Elementary Algebra
17th Edition
ISBN: 9780998625713
Author: Lynn Marecek, MaryAnne Anthony-Smith
Publisher: OpenStax - Rice University
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Textbook Question
Chapter 10.1, Problem 27E
In the following exercises, solve the following
27.
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Please draw a graph that represents the system of equations f(x) = x2 + 2x + 2 and g(x) = –x2 + 2x + 4?
Given the following system of equations and its graph below, what can be determined about the slopes and y-intercepts of the system of equations?
7
y
6
5
4
3
2
-6-5-4-3-2-1
1+
-2
1 2 3 4 5 6
x + 2y = 8
2x + 4y = 12
The slopes are different, and the y-intercepts are different.
The slopes are different, and the y-intercepts are the same.
The slopes are the same, and the y-intercepts are different.
O The slopes are the same, and the y-intercepts are the same.
Choose the function to match the graph.
-2-
0
-7
-8
-9
--10-
|--11-
-12-
f(x) = log x + 5
f(x) = log x - 5
f(x) = log (x+5)
f(x) = log (x-5)
9
10
11
12
13 14
Chapter 10 Solutions
Elementary Algebra
Ch. 10.1 - Solve: x2=81 .Ch. 10.1 - Solve: y2=121 .Ch. 10.1 - Solve: x250=0 .Ch. 10.1 - Solve: y227=0 .Ch. 10.1 - Solve: 2x2=98 .Ch. 10.1 - Solve: 3z2=108 .Ch. 10.1 - Solve: c2+12=0 .Ch. 10.1 - Solve: d2+81=0 .Ch. 10.1 - Solve: 12x2+4=24 .Ch. 10.1 - Solve: 34y23=18 .
Ch. 10.1 - Solve: 5r22=34 .Ch. 10.1 - Solve: 3t2+6=70 .Ch. 10.1 - Solve: (q+5)2=1 .Ch. 10.1 - Solve: (r3)2=25 .Ch. 10.1 - Solve: (a3)2=18 .Ch. 10.1 - Solve: (b+2)2=40 .Ch. 10.1 - Solve: (x13)2=59 .Ch. 10.1 - Solve: (y34)2=716 .Ch. 10.1 - Solve: (a5)2+4=24 .Ch. 10.1 - Solve: (b3)28=24 .Ch. 10.1 - Solve: (3r+4)2=8 .Ch. 10.1 - Solve: (3r+4)2=8 .Ch. 10.1 - Solve: x26x+9=12 .Ch. 10.1 - Solve: y2+12y+36=32 .Ch. 10.1 - Solve: 9m212m+4=25 .Ch. 10.1 - Solve: 16n2+40n+25=4 .Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - Paola has enough mulch to cover 48 square feet....Ch. 10.1 - Kathy is drawing up the blueprints for a house she...Ch. 10.1 - Explain why the equation x2+12=8 has no solution.Ch. 10.1 - Explain why the equation y2+8=12 has two...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Solve c2+4c=5 by completing the square.Ch. 10.2 - Solve d2+10d=9 by completing the square.Ch. 10.2 - Solve r24r=12 by completing the square.Ch. 10.2 - Solve t210t=11 by completing the square.Ch. 10.2 - Solve y210y=35 by completing the square.Ch. 10.2 - Solve z2+8z=19 by completing the square.Ch. 10.2 - Solve x216x=16 by completing the square.Ch. 10.2 - Solve y2+8y=11 by completing the square.Ch. 10.2 - Solve a2+4a+9=30 by completing the square.Ch. 10.2 - Solve b2+8b4=16 by completing the square.Ch. 10.2 - Solve p2=5p+9 by completing the square.Ch. 10.2 - Solve q2=7q3 by completing the square.Ch. 10.2 - Solve (c2)(c+8)=7 by completing the square.Ch. 10.2 - Solve (d7)(d+3)=56 by completing the square.Ch. 10.2 - Solve 2m2+16m8=0 by completing the square.Ch. 10.2 - Solve 4n224n56=8 by completing the square.Ch. 10.2 - Solve 3r22r=21 by completing the square.Ch. 10.2 - Solve 4t2+2t=20 by completing the square.Ch. 10.2 - Solve 4x2+3x=12 by completing the square.Ch. 10.2 - Solve 5y2+3y=10 by completing the square.Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - Rafi is designing a rectangular playground to have...Ch. 10.2 - Yvette wants to put a square swimming pool in the...Ch. 10.2 - Solve the equation x2+10x=25 (a) by using the...Ch. 10.2 - Solve the equation y2+8y=48 by completing the...Ch. 10.3 - Solve 3y25y+2=0 by using the Quadratic Formula.Ch. 10.3 - Solve 4z2+2z6=0 by using the Quadratic Formula.Ch. 10.3 - Solve a22a15=0 by using the Quadratic Formula.Ch. 10.3 - Solve b2+10b+24=0 by using the Quadratic Formula.Ch. 10.3 - Solve 2p2+8p+5=0 by using the Quadratic Formula.Ch. 10.3 - Solve 5q211q+3=0 by using the Quadratic Formula.Ch. 10.3 - Solve 3m2+12m+7=0 by using the Quadratic Formula.Ch. 10.3 - Solve 5n2+4n4=0 by using the Quadratic Formula.Ch. 10.3 - Solve 4a23a+8=0 by using the Quadratic Formula.Ch. 10.3 - Solve 5b2+2b+4=0 by using the Quadratic Formula.Ch. 10.3 - Solve x(x+2)5=0 by using the Quadratic Formula.Ch. 10.3 - Solve y(3y1)2=0 by using the Quadratic Formula.Ch. 10.3 - Solve 14c213c=112 by using the Quadratic Formula.Ch. 10.3 - Solve 19d212d=12 by using the Quadratic Formula.Ch. 10.3 - Solve r2+10r+25=0 by using the Quadratic Formula.Ch. 10.3 - Solve 25t240t=16 by using the Quadratic Formula.Ch. 10.3 - Determine the number of solutions to each...Ch. 10.3 - Determine the number of solutions to each...Ch. 10.3 - Identify the most appropriate method to use to...Ch. 10.3 - Identify the most appropriate method to use to...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - 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In the following exercises, determine the number...Ch. 10.3 - In the following exercises, identify the most...Ch. 10.3 - In the following exercises, identify the most...Ch. 10.3 - In the following exercises, identify the most...Ch. 10.3 - In the following exercises, identify the most...Ch. 10.3 - A flare is fired straight up from a ship at sea....Ch. 10.3 - An architect is designing a hotel lobby. She wants...Ch. 10.3 - Solve the equation x2+10x=200 (a) by completing...Ch. 10.3 - Solve the equation 12y2+23y=24 (a) by completing...Ch. 10.4 - The product of two consecutive odd integers is 99....Ch. 10.4 - The product of two consecutive odd integers is...Ch. 10.4 - Find the dimensions of a triangle whose width is...Ch. 10.4 - If a triangle that has an area of 110 square feet...Ch. 10.4 - The sun casts a shadow from a flag pole. The...Ch. 10.4 - The distance between opposite corners of a...Ch. 10.4 - The length of a 200 square foot rectangular...Ch. 10.4 - A rectangular tablecloth has an area of 80 square...Ch. 10.4 - An arrow is shot from the ground into the air at...Ch. 10.4 - A man throws a ball into the air with a velocity...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - A bullet is fired straight up from a BB gun with...Ch. 10.4 - A city planner wants to build a bridge across a...Ch. 10.4 - Make up a problem involving the product of two...Ch. 10.4 - Make up a problem involving the product of two...Ch. 10.5 - Graph y=x2 .Ch. 10.5 - Graph y=x2+1 .Ch. 10.5 - Determine whether each parabola opens upward or...Ch. 10.5 - Determine whether each parabola opens upward or...Ch. 10.5 - For the parabola find: (a) the axis of symmetry...Ch. 10.5 - For the parabola y=2x24x3 find: (a) the axis of...Ch. 10.5 - Find the intercepts of the parabola y=x2+2x8 .Ch. 10.5 - Find the intercepts of the parabola y=x24x12 .Ch. 10.5 - Find the intercepts of the parabola y=3x2+4x+4 .Ch. 10.5 - Find the intercepts of the parabola y=x24x5 .Ch. 10.5 - Find the intercepts of the parabola y=x212x36 .Ch. 10.5 - Find the intercepts of the parabola y=9x2+12x+4 .Ch. 10.5 - Graph the parabola y=x2+2x8 .Ch. 10.5 - Graph the parabola y=x28x+12 .Ch. 10.5 - Graph the parabola y=3x2+12x12 .Ch. 10.5 - Graph the parabola y=25x2+10x+1 .Ch. 10.5 - Graph the parabola y=2x26x+5 .Ch. 10.5 - Graph the parabola y=2x21 .Ch. 10.5 - Graph the parabola y=5x2+10x+3 .Ch. 10.5 - Graph the parabola y=3x26x+5 .Ch. 10.5 - Find the maximum