David L. Johnson, Jr. v. State of Indiana

Description

• exposé - matière potentielle : on a mental health assessment
• exposé - matière potentielle : the law
• exposé - matière potentielle : the case
• revision
• exposé
• exposé - matière potentielle : on the mental health assessment
• redaction

FOR PUBLICATION ATTORNEY FOR APPELLANT: ATTORNEYS FOR APPELLEE: MATTHEW J. MCGOVERN GREGORY F. ZOELLER Evansville, Indiana Attorney General of Indiana BRIAN REITZ Deputy Attorney General Indianapolis, Indiana IN THE COURT OF APPEALS OF INDIANA DAVID L. JOHNSON, JR., ) ) Appellant-Defendant, ) ) vs. ) No. 82A01-1103-CR-130 ) STATE OF INDIANA, ) ) Appellee-Plaintiff. ) APPEAL FROM THE VANDERBURGH SUPERIOR COURT The Honorable Mary Margaret Lloyd, Judge Cause No.

• a.j.
• a. j.
• felony charge of neglect
• johnson
• johnson to an executed term of forty years
• trial court
• jury
• evidence

Sujets

• The Law
• Révision
• Exposé
• Redaction
• Record
• McGovern
• Motion

Informations

• Publié par: romek
• Nombre de lectures: 30
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Then You added, subtracted, and multiplied radical expressions. (Lesson 103)

Now  Solve radical equations.  Solve radical equations with extraneous solutions.

NewVocabulary radical equations extraneous solutions

Math Online glencoe.com  Extra Examples  Personal Tutor  SelfCheck Quiz  Homework Help

Radical Equations Why? The waterline length of a sailboat is the length of the line made by the water’s edge when the boat is full. A sailboat’s hull speed is the fastest speed that it can travel. You can estimate hull speedhby using the formulah=1.34 √ , whereis the length  of the sailboat’s waterline.

Radical Equations  Equations that contain variables in the radicand, likeh=1.34 √ ,  are calledradical equations. To solve, isolate the desired variable on one side of the equation first. Then square each side of the equation to eliminate the radical.

For Your

EXAMPLE 1 Variable as a Radicand SAILINGIdris and Sebastian are sailing in a friend’s sailboat. They measure the hull speed at 9 nautical miles per hour. Find the length of the sailboat’s waterline. Round to the nearest foot.  UnderstandYou know how fast the boat will travel and that it relates to the length.  PlanThe boat travels at 9 nautical miles per hour. The formula for hull speed ish=1.34 √ .   Solveh=1.34 √  Formula for hull speed  _ _ 9=1.34 √  Substitute 9 forh.  √ 9 1.34  = Divide each side by 1.34. 1.34 1.34  6.71641791= √  Simplify.  2 2 ( 6.716417912 ) = ( √  ) Square each side of the equation.   45.11026954≈ Simplify. The sailboat’s waterline length is about 45 feet.  CheckCheck the results by substituting your estimate back into the original formula. Remember that your result should be about 9. h=1.34 √  Formula for hull speed  91.344  5 h=9 and=45 √ 91.34 ( 6.708203932 √ 4  5=6.708203932 ) 9≈8.98899327 Multiply. 624 10 Chapter Radical Functions and Geometry

Watch Out! Squaring Each Side Remember that when you square each side of the equation, you must square the entire side of the equation, even if there is more than one term on the side.

StudyTip Extraneous SolutionsWhen checking solutions for extraneous solutions, we are only interested in principal roots. For example, while √ 1=±1, we are  only interested in 1.

✓ Check Your Progress 1.DRIVINGThe equationv= √ 2.5r represents the maximum velocity that a car  can travel safely on an unbanked curve whenvis the maximum velocity in miles per hour andris the radius of the turn in feet. If a road is designed for a maximum speed of 65 miles per hour, what is the radius of the turn?

Personal Tutor glencoe.com

When a radicand is an expression, isolate the radical first. Then square both sides of the equation.

EXAMPLE 2 Expression as a Radicand  Solve √ a+5+7=12. √ a  +  5+7=12 Original equation 2 2 √ a  +  5=5 Subtract 7 from each side. ( √ a  +  5 ) =5 Square each side.  a+5=25 Simplify.  a=20 Subtract 5 from each side. ✓ Check Your Progress Solve each equation. 2A. √ c  -  3-2=4 2B.4+ √ h+1=14  Personal Tutor glencoe.com

Extraneous Solutions Squaring each side of an equation sometimes produces a solution that is not a solution of the original equation. These are calledextraneous solutions. Therefore, you must check all solutions in the original equation.

