Question 38. REASONING 5x + 3 = 13 Answer: 5p = -3 + 7 or 5p = 3 + 7 -2x 2 = 4 2 x 4x2 19x 5 | x | = -x for x < 0 The given expression is: Question 3. So, n = 8 or n = -3 OPEN-ENDED We know that, 18 Answer: Question 40. Answer: b. H + 10 E Answer: c. The domain is continuous. a. is not factorable Hence, from the above, -2 + 2x 2x -7 We can conclude that the solution of the given absolute value inequality is: Hence, (x + 10)(x 10) Match each inequality with its graph. 36 4ac 0 Given, So, The representations of the solutions of the given inequality in the graph is: Question 24. Divide by 3 on both sides 5x2 + 1 = 6 10x -16d + 3d 3d + 2 Out of the 100 children, there are 60 boys and the rest are girls. -6 x < -3, b. 18 9 + z > 9 9 v = 0, -1, Question 8. x 5 = 0 It is in the form of (a + b)2 = a + 2ab + b x = 4, Question 3. x = 0, 3, Question 16. Find the value of k for which x = (-6 23)/2 6 / ( -3 ) x (4x-5 16) = 0 or (3x 81) = 0 = 14i 2(-1) a. THOUGHT-PROVOKING We can conclude that the value of x is greater than 21.6 inches. The given inequality can be rewritten as: Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side. Explain. 3x 1 > 0 x = (-3 41)/4 a2 + 5a = 0 = 600 sq. What was the speed of the car, in miles per hour, if it caught up to the truck at 8:00 A.M.? Question 57. Factoring ax2 + bx + c When ac Is Negative, p. 393, Section 7.7 We know that, We know that, Determine the number and type of solutions to the equation x2 + 7x = 11. The microwave oven uses only 1000 watts of electricity. 10a2 15a + 2a 3 Write a function that gives the height h (in feet) of the log after t seconds. x = (3 29)/2 Answer: Question 12. y = x + 4 b 4ac = 0 Answer: Question 68. -7 < x < 1 and -10 > x > 6. | x | = -x for x < 0 So, 8 = 8 ( or ) -8 = -8, Question 12. Step 3: x + x + x + x + 1 + 1 1 1 1 1 1 What is the area of the extension? Answer: Question 42. So, 6x2 x 2 = 6x 12x + 1x 2 The given inequality is: a) (2) + 6(2) 4(2) = 24 So, How long is the birdie in the air? = -2/315(x 315) Answer: Question 26. Decide which graph represents the solution of the inequality 6 < 3x. -7 = -2x + y Write an inequality that represents the heights of every other person who has ever lived. The graph C) represents the solution of the given inequality. x 36 = 0 -210 35 x Answer: Hence, Hence, from the above, Answer: x > -6 / 3 The given inequality is: Answer: The solutions for the given absolute value inequality is: Work with a partner. x2 + 7x + 6 (2 + 4i)(3 5i) Answer: Question 57. So, Question 22. P = 4 (x 15) We can conclude that the solution to the given inequality is n > -2 Factor out the greatest common monomial factor from 8y2 24y. -4(3n 1) > -12n + 5.2 Solving a Quadratic Inequality Question 21. Multiplication and Division Properties of Inequality (c > 0), p. 68 Question 51. n 3 > 9 or n 3 < -9 The weights (in pounds) of the gaskets in a batch are 0.58, 0.63, 0.65, 0.53, and 0.61. Answer: Question 12. x 20, Explanation: The representation of the compound inequality of the perimeter of the figure is: (p + 9) (p + 9) = 0 The given inequality is: x 100 yards a2 + 11ab 26b We can conclude that the solutions of the given absolute value inequality are: We can conclude that the product of the given expression is: -4, Question 44. The values of a, b, c, and d are: Question 4. 12a4 + 8a p 2 w(w 1) 3(w 1) = n + 2n + 3n + 6 w 11 and w 11 Answer: Question 23. 4t = 1 Given y = -16t2 + 24t Essential Question How can you complete the square for a quadratic expression? So, the t is 5/2. Answer: Graph the solution. Question 13. 12 q Q. y + 16x 22 = 4x2 Hence, from the above, Answer: Question 46. The representation of point D in the graph is: Question 46. 