or minimum value of the quadratic...Ch. 10.5 - Find the maximum or minimum value of the quadratic...Ch. 10.5 - The quadratic equation h=16t2+128t+32 is used to...Ch. 10.5 - A toy rocket shot upward from the ground at a rate...Ch. 10.5 - In the following exercises, graph: 163. y=x2+3Ch. 10.5 - In the following exercises, graph: 164. y=x2+1Ch. 10.5 - In the following exercises, determine if the...Ch. 10.5 - In the following exercises, determine if the...Ch. 10.5 - In the following exercises, determine if the...Ch. 10.5 - In the following exercises, determine if the...Ch. 10.5 - In the following exercises, find (a) the axis of...Ch. 10.5 - In the following exercises, find (a) the axis of...Ch. 10.5 - In the following exercises, find (a) the axis of...Ch. 10.5 - In the following exercises, find (a) the axis of...Ch. 10.5 - In the following exercises, find the x- and...Ch. 10.5 - In the following exercises, find the x- and...Ch. 10.5 - In the following exercises, find the x- and...Ch. 10.5 - In the following exercises, find the x- and...Ch. 10.5 - In the following exercises, find the x- and...Ch. 10.5 - In the following exercises, find the x- and...Ch. 10.5 - In the following exercises, graph by using...Ch. 10.5 - In the following exercises, graph by using...Ch. 10.5 - In the following exercises, graph by using...Ch. 10.5 - In the following exercises, graph by using...Ch. 10.5 - In the following exercises, graph by using...Ch. 10.5 - In the following exercises, graph by using...Ch. 10.5 - In the following exercises, graph by using...Ch. 10.5 - 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Round answers...Ch. 10.5 - In the following exercises, solve. Round answers...Ch. 10.5 - In the following exercises, solve. Round answers...Ch. 10.5 - In the following exercises, solve. Round answers...Ch. 10.5 - In the following exercises, solve. Round answers...Ch. 10.5 - In the following exercises, solve. Round answers...Ch. 10.5 - In the previous set of exercises, you worked with...Ch. 10.5 - In the previous set of exercises, you worked with...Ch. 10.5 - For the revenue model in Exercise 10.205 and...Ch. 10.5 - For the revenue model in Exercise 10.206 and...Ch. 10 - In the following exercises, solve using the Square...Ch. 10 - In the following exercises, solve using the Square...Ch. 10 - In the following exercises, solve using the Square...Ch. 10 - In the following exercises, solve using the Square...Ch. 10 - In the following exercises, solve using the Square...Ch. 10 - In the following exercises, solve using the Square...Ch. 10 - In the following exercises, solve using the Square...Ch. 10 - In the following exercises, solve using the Square...Ch. 10 - In the following exercises, solve using the Square...Ch. 10 - In the following exercises, solve using the Square...Ch. 10 - In the following exercises, solve using the Square...Ch. 10 - In the following exercises, solve using the Square...Ch. 10 - 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In the following exercises, complete the square to...Ch. 10 - In the following exercises, complete the square to...Ch. 10 - In the following exercises, complete the square to...Ch. 10 - In the following exercises, complete the square to...Ch. 10 - In the following exercises, complete the square to...Ch. 10 - In the following exercises, solve by completing...Ch. 10 - In the following exercises, solve by completing...Ch. 10 - In the following exercises, solve by completing...Ch. 10 - In the following exercises, solve by completing...Ch. 10 - In the following exercises, solve by completing...Ch. 10 - In the following exercises, solve by completing...Ch. 10 - In the following exercises, solve by completing...Ch. 10 - In the following exercises, solve by completing...Ch. 10 - In the following exercises, solve by completing...Ch. 10 - In the following exercises, solve by completing...Ch. 10 - In the following exercises, solve by completing...Ch. 10 - In the following exercises, solve by completing...Ch. 10 - 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Rounding...Ch. 10 - In the following exercises, solve. Rounding...Ch. 10 - Use the Square Root Property to solve the...Ch. 10 - Use Completing the Square to solve the quadratic...Ch. 10 - Use the Quadratic Formula to solve the quadratic...Ch. 10 - Solve the following quadratic equations. Use any...Ch. 10 - Solve the following quadratic equations. Use any...Ch. 10 - Solve the following quadratic equations. Use any...Ch. 10 - Solve the following quadratic equations. Use any...Ch. 10 - Solve the following quadratic equations. Use any...Ch. 10 - Use the discriminant to determine the number of...Ch. 10 - Use the discriminant to determine the number of...Ch. 10 - Solve by factoring, the Square Root Property, or...Ch. 10 - Solve by factoring, the Square Root Property, or...Ch. 10 - For each parabola, find (a) which ways it opens,...Ch. 10 - For each parabola, find (a) which ways it opens,...Ch. 10 - For each parabola, find (a) which ways it opens,...Ch. 10 - For each parabola, find (a) which ways it opens,...Ch. 10 - For each parabola, find (a) which ways it opens,...Ch. 10 - Graph the following parabolas by using intercepts,...Ch. 10 - Graph the following parabolas by using intercepts,...Ch. 10 - Solve. 342. A water balloon is launched upward at...
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- Which of the following represents the graph of f(x)=3x-2? 7 6 5 4 ++ + + -7-6-5-4-3-2-1 1 2 3 4 5 6 7 -2 3 -5 6 -7 96 7 5 4 O++ -7-6-5-4-3-2-1 -2 -3 -4 -5 -7 765 432 -7-6-5-4-3-2-1 -2 ++ -3 -4 -5 -6 2 3 4 5 6 7 7 6 2 345 67 -7-6-5-4-3-2-1 2 3 4 5 67 4 -5arrow_forward13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of the following sets and the cardinal number of each set. a) W° and n(W) b) (VUW) and n((V U W)') c) VUWUX and n(V U W UX) d) vnWnX and n(V WnX)arrow_forward9) Use the Venn Diagram given below to determine the number elements in each of the following sets. a) n(A). b) n(A° UBC). U B oh a k gy ท W z r e t ་ Carrow_forward
- 5) Describe the difference between disjoint sets and overlapping sets.arrow_forward12) Suppose U = {a,b,c,d,e) and A = {a, b, c, e) and B = (c,d,e). Determine (An B).arrow_forward1) Use the roster method to list the elements of the set consisting of: a) All positive multiples of 3 that are less than 20. b) Nothing (An empty set).arrow_forward
- 2) Let M = {all postive integers), N = {0,1,2,3... 100), 0= {100,200,300,400,500). Determine if the following statements are true or false and explain your reasoning. a) NCM b) 0 C M c) O and N have at least one element in common d) O≤ N e) o≤o 1arrow_forward4) Which of the following universal sets has W = {12,79, 44, 18) as a subset? Choose one. a) T = {12,9,76,333, 44, 99, 1000, 2} b) V = {44,76, 12, 99, 18,900,79,2} c) Y = {76,90, 800, 44, 99, 55, 22} d) x = {79,66,71, 4, 18, 22,99,2}arrow_forward3) What is the universal set that contains all possible integers from 1 to 8 inclusive? Choose one. a) A = {1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8} b) B={-1,0,1,2,3,4,5,6,7,8} c) C={1,2,3,4,5,6,7,8} d) D = {0,1,2,3,4,5,6,7,8}arrow_forward
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