EXAMPLE 3 Variable on Each Side Solve √ k+1=k-1. Check your solution.  √ k  +  1=k-1 Original equation 2 2 2k plify. 2 ( √ k  +  1 ) = ( k-1 ) Square each side.  k+1=k- +1 Sim 2  0=k-3k Subtractkand 1 from each side.  0=k ( k-3 ) Factor. k=0 ork-3=0 Zero Product Property  k=3 Solve. CHECK √ k  +  1=k-1 Original equation √ k  +  1=k-1 Original equation √ 0+10-1 k=0 √ 3+13-1 k=3   √ 1-1 Simplify. √ 42 Simplify.    1≠-1✘ False 2=2 True Since 0 does not satisfy the original equation, 3 is the only solution. ✓ Check Your Progress Solve each equation. Check your solution. 3A. √ t  +  5=t+3 3B.x-3= √ x-1  Personal Tutor glencoe.com Lesson 10-4 Radical Equations  625

✓ Check Your Understanding Example 1 1. GEOMETRYThe surface area of a basketball isxsquare inches. What is the radius 2 p. 624 of the basketball if the formula for the surface area of a sphere isSA= 4πr? Examples 2 and 3 Solve each equation. Check your solution. p. 625    2. √ 10h+1=21 3. √ 7  r  +  2+3=7 4.5+ √ g-3=6  5. √ 3  x  -  5=x-5 6. √ 2  n  +  3=n 7. √ a  -  2+4=a

=StepbyStep Solutionsbegin on page R12. Practice and Problem Solving Extra Practicebegins on page 815. p. 624 √ _ 7 Example 1 9  .8    8. EXERCISESuppose the functionS=π,whereSrepresents speed in meters per second andis the leg length of a person in meters, can approximate the maximum speed that a person can run.  a.speed of a person with a leg length ofWhat is the maximum running 1.1 meters to the nearest tenth of a meter?  b.What is the leg length of a person with a running speed of 2.7 meters per second to the nearest tenth of a meter?  c.person’s leg length increases, does their speed increase or decrease?As a Explain. Examples 2 and 3 Solve each equation. Check your solution. p. 625 √ a  +11=21 10. √ t √  -4=7 11.n-3=6  9  12. √ c  +  1  0=4 13. √ h-5=2 √ 3 14. √ k  +  7=3 √ 2        15.y= √ 12-y 16. √ u+6=u 17. √ r  +3=r-3 8. √  2  t=1+t 19.5 √ a  -  3+4=14 20.2 √ x  -  1  1-8=4  11- 21.The amount of timet, in seconds, that it takes a simple pendulum to complete a full swing is called the period of the pendulum. It is given by t=2π √ _ ,whereis the length of the pendulum, in feet.   32 a.The Giant Swing completes a period in about 8 seconds. About how long is the pendulum’s arm? Round to the nearest foot. b.Does increasing the length of the pendulum increase or decrease the period? Explain. Solve each equation. Check your solution. 4 22. √ 6  a  -  6=a+1 23. √ x+9x+15=x+524.6 √ _ -3=0 2 5  k  DollarCityinBrans S o i n lv , er 25. _ -10=4 26. √ 2a-121=a 27. √ 5x-9=2x 5  y   2 2 √ 6 The Giant Swing at  28. GEOMETRYThe formula for the slant heightcof a cone is reaches a height of the radius of its base. Find the height of the cone if the r h Missouri, swings riders at 2  2  c= √ h+r ,wherehis the height of the cone andris 45 miles per hour and 7 stories. slant height is 4 and the radius is 2. Round to the nearest tenth. Source:Silver Dollar City Amusement Park 626  Chapter10 Radical Functions and Geometry

Packaging has several objectives, including physical protection, information transmission, marketing, convenience, security, and portion control. C Source:Packaging World

