Graph the equation using the slope and y-intercept, as in Examples 6 and 7. 3x + 4y - 8 = 0
> Determine (a) the volume and (b) the surface area of the three-dimensional figure. When appropriate, use the key on your calculator and round your answer to the nearest hundredth.
> In which quadrants will the set of points that satisfy the equation x + y = 1 lie? Explain.
> Draw the graph of the function and state the domain and range. f (1x) = 4x+1
> 6x2 - 11x + 4 Factor the trinomial.
> Draw the graph of the function and state the domain and range. y = 2x - 1
> Recreational Vehicles The green graph shows the number of recreational vehicles sold in the United States, in thousands, for the years 2009–2014. The red dashed line can be used to approximate the number of recreational vehicles, in tho
> Draw the graph of the function and state the domain and range. y = 3x - 1
> 4x2 + 20x + 21 Factor the trinomial.
> Draw the graph of the function and state the domain and range.
> Determining a Test Grade The graph below shows the hours studied and the test grades on a biology test for 7 students. The red line on the graph can be used to approximate the test grade the average student receives for the number of hours he or she stud
> Draw the graph of the function and state the domain and range. f (x) = 4x
> x2 + 5x + 4 Factor the trinomial.
> 2x2 - 9x + 10 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
> Earning Simple Interest When $1000 is invested in a savings account paying simple interest for a year, the interest, i, in dollars, earned can be found by the formula i = 1000r, where r is the interest rate in decimal form. (a) Graph i = 1000r, for r up
> (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
> 2x2 - x – 3 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
> 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
> 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
> Solve the equation, using the quadratic formula. If the equation has no real solution, so state. 5x2 - 4x = -2
> (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
