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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

Here is a list of the factoring techniques that we have discussed.a. Factoring out the GCFb. Factoring by groupingc. Factoring trinomials by trial and errord. Factoring the difference of two squares
Here is a list of the factoring techniques that we have discussed.a. Factoring out the GCFb. Factoring by groupingc. Factoring trinomials by trial and errord. Factoring the difference of two squares
A satellite dish in the shape of a parabolic surface has a diameter of 20 feet. If the receiver is to be placed 6 feet from the base, how deep should the dish be?
Here is a list of the factoring techniques that we have discussed.a. Factoring out the GCFb. Factoring by groupingc. Factoring trinomials by trial and errord. Factoring the difference of two squares
a + (-a)=________: The sum of a real number and its additive_______ is________ , the additive________ .
a · 1/a = 1, a ≠ 0: The product of a nonzero real number and its multiplicative________ is________ , the multiplicative________ .
In Exercises 49–56, identify each equation without completing the square.y2 + 8x + 6y + 25 = 0
In Exercises 15–58, find each product.(x + 3)(x - 3)
Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. V200x³ V10x-1
Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. V500x³ 10x-1
In Exercises 15–58, find each product.(3x + 2)(3x - 2)
In Exercises 33–44, add or subtract terms whenever possible. EA9 + ENL
Read the Blitzer Bonus on page 47. The future is now: You have the opportunity to explore the cosmos in a starship traveling near the speed of light. The experience will enable you to understand the
Use a graphing utility and x-intercepts to verify any of the real solutions that you obtained for three of the quadratic equations in Exercises 65–74.Taken Soluti0ns set from exercise 65-7465. The
Does your graphing utility have a feature that allows you to solve linear systems by entering coefficients and constant terms? If so, use this feature to verify the solutions to any five exercises
Use the Table feature of a graphing utility to verify any three of the decompositions that you obtained in Exercises 9–42.Data from exercise 9-42 9. 11. 13. X (x − 3)(x - 2) 3x + 50 (x - 9) (x +
Because x + 5 is linear and x2 - 3x + 2 is quadratic, I set up the following partial fraction decomposition: 7x² + 9x + 3 (x + 5)(x² 3x + 2) A x + 5 + x² Bx + C -3x + 2
Use a graphing utility to verify any five of the graphs that you drew by hand in Exercises 1–26.Data from exercise 1-26 1. x + 2y = 8 3. x2y> 10 2. 3x6y≤ 12 4. 2xy > 4
In Exercises 1–5, use matrices to find the complete solution to each system of equations, or show that none exists. √x - 2y + 2z = -2 2x + 3y z = 1
Fill in each blank so that the resulting statement is true.Using Gaussian elimination to solvewe obtain the matrixTranslating this matrix back into equation form gives __________Solving Equation 2
Use matrices to solve this system: x = y + z = 17 2x + 3y + z = 8 -4x + y + 5z = -2. N
In Exercises 6–10, perform the indicated matrix operations or solve the matrix equation for X given that A, B, and C are defined as follows. If an operation is not defined, state the reason.A + C A
In Exercises 67–70, determine whether each statement makes sense or does not make sense, and explain your reasoning.When using Cramer’s Rule to solve a linear system, the number of determinants
Show that the equation of a line through (x1 , y1) and (x2 , y2) is given by the determinant equation in Exercises 53.Data from exercise 53Use the determinant to write an equation of the line passing
In Exercises 83–88, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.is an invertible matrix. 1 -1 -3] 3]
Find values of a for which the following matrix is not invertible: [a 1 a +1 4 a - 2
In Exercises 1–5, graph the conic section with the given equation. For ellipses, find the foci. For hyperbolas, find the foci and give the equations of the asymptotes. For parabolas, find the
In Exercises 1–5, graph each ellipse. Give the location of the foci. (x - 2)² (y + 1)² + 16 25 = 1
Fill in each blank so that the resulting statement is true.The equation 9x2 - 4y2 = 36 can be written in standard form by_________ both sides by_________ .