 MULTIPLE REPRESENTATIONSIn this problem, you will solve a radical equation by 29 graphing. Consider the equation √ 2  x  -  7=x-7. a. GRAPHICALClear theY=list. Enter the left side of the equation as Press GRAPH . Y1= √ 2  x  -  7. Enter the right side of the equation asY2=x-7. b. GRAPHICALSketch what is shown on the screen. c. ANALYTICALUse theintersectfeature on the CALC menu to find the point of intersection. d. ANALYTICALSolve the radical equation algebraically. How does your solution compare to the solution from the graph? 30.CKAGINGA cylindrical container of chocolate drink mix has a volume of 162 cubic inches. The radiusrof the container can be found by using the formula r= _ ,whereVis the volume of the container andhis the height.  V  √ πh a.If the radius is 2.5 inches, find the height of the container. Round your answer to the nearest hundredth. b.If the height of the container is 10 inches, find the radius of the container. Round to the nearest hundredth

H.O.T. Problems UseHigherOrderThinking Skills 31. FIND THE ERRORJada and Fina solved √ 6-b= √ b+10. Is either of them   correct? Explain. Jada Fia 22 2 10) ( √ 6  –  b)= ( √ b  + 1  0) √ 6  -  b= √ b  + 1  0 √ 6  –  b= √  b +  1  0 6 – b = b + 10 2 ( √ 6  –  b)=( √  b +  6 – b = b + 10 2b = 4 b = 2 –2b = 4 b = –2 Chk √ 6  –  (2  ) √ (  2)  + 1  0 no sOlutôN √  4 ≠ √ 1  2 ✘ √ (  –2  ) +  1  0Check √ 6 – (–  2)  √ 8= √ 8✔   32. REASONINGWhich equation has the same solution set as √ 4= √ x+2? Explain   A. √ 4= √ x  + √ 2 B.4=x+2 C.2- √ 2= √  x    33. REASONINGExplain how solving the equation 5= √ x  +1 is different from solving the equation 5= √ x+1.  34. OPEN ENDEDWrite a radical equation with a variable on each side. Then solve the equation. 35. REASONINGIs the following equationsometimes,alwaysornevertrue? Explain.  2 √ (x-2)=x-2 x+9=36. CHALLENGESolve √  √ 3+ √  x.  37. WRITING IN MATHWrite some general rules about how to solve radical equations. Demonstrate your rules by solving a radical equation. Lesson 10-4 Radical Equations  627

Standardized Test Practice

38. SHORTRESPONSEZack needs to drill a hole40.What is the slope of a line that is parallel at each of the pointsA,B,C,D, andEon tothe line? circleP. y $ % # 1 0 x 110° " & If Zack drills holes so thatm∠APE=110°  F-3 H3 and the other four angles are equal in measure, what ism∠CPD? _ _ 1 1  G-J 3 3 39.Which expression is undefined whenw=3? w _ +1 w 2 -3w 41.What are the solutions of w-3 w+1   A C √ x+3-1=x-4? _ _ w 2  A1, 6 C1 2 w-3w 3w  B D 3w  B-1,-6 D6 3

Spiral Review 42.ELECTRICITYThe voltageVrequired for a circuit is given byV= √ PR, wherePis  the power in watts andRis the resistance in ohms. How many more volts are needed to light a 100-watt light bulb than a 75-watt light bulb if the resistance of both is 110 ohms? (Lesson 103) Simplifyeachexpression. (Lesson 102) 43. √ 6∙ √ 8 44. √ 3∙ √ 6 45.7 √ 3∙2 √ 6     2  7 5c 49.P 96 HY fe SI e C t. AL (L S es C s I o E t n N s 9 C e 5 E c ) Arpjoceitelis sisvi s g h dnobenyh ot =9 t 6 rsa t ig - ht up 2 Itel. (s)ofhevalue rgmorfveldnuo t sht ne h h ei w g h h i _ , s  3 46. _  47. √ _ 5  48. 2 2 5  √ 9xy √ 2 a  4d  √ 16xy in feet, after16t. Find t Factor each trinomial, if possible. If the trinomial cannot be factored using integers, writeprime. (Lesson 84) 2 2 2 50.2x+7x+5 51.6p+5p-6 52.5d+6d-8 2 2 2 53.8k-19k+9 54.9g-12g+4 55.2a-9a-18 Determine whether each expression is a monomial. Writeyesorno. Explain. (Lesson 71) 3 x1 _ 14 x 58.a-2b 59.4n+5p 60. _ 2 5 56.12 57.4 61.abc y

Skills Review

Simplify. (Lesson 11) 2 6 62.9 63.10

5 2 64.4 65. ( 8v )

628  Chapter10 Radical Functions and Geometry

 66. _ ) 3 2 w ( 9

3 2 67. ( 10y )