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mathematics
algebra and trigonometry graphs

Questions and Answers of Algebra And Trigonometry Graphs

In Exercises:a) Find the vertex.b) Find the axis of symmetry.c) Determine whether there is a maximum or a minimum value and find that value.d) Graph the function.g(x) = -2x2 + 2x + 1
Solve.2x2 = 6x
Solve.18x + 9x2 = 0
Solve.x2 + 3x - 4 = 0
Solve.3y3 - 5y2 - 2y = 0
Solve.2x2 + 6 = -7x
Solve.3t3 + 2t = 5t2
Solve R = √3np for n.
Solve.4x2 = 24
Solve.7x3 + x2 - 7x - 1 = 0
Express in terms of i. V-49 -√-64
Find the zeros of f(x) = 4x2 - 8x - 3 by completing the square. Show your work.
Express in terms of i.√-43
Express in terms of i. V-12.V-20
In Exercises:a) Find the discriminant b2 - 4ac, and then determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist.b) Solve
Express in terms of i.-√-25
In Exercises:a) Find the discriminant b2 - 4ac, and then determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist.b) Solve
Solve.x4 + 5x2 - 6 = 0
Solve.2x - 5√x + 2 = 0
The sum of the base and the height of a triangle is 16 in. Find the dimensions for which the area is a maximum.
Is the sum of two imaginary numbers always an imaginary number? Explain your answer.
The graph of a quadratic function can have 0, 1, or 2 x-intercepts. How can you predict the number of x-intercepts without drawing the graph or (completely) solving an equation?
Discuss two ways in which we used completing the square in this chapter.
Solve. Give exact solutions.3x2 + 10x = 8
A berry farmer needs to separate and enclose two adjacent rectangular fields, one for blueberries and one for strawberries. If a lake forms one side of the fields and 240 yd of fencing is available,
Solve. Give exact solutions.r2 - 2r + 10 = 0
Solve. Give exact solutions.x2 = 10 + 3x
Designs for #1 Canines has determined that when x hundred portable doghouses are produced, the average cost per doghouse is given by C(x) = 0.1x2 - 4.2x + 72.4, where C(x) is in hundreds of dollars.
Solve. Give exact solutions.x = 2√x - 1
Solve. Give exact solutions.y4 - 3y2 + 1 = 0
Solve. Give exact solutions.(x2 - 1)2 - (x2 - 1) - 2 = 0
Solve. Give exact solutions.(p - 3)(3p + 2)(p + 2) = 0
Solve. Give exact solutions.x3 + 5x2 - 4x - 20 = 0
Harry and Rebecca leave a campsite, Harry biking due north and Rebecca biking due east. Harry bikes 7 km/h slower than Rebecca. After 4 hr, they are 68 km apart. Find the speed of each bicyclist.
Two seconds after a chlorine tablet has been dropped into a well, a splash is heard. The speed of sound is 1100 ft/sec. How far is the top of the well from the water?
Solve: √4x + 1 + √2x = 1.A. There are two solutions.B. There is only one solution. It is less than 1.C. There is only one solution. It is greater than 1.D. There is no solution.
Find b such that f(x) = -3x2 + bx - 1 has a maximum value of 2.
Solve graphically. Round solutions to three decimal places, where appropriate.x2 - 8x + 12 = 0
Is the product of two imaginary numbers always an imaginary number? Explain your answer.
Solve graphically. Round solutions to three decimal places, where appropriate.5x2 + 42x + 16 = 0
Solve graphically. Round solutions to three decimal places, where appropriate.7x2 - 43x + 6 = 0
Solve graphically. Round solutions to three decimal places, where appropriate.10x2 - 23x + 12 = 0
Solve graphically. Round solutions to three decimal places, where appropriate.6x + 1 = 4x2
Solve graphically. Round solutions to three decimal places, where appropriate.3x2 + 5x = 3
Solve graphically. Round solutions to three decimal places, where appropriate.2x2 - 4 = 5x
Explain why |x| < p has no solution for p ≤ 0.
Solve graphically. Round solutions to three decimal places, where appropriate.4x2 - 2 = 3x
Explain why all real numbers are solutions of |x | > p, for p < 0.
Solve.|3x - 1| > 5x - 2
Solve.|x + 2| = |x − 5|
Solve.|p - 4| + |p + 4] < 8
Solve.|x | + |x + 1| < 10
Solve.|x − 3| + |2x + 5| > 6
Solve.x1/3 = -2
Solve.t1/5 = 2
Solve.t1/4 = 3
Solve.m1/2 = -7
Solve(A chemistry formula for gases) P₁V₁ T₁ = P₂V₂ T2 , for T₁
Solve(A formula from optics) -1 || F 1 1 + m P' for F
