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OBJECTIVE 4

4-A) The perimeter of a rectangular garden is 42 feet. The length of the garden is 5 feet more than twice the width . Which system of equations will determine the length, l, and the width, w, of the garden?. THE SECOND EQUATION IS WRITTEN USING THE FACT THAT THE LENGTH IS 5 MORE

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OBJECTIVE 4

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  1. 4-A) The perimeter of a rectangular garden is 42 feet. The length of the garden is 5 feet more than twice the width. Which system of equations will determine the length, l, and the width, w, of the garden? THE SECOND EQUATION IS WRITTEN USING THE FACT THAT THE LENGTH IS 5 MORE THAN TWICE THE WIDTH: l = 2w+ 5 l = 2w+ 5 w w WE NEED TO USE THE INFORMATION GIVEN IN THE PROBLEM TO WRITE TWO EQUATIONS. THE FIRST EQUATION IS WRITTEN USING THE FACT THAT THE PERIMETER IS 42: l = 2w+ 5 2w+ 2l =42 A) 2l + w =42 2w + l =5 C) 2l + w =42 2l -w =5 B) 2l + 2w =42 l =5 -2w D) 2l + 2w =42 l =2w + 5 D IS THE RIGHT ANSWER! E 2l + 2w =42 w =2l -5 OBJECTIVE 4

  2. 4-B) On a trip Joel drove 25 miles more than half the number of miles Rita drove. Together they drove 340 miles. How many miles did Joel drive? F 130 mi G 170 mi H 195 mi J 210 mi K 315 mi 25 miles more half the number of miles Rita drove Together they drove 340 miles WE USE THE FIRST SENTENCE TO WRITE ONE EQUATION: (1/2) R + 25 J = WE USE THE SECOND SENTENCE TO WRITE ANOTHER EQUATION: J + R = 340 NOW, WE USE THE TWO EQUATIONS TO FIND HOW MANY MILES JOEL DROVE USING A T-I 82 CALCULATOR: OBJECTIVE 4

  3. J = (1/2)R + 25 J + R = 340 BEFORE WE CAN ENTER THESE EQUATIONS IN A TI- 82, WE NEED TO HAVE ONE VARIABLE ON ONE SIDE OF = BY ITSELF. IN THE SECOND EQUATION MOVE R TO THE RIGHT SIDE AND CHANGE ITS SIGN. WE ALSO LET J = Y AND R = X. ZOOMED ONCE 1)NOW WE ENTER THESE EQUATIONS IN A TI-82. PRESS Y= AND ENTER BOTH EQUATIONS. NOT ZOOMED ZOOMED TWICE 3) ZOOM OUT BY PRESSING ZOOM, 3, AND ENTER TWICE. YOU NEED TO ZOOM OUT UNTIL YOU SEE BOTH GRAPHS AND THEIR INTERSECTION ON THE SCREEN. ZOOMED 3 TIMES Y = (1/2)X + 25 Y = 340 - X 2)PRESS GRAPH. NOW,WE CALCULATE THE COORDINATES OF THE INTERSECTION POINT. OBJECTIVE 4

  4. 4-B) On a trip Joel drove 25 miles more than half the number of miles Rita drove. Together they drove 340 miles. How many miles did Joel drive? F 130 mi G 170 mi H 195 mi J 210 mi K 315 mi THIS IS THE SCREEN AFTER ZOOMING 3 TIMES: THE CORRECT ANSWER ZOOMED 3 TIMES 5) PRESS 5, THEN ENTER 3 TIMES. 4) PRESS 2ND, THEN TRACE. THE COORDINATES ARE GIVEN AS: X=210 AND Y=130. BUT, WE KNOW THAT X=R AND Y=J. SO THE CORRECT ANSWER IS F 130 mi. REMEMBER YOU WERE ASKED TO FIND THE NUMBER OF MILES Joel DROVE. OBJECTIVE 4

  5. 4-C) Numbers above 3 make the right side greater. 3 makes the two sides equal. Numbers below 3 (which are greater than 3!) make the left side greater than the right side. So, d is correct! We use a TI-82 to answer this Question: 3)Look for the number in x column that makes the left side of > equal to the right side (use arrow up or down!). • Enter the right side in Y2 and the left • side in Y1: 2)Press 2nd WINDOW and set the Tbl to 0.5. OBJECTIVE 4

  6. 4-C) Therefore the answer is d. We use a different method to answer 4-C. 3)The graph shows all X’s that make the logical statement 4x - 1 > 2x + 5 a true statement; the graph of all X’s which make Y have a value of 1. These X’s are also the solutions of the inequality given. 1)Enter the expressions in Y1. To enter > press 2nd , math, then 3. 2)Press GRAPH. Note:When X is 3 Y is 0; This means that 3 is not a solution. To see this press 2nd GRAPH. OBJECTIVE 4

  7. End-of-Course Test Algebra I THIS IS THE END OF OBJECTIVE 4 REVIEW. YOU NEED TO WORK OUT THE PROBLEMS RELATED TO THIS OBJECTIVE. YOUR TEACHER WILL PROVIDE YOU WITH THE WORKSHEETS. WE WILL COVER OBJECTIVE 5 NEXT. CREATED BY R.KHADEM/ Adapted by Rene Patterson

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