In Exercises 27–32, find the standard form of the equation of each hyperbola. 10 HE + @ X KII H N
In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.Focus: (7, -1); Directrix: y = -9
In Exercises 33–42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. (x+4)² (y + 3)² 9 16 1
In Exercises 37–50, graph each ellipse and give the location of its foci. (x - 2)² (1)² 9 4 = 1
In Exercises 39–42, identify the conic represented by each equation without completing the square.y2 + 4x + 2y - 15 = 0
In Exercises 43–50, convert each equation to standard form by completing the square on x and y. Then graph the hyperbola. Locate the foci and find the equations of the asymptotes.16x2 - y2 + 64x -
In Exercise 71, if the diameter of the dish is halved and the depth stays the same, how far from the base of the smaller dish should the receiver be placed?Data from Exercise 71A satellite dish, like
Graph x2/a2 - y2/b2 = 1 and x2/a2 - y2/b2 = -1 in the same viewing rectangle for values of a2 and b2 of your choice. Describe the relationship between the two graphs.
Describe one similarity and one difference between the graphs of y2 = 4x and (y - 1)2 = 4(x - 1).
Graph x2/16 - y2/9 = 1 and x| x|/16 - y| y|/9 = 1 in the same viewing rectangle. Explain why the graphs are not the same.
A restaurant offers the following lunch menu.If one item is selected from each of the four groups, in how many ways can a meal be ordered? Describe two such orders. Beverages
Here is a list of the factoring techniques that we have discussed.a. Factoring out the GCFb. Factoring by groupingc. Factoring trinomials by trial and errord. Factoring the difference of two squares
In Exercises 73–76, determine whether each statement makes sense or does not make sense, and explain your reasoning.I use binomial coefficients to expand (a + b)n, where isthe coefficient of
Use the nCr key on a graphing utility to verify your answers in Exercises 1–8. 1. 56 2. 21 3. 12 4. 11 5. 1 6. 105 7. 4950 8. 4950
Here is a list of the factoring techniques that we have discussed.a. Factoring out the GCFb. Factoring by groupingc. Factoring trinomials by trial and errord. Factoring the difference of two squares
Use a graphing utility with an nPr menu item to verify your answers in Exercises 1–8.Data from exercise 1-8 1. 3024 2. 210 3. 6720 4.5040 5.720 6.362,880 7.1 8. 1
Research and present a group report on state lotteries. Include answers to some or all of the following questions: Which states do not have lotteries? Why not? How much is spent per capita on
In the sequence 21,700, 23,172, 24,644, 26,116, . . . , which term is 314,628?
Use a graphing utility with an nCr menu item to verify your answers in Exercises 9–16.Data from Exercise 9-16 9. 126 10. 210 11. 330 12. 792 13. 1 14. 1 15. 1 16. 1
In Exercises 83–86, determine whether each statement makes sense or does not make sense, and explain your reasoning.I used the combinations formula to determine how many different four-note sound
Use the SEQ (sequence) capability of a graphing utility to verify the terms of the sequences you obtained for any five sequences from Exercises 1–12 or 19–22.Graphing utility from exercise 1-121.
Here is a list of the factoring techniques that we have discussed.a. Factoring out the GCFb. Factoring by groupingc. Factoring trinomials by trial and errord. Factoring the difference of two squares
Here is a list of the factoring techniques that we have discussed.a. Factoring out the GCFb. Factoring by groupingc. Factoring trinomials by trial and errord. Factoring the difference of two squares
Use the SUM SEQ (sum of the sequence) capability of a graphing utility to verify any five of the sums you obtained in Exercises 29–42.Data from exercise 29-4229. 5 + 10 + 15 + 20 + 25 + 30 = 10530.
Fill in each blank so that the resulting statement is true.Negative exponents in denominators can be evaluated using 1 || b = 0.
Here is a list of the factoring techniques that we have discussed.a. Factoring out the GCFb. Factoring by groupingc. Factoring trinomials by trial and errord. Factoring the difference of two squares
Show the each equation-(-a) = _________.