Solve(A formula for resistance) 1 t 1 a + - b for t
Solve(An electricity formula) W = 1 V LC for C
Solve(A geometry formula) S = A V 6' for A
Solve(A compound-interest formula) I= = A VP 1, for P
Solve(A formula for work rate) 1 t || 1 a + 1 b' for t
Solve(A pendulum formula) T = 2TT •100 for g
Solve(A formula from optics) 1 F || 1 m + 1 P for p
Use a graphing calculator to find the zeros of the function. Round to three decimal places.f(x) = 3x2 + 2x - 4
Solve(A formula for escape velocity) V² R²2 2g R+h' for h
Use a graphing calculator to find the zeros of the function. Round to three decimal places.f(x) = 9x2 - 8x - 7
Together, China and the United States, the top two pork producers worldwide, produced 64,308,000 metric tons of pork in 2013. China produced 1,260,000 metric tons more than five times the number of
Use a graphing calculator to find the zeros of the function. Round to three decimal places.f(x) = 5.02x2 - 4.19x - 2.057
Use a graphing calculator to find the zeros of the function. Round to three decimal places.f(x) = 1.21x2 - 2.34x - 5.63
Solve.x4 - 3x2 + 2 = 0
Solve.x4 + 3 = 4x2
Solve.x4 + 3x2 = 10
Solve.x4 - 8x2 = 9
In 2014, the average student loan debt per college graduate was about $33,050. This was about 77.6% more than the average student loan debt per college graduate in 2004. What was the average student
Solve.(x - 3)2/3 = 2
Solve.y4 + 4y2 - 5 = 0
Solve.y4 - 15y2 - 16 = 0
Solve.x2/3 = x
The number of U.S. forces in Afghanistan decreased to approximately 34,000 in 2014 from a high of about 100,000 in 2010. The amount of U.S. funding for Afghan security forces also decreased during
The cost of a 30-sec Super Bowl ad has increased more than 70% since 2004. The function C(x) = 0.17x + 2.25 can be used to estimate the cost of a 30-sec ad, in millions of dollars, x years after
The cost of a 30-sec Super Bowl ad has increased more than 70% since 2004. The function C(x) = 0.17x + 2.25 can be used to estimate the cost of a 30-sec ad, in millions of dollars, x years after
In 1946, the lowest price of a World Series ticket was $1.20. By 2012, the lowest price of a ticket had increased to $110. Find the average rate of change in the lowest price of a World Series ticket
The three countries with the most rice production are China, India, and Indonesia. The equation y = 9.06x + 410.81 provides a good estimate of world rice production in millions of metric tons, where
The population of Detroit, Michigan, decreased from 1,027,974 in 1990 to 688,701 in 2013. Find the average rate of change in the population of Detroit, Michigan, over the 23-year period.
Find the domain of the function. Do not use a graphing calculator. f(x) (x - 2) (x + 9) x3
Find the domain of the function. Do not use a graphing calculator. f(x) = √4 - x
The following table lists the numbers of commercial and savings banks in the United States for various years. a) Model the data with a linear function. Let the independent variable represent
In Exercises, determine the domain and the range of the function. ул -5-4-3-2-1 5432 -3 -4 + in -5 h 1 2 3 4 5 x
In Exercises, the table of data contains input–output values for a function. Answer the following questions for each table.a) Is the change in the inputs x the same?b) Is the change in the outputs
In Exercises, the table of data contains input–output values for a function. Answer the following questions for each table.a) Is the change in the inputs x the same?b) Is the change in the outputs
Find the slope and the y-intercept of the graph of the linear equation. Then write the equation of the line in slope–intercept form. H ул 2 4 Xx
Find the slope and the y-intercept of the graph of the linear equation. Then write the equation of the line in slope–intercept form. -4-2 円 V< y 2 て -4 H H 2 2 4 x
Graph the equation. y || -3x+1
Find the slope and the y-intercept of the graph of the linear equation. Then write the equation of the line in slope–intercept form. -4-2 УЛ 2 -4 2 4 IT x
Graph the equation.3x - 6y = 6
Graph the equation.y = - 1/2 x + 3
Graph the equation.y = 2 - x2

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