slope exists (see Example 9). y = -4
> Fill in the blank to make a true statement. (66). 1 nanogram = _________ micrograms (68). 1 megagram = _________ nanograms
> Indicate whether the graph shown represents a consistent, inconsistent, or dependent system.
> Graph the equation, using the x- and y-intercepts, as in Example 4. 6x = 3y – 9
> Which of the following inequalities have the same graph? Explain how you determined your answer. (a) 2x - y < 8 (b) -2x + y > -8 (c) 2x - 4y < 16 (d) y > 2x - 8
> Graph the equation and state the slope of the line if the slope exists (see Example 9). x = -2
> Salaries Jose’s salary can be modeled by the equation y = 39,000 + 1200t, and Charlie’s salary can be modeled by the equation y = 45,000 + 700t, where t represents the number of years since 2014. The graph at the top o
> Graph the equation, using the x- and y-intercepts, as in Example 4. 2x - y = 4
> Fill in the blanks with an appropriate word, phrase, or symbol(s). 2. Two lines that do not lie in the same plane and do not intersect are called _________ lines. 4. Two angles, the sum of whose measures is 90°, are called _________ angles. 6. An angle w
> A company makes car seats and strollers. Each car seat and stroller passes through three processes: assembly, safety testing, and packaging. A car seat requires 1 hr in assembly, 2 hr in safety testing, and 1 hr in packaging. A stroller requires 3 hr in
> Determine which ordered pairs satisfy the given equation.
> Write a system of equations that can be used to solve the problem. Then solve the system and determine the answer. MODELING—Golf Club Membership Membership in Oakwood Country Club costs $3000 per year and entitles a member to play a round of golf for a g
> Graph the equation, using the x- and y-intercepts, as in Example 4. 3x - y = -6
> A dietitian prepares a special diet using two food groups, A and B. Each ounce of food group A contains 3 units of vitamin C and 1 unit of vitamin D. Each ounce of food group B contains 1 unit of vitamin C and 2 units of vitamin D. The minimum daily requ
> Determine which ordered pairs satisfy the given equation. 2x - 3y = 9 (0, -3) (2, 1) (-3, -5)
> Write a system of equations that can be used to solve the problem. Then solve the system and determine the answer. MODELING—Copy Service Jayne recently purchased a high-speed copier for her home office and wants to purchase a service contract on the copi
> Teresa’s five test grades for the semester are 86%, 78%, 68%, 92%, and 72%. Her final exam counts one-third of her final grade. What range of grades on her final exam would result in Teresa receiving a final grade of B in the course? (See Example 9.)
> A company manufactures two types of washers, top load and front load. The company can manufacture a maximum of 18 washers per day. It makes a profit of $20 on top load machines and $25 on front load machines. No more than 5 front load machines can be man
> Determine which ordered pairs satisfy the given equation.
> (2). The name of the system of measurement primarily used in the United States today is the U.S. _________ system. (4). Three advantages of the metric system are that a) It is the worldwide accepted system of _________. b) There is only one base unit of
> Write a system of equations that can be used to solve the problem. Then solve the system and determine the answer. MODELING—Nut and Pretzel Mix Dave wants to purchase 20 pounds of party mix for a total of $30. To obtain the mixture, he will mix nuts that
> The Palm Beach State College Planning Committee wants to rent tents for the spring job fair. Rent-a-Tent charges $325 for setup and delivery of its tents. This fee is charged regardless of the number of tents delivered and set up. In addition, Rent-a-Ten
> The bookstore at St. Petersburg College sells Apple tablets and Samsung tablets. Based on demand, it is necessary to stock at least twice as many Apple tablets as Samsung tablets. The costs to the store are $300 for an Apple tablet and $200 for a Samsung
> Determine which ordered pairs satisfy the given equation. 3x - y = -5 (0, 5) (-1, 2) (2, 1)
> Write a system of equations that can be used to solve the problem. Then solve the system and determine the answer. MODELING—Landscaping The Garden Factory purchased 4 tons of topsoil and 3 tons of mulch for $1529. The next week the company purchased 2 to
> The minimum speed for vehicles on a highway is 40 mph, and the maximum speed is 55 mph. If Philip has been driving nonstop along the highway for 4 hr, what range in miles could he have legally traveled?