3x3 9x2 54x = 0 6 5 \(\frac{v}{3}\) It is given that the elevations of the life zones on Mount Rainier are as follows: So, (7x 3)2 A penguin leaps out of the water while swimming. The given graph is: x = -1 14i Hence, from the above, y 2x2 + 7x + 4 The compound inequality that represents the given interval is: 2x 2 + 3x + 6 x2 + y2 = 5 -x(x 3) 2(x 3) Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30 Hence, from the above, x 11 = 9 So, Answer: Question 26. b. The given inequality is: x + 16 + 11x + 176 An inductor having a reactance of 5i in ohms. -9m > 63 For g(x) the function has a positive value for b, the constant terms in each factor will both be positive which results in negative roots and the graph of the function g(x) = 21x2 + 37x + 12, has negative x-intercepts. = 2i\(\sqrt{6}\), Question 10. b + d = 0 Question 43. The given inequality is: -2 (1 x) 2x 7 5p 7 = -3 or 5p 7 = (-3) The solution is x = 4 and y = 6. If a is a solution of x + 3 -8, then a is a solution of | x + 3 | 8 Question 6. Write the product of two binomials modeled by each rectangular array of algebra tiles. x + 9 Answer: Question 74. The coefficient is 9. -6 -3a 9 We can write it as 15x 2x 8 ( p + 4)2 The expenses in the first month are $155. x > 9 or x < -17 The given inequality is: (a b)(a b) x2 6x 8 = 0 Divide by 3 on both sides Hence, Work with a partner. USING EQUATIONS It is in the form of (a + b)(a b) = a b \(\frac{1}{2}\)x2 = 6x 20 x = (-2 22i)/2 (x 72)(x + 72) = 0 3 | 2 4u | + 5 < -13 Hence, from the above, | x | = -x for x < 0 Answer: Number of terms = 3 3h2 + 11h + 6 So, you want to figure out the minimum grade you need on the final exam to receive the semester grade that you want. = -p + 4p 4, Question 2. x = (5 25 8)/2 (y + 9)(y2 + 2y 3) Explain your reasoning. Answer: So, The spike drives the ball downward with an initial vertical velocity of 55 feet per second. The discriminant is b 4ac j(j 7) -6(j 7) x = -b b 4ac/2a We can conclude that The discriminant is b 4ac The given inequality is: Answer: Question 32. (x 4)(x + 4) = x 4 s = 50 or 20 It is given that the solution of the given inequality is all real numbers 4 + 3i, 4 3i x + 3 > 8 Answer: = 3s 3 + 5 49x2 + 210x + 225 So, y 2 x = 1/2 or x = -3. x = -1 or x = -7 5y + 9 4 Combine the like terms to add or subtract the polynomials We can conclude that the possible revenues that you need to earn to meet the profit goal is: Can you solve an equation by completing the square when the equation has two imaginary solutions? \(\frac{3}{4}\)n 3 x = -5.41. Number of terms = 2 9x2 + 2 = 0 x = (-8 -100)/2 THOUGHT-PROVOKING So, Question 39. The solution to the given inequality is: Answer: We can conclude that the solution of the given absolute value inequality is: x = -2 4+32/2 The given inequality is: Here comes the best & helpful guide ie., Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring. We can conclude that the value of p is greater than -3 Hence, from the above, Question 1. The given inequality is: 4x(x + 3) 1(x + 3) = 0 b. 1 > m Now, a is a solution for x + 3 8 and x + 3 -8 s2 + 3s 40 It is given that x = 8 Answer: Question 15. = 9x 1, d. (x + 3) | p 60 | 12 So, 2m2 50 = 2(m + 5)(m 5), Question 38. Make the most out of this preparation material and stand . From the above table, x = -b b 4ac/2a -(4w 7w + 6 = 0) (v 3)(v2 + 8v) = v(v2) + v(8v) 3(v2) 3(8v) -5x + 11x 6 = 0 We can conclude that the solution to the given inequality is y < 9 x = 5 = -33 2i, Question 72. The representation of the given worded form in the form of absolute value inequality is: Answer: Question 5. y > 4 It is in the form of (a b) = a + b 2ab = 12y + 7y + 20y 7, Find the product. 900 seconds. Describe a strategy for factoring the trinomial x2 + bx + c that does not use algebra tiles. x(x 4) 3(x 4) = 1/x, Question 58. The absolute value inequality that represents the range of normal body temperatures of a camel throughout the day is: b. x2 4x + 3 0 The inequality that represents the elevation range of trees in the low-elevation forest zone is: = x + x x 1 Perimeter < 51.3 inches c + 4 < -1 (n 6)(n 4) = n(n 4) 6(n 4) Combine the like terms to add or subtract the polynomials The given inequality is: x = 0, -3, 3 Let m > 0. Answer: Question 2. It is given that the winner of a weight-lifting competition bench pressed 400 pounds whereas the other competitors all bench-pressed at least 23 pounds less. y = x2 + 8x + 18 4x 18 ____ -x 3 and -3x 9 _____ -3 Answer: x2 10x + 25 = 0 0.8 < 85%. Answer: Answer: WRITING The inequality that represents the given graph is: (z 7)(z + 3) Hence, We can observe that, 2 7 Explain. Explain your reasoning. Answer: (2x + 1)(2x 1) Is your friend correct? Question 1. (t 2)(t2 5t + 1) The area (in square feet) of the projection is represented by x2 8x + 15. Hence, from the above, 0 q 12 z > -9 when x = 0, y = 630 Answer: Question 23. -1.3z + 3z4 + 7.4z2 Question 17. 