Evaluate each exponential expression in Exercises 1–22. 37
In Exercises 15–58, find each product.(7x + 4)(3x + 1)
In Exercises 15–58, find each product.(4x2 + 5x)(4x2 - 5x)
Fill in each blank so that the resulting statement is true.If 4p = 4, then the equation of the directrix is________ . (-2,-1)
In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola.8x2 + 4y = 0
Write the slope-intercept form of the equation of the line passing through (1, -4) and (-5, 8).
In Exercises 19–22, find the standard form of the equation of the conic section satisfying the given conditions.Ellipse; Endpoints of major axis: (-8, 2), (10, 2); Foci: (-4, 2), (6, 2)
In Exercises 23–24, find the standard form of the equation of each hyperbola satisfying the given conditions.Foci: (-8, 0), (8, 0); Vertices: (-3, 0), (3, 0)
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s).x2 - 6x + 3, for x = 7
Fill in each blank so that the resulting statement is true. x² x - 4 3 3
Fill in each blank so that the resulting statement is true.The product rule for square roots states that if a and b are nonnegative, then √ab = ______.
Every real number is either a/an number or a/an_______ number.
Consider the set:List all numbers from the set that area. Natural numbers,b. Whole numbers,c. Integers,d. Rational numbers,e. Irrational numbers,f. Real numbers. {-17,-3, 0, 0.75, V2, T, V81}.
In Exercises 1–10, factor out the greatest common factor.x(2x + 1) + 4(2x + 1)
The set of numbers in the form a/b , where a and b belong to the set in Exercise 8 and b ≠ 0, is called the set of_________ numbers.
The set of numbers whose decimal representations are neither terminating nor repeating is called the set of______ numbers.
The notation |x| is read the of x. If x ≥ 0, then |x| = . If x < 0, then |x| =_______ . If x < 0, then |x| =______ .
The commutative properties state that a + b =_______ and ab =_______ .
The associative properties state that (a + b) + c =_______ and_______ = a(bc).
The distributive property states that a(b + c) =________ .
In Exercises 11–16, factor by grouping.x3 - x2 - 5x + 5
Simplify the expression. Assume that all variables are positive. 8.x V 27 2√x
Simplify the expression. Assume that all variables are positive. n 125 "At-
Simplify the expression. Assume that all variables are positive. xy² + √x³y
Simplify the expression. Assume that all variables are positive. 81a³b² - Vab
Simplify the expression. Assume that all variables are positive. /64x³ = √x + 3√x
Simplify the expression. Assume that all variables are positive. 2√3z + 3√12z + 3√/48z
Simplify the expression. Assume that all variables are positive. FA+EA - HA
Simplify the expression. Assume that all variables are positive. 9A-9A07
Simplify the expression. Assume that all variables are positive. 23VI1 2 V44 8
Simplify the expression. Assume that all variables are positive. 8 15V8 4 2V2 5
Simplify the expression. Assume that all variables are positive. V2a + 1+ V8a + 4
Simplify the expression. Assume that all variables are positive. V4x + 8 + √x + 2
Simplify the expression. Assume that all variables are positive. *Λ - ΛΕ
Simplify the expression. Assume that all variables are positive. √xy - 2xy
Simplify the expression. Assume that all variables are positive. XAE-XAS
Simplify the expression. Assume that all variables are positive. 2V/16 + 2√2
Simplify the expression. Assume that all variables are positive. √5 + 2√5
Simplify the expression. Assume that all variables are positive. √44-4VII
Simplify the expression. Assume that all variables are positive. 9√18-2V8
Simplify the expression. Assume that all variables are positive. 3√28 + 3√7
Simplify the expression. Assume that all variables are positive. 18√3+ 3√3
Simplify the expression. Assume that all variables are positive. PAL + PAT
Simplify the expression. Assume that all variables are positive. ۲۸ - ۸۸ r

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