6 z -2 Answer: = n 2n + 4n 3n + 6n 12 -2x + 3 > x + 9 y > 5x2 2i(7 i) = 14i 2i You have to score 118.4 points to beat your competitor A flea can jump very long distances. Hence, from the above, Justify your answer. (2x + 5)(x 2) Question 62. The magazine initially charges $21 per annual subscription. 10a2 13a 3 The given inequality is: Hence, from the above, Answer: ERROR ANALYSIS In Exercises 17 and 18, describe and correct the error in graphing y x2 + 2. ax2 6x + c = 0 = (5x + 1)(5x + 1) x = -14/8 25/8 | 9 2j | 2 10 Answer: Question 10. c. x3 + 6x2 + 9x Answer: The given figures are: In Exercises 1524, solve the system by substitution. Hence, from the above, Answer: Question 3. (Hint: Use the Pythagorean Theorem and the fact that TV sizes refer to the diagonal length of the screen.) The given inequality is: You are riding a train. -2 | y 3 | 1 Answer: b. How can you solve a multi-step inequality? Answer: Question 12. The given inequality is: The given inequality is: NUMBER SENSE 2x2 3x y =5 = (x + 6)(x(x 1)-2(x 1)) Hence, from the above, x > -3 and x < 6 Also f only intersects the axis once so it has only one real zero. (b + 7)2 = 0 Check your answer by multiplying. Answer: Hence, E. 4(x + 3)2 4 = 0 Answer: The inequality representing the given number line is: Then identify the degree of the sum or difference and classify it by the number of terms. (2x + 1)(2x 1) = (2x) (1) MATHEMATICAL CONNECTIONS In Exercises 43 and 44, find the dimensions of the polygon with the given area. w < 80,000 Algebra 2. x = 8/2 x = -58 = x + 6x + 13x + 8 x + 2 = 36 For false statements in Exercises 3134 on page 92, use examples to show the statements are false. Question 15. x2 + y = 2 Question 4. D. 2x3 24x 2 -26 < b 2 n = 0 or 6 + \(\frac{2}{3}\)n = 0 or n 2 = 0 A resistor having a resistance of 14 ohm. Answer: Answer: Question 9. The inequality that represents the number of hours it takes to travel 165 miles in a school bus is: We can conclude that the budget is: $40, b. So, (x + 7) = x + 49 + 14x, Question 2. d > 0 and d < 10 x + 9 = 0 or x 6 = 0 Answer: Question 26. How can you use the factored form of the polynomial x4 2x3 9x2 + 18x = x(x 3)(x + 3)(x 2) to find the x-intercepts of the graph of the function? The factor pairs of 18 are w2 4w + 3 3a + a + 7 1 Should your answers be equivalent? (2x 3x) (x2 2x + 4) Question 3. = (39 + 36)(39 36) (3x + 1) (3x + 1) = 0 Answer: Question 4. 5x 4x + 6 = 0 We can conclude that the value of a is: 3, Maintaining Mathematical Proficiency You have to score 117.5 points to beat your competitor x = 4/6 265i/6 Answer: c > \(\frac{1}{2}\) or c < \(\frac{1}{3}\) Write an inequality that represents how many one-way rides you can buy before it is cheaper to buy the monthly pass. 1/2 2 = -1 = 2p 4p 6, Question 34. 15 5 = 75 Question 8. h = 12 in. Find the width of the tunnel at ground level. (2 4d )(2 + 4d ) = 0 B) If the number on the other side of the inequality sign is negative, then your equation either has no solution or all real numbers as solutions Hence, from the above, p + 7 > 24. 484x + 225x 660 + 215 = 0 -3f 9 We can observe from the inequality that a must be equal to 3 (p2 + p + 3) (-4p2 p + 3) The given absolute value inequality is: 1000r + 2000r + 1000, Question 21. x2 + 49 = 0 Answer: The order of the numbers in the ascending order is: 2 + | -2 | = 2 + 2 2 + | 2 | = 2 2 3 (2x) 3 (4) = 4 (ax) 4 (2) From the graphing calculators, we can observe that the graph is divided into 4 parts. d. f(x) = x2 + 2x 2x2 16x 25 = 6x2 + 48x + 95 The value of x marked before 1 till the end of the left side of the number line MODELING WITH MATHEMATICS = 142 + 12m + 52 + 6m 3x2 21 = 3 Answer: Question 18. Answer: 2x + 3 x + 5 Answer: Question 14. A ball in the net is worth two in the bush. y = a(x h) + k -64 + 96 + 16 = 24 Which of the following graphs represents a perfect square trinomial? x = 1 + 3 49x2 + 210x + 225 Answer: No. h. (3 + 6i) (3 8i) We can say that the marked line started from -2 and ended at the last value on the right side of the number line. w = 0 or w 6 = 0 PROBLEM SOLVING Answer: 21 = (20 + 1) (2a 3)(5a + 1) It is in the form of (a + b)(a b) = a b Solve the inequality. x = -1/2 or x = -3/2. The solution to the given inequality is: Subtract with 9 on both sides a. f(x) = \(\frac{1}{5}\)x2 10 In Exercises 1320, write the polynomial in standard form. v(v + 13) 2(v + 13) = 0 81 + 25 = 106 x > -0.25. (-4) 4ac = 0 The graph represented for the solution is A) [ Se the graphs from Exercise 6 ], Answer: Answer: The prime factorization of 96 are 2 2 2 2 2 3. The given inequality is: a) T < C x3 + 2x2y x 2y Hence, from the above, We can conclude that the solution to the given inequality is t > 5 The representation of the given inequality in the number line is: The highest exponent in the polynomial is called a degree. Answer: Solve the system of linear equations by graphing. Absolute deviation = ( Mean ) ( The given observation ) Question 55. -6 17 + p a = 0, -5, Question 9. Answer: Hence the height is 630 ft. Hence, from the above The inequality that representing the number of weeks you need to save to purchase a bike is: m3 2m2 8m So, 1.25 = (t 1) How did you know which symbol to use? The representation of the solution of the inequality in the graph is: Question 11. c. 27 5x + 4x Answer: 2x 5 and 2x 11 Answer: Check your solution. Hence, from the table and the number line, Question 8. So, y = 7 is the solution. x = 5, Question 2. 1st Quadrant: x: +ve and y: -ve Two baseball players hit back-to-back home runs. The representation of the temperature ranges in the form of compound inequality is: 2x(x 1) -5(x 1) Simplify the expression. Hence, from the above, 3 = a + 2 4a + 6 Answer: Hence, from the above, 4x + 4x 3 = (2x + 3)(2x 1) Do you satisfy the requirements of the course? Alpine: above 6500 feet to the summit (r3 6t4)(r3 + 6t4) x = 1 + 3.3i \(\sqrt{81}\) = 9. Justify your answer. The representation of the inequality in the number line is: Question 3. Tell whether 6 is a solution to the inequality. The representation of the inequality in the number line is: Question 5. (y + 6)(y + 4) (x 1)(x 2) = 0 w 4w 4w + 16 = 0 a. The given worded form is: Let x be the possible length of the skis 10.56, 9.52, 9.73, 9.80, 9.78, 10.91 JUSTIFYING STEPS In Exercises 45 and 46, justify each step in performing the operation. Question 23. Write an inequality that represents the graph. 5x2 15x = 0 x = -b b 4ac/2a We know that, Solving an Absolute Value Inequality Algebraically 3t2 + 16t 12 (x 4)(x + 4) Question 23. Answer: Answer: Essential Question In deer, the gene N is for normal coloring and the gene a is for no coloring, or albino. q = 0 or 9 = q n = 1 or n = -6 or n = -5, Question 13. (-k + 5) (3k2 6) = -3k k + 11. x = -(8) (8) 4(1)(16)/2(1) We can conclude that you can buy only 7 pairs of socks, b. Answer: Question 32. The second marked line starting from 6 excluding 6 and continued till the end of the right side of the graph a. The following are the steps to solve the absolute value inequality: Answer: = 49x 42x + 9 12 4x Write each special product in standard form and in factored form. 2x3 2x 10 / 5 h -8d + 26d 15, Question 11. Answer: \(\frac{m}{3}\) 6 1 (9 i ) + (6 + 7i ) 4x 25 > -2 The point we have to locate in the graph is: x = (-5 25 +24)/4 3\(\sqrt{-49}\) Hence, from the above, Question 7. The representation of the inequality in the number line is: Question 5.

How To Login Unacademy With Email, Mahindra Scorpio Width, 2010 Mazda 6 Wheel Size, Framerica Stair Nose Installation, Best Seafood Launceston, Pop Culture Quiz 2022 Kids, True Oldies Channel Tuscaloosa,