2.3+Diving+In+0910

Adit Mahmood 4/19/10   Block 8F
 * 2.3 **





  || A=30(50+20) = (30*50) + (30*20) = 1500 + 600  =2100  A= (30*50) + (30*20) = 1500 + 600 =2100  ** A2. ** A=30(25+10) = (30*25) + (30*10) = 750 + 300  = 1050  A= (30*25) + (30*10) = 750 + 300 = 1050   ** A3. ** A= R(25+15) = 25R + 15R = 40R A= (25*R) (15*R) = 25R + 15R = 40R A= R(S * T) = (R*S) + (R*T) = Sr + Jr A = (R*S) + (R*T) = Sr + Jr Rectangles 1, 3, 5 are equal to this requirement. The only one that fits is Rectangle 2. The Factored form is X(5+4). This is equivalent since if you break it up, you get 5X + 4X.  ** X Values ** ** 5X + 10 ** || ** Area ** || 1 ||   15  ||  2  ||   20  ||  3  ||   25  ||  4  ||   30  ||  5  ||   35  || ** X Values ** ** 5(X+2) ** || ** Area ** || 1 ||   15  ||  2  ||   20  ||  3  ||   25  ||  4  ||   30  ||  5  ||   35  || **3B.** X(3+5) = 3X + 5X X
 * A. **** Below are 4 diagrams of pools with swimming and diving sections. For each design show 2 methods for calculating the area for the water. Then tell which method requires fewer steps. **
 * A1. **
 * 30M **
 * 50M 20M **
 * 30M **
 * 25M 10M **
 * R **
 * 25M 15M **
 * A4. **
 * || [[image:file:///C:/Users/Adit/AppData/Local/Temp/msohtmlclip1/01/clip_image006.gif width="317" height="152"]] ||
 * || [[image:file:///C:/Users/Adit/AppData/Local/Temp/msohtmlclip1/01/clip_image006.gif width="317" height="152"]] ||
 * R **
 * S T **
 * __ F.U __**
 * 1A. Which of the rectangles have an area of 5(4+X) **
 * 1C. Which of the rectangles have an area of 5x + 4x? **
 * 1D. Write an expression in factored form that is equivalent to 5X + 4X. Explain how you know its equivalent. **
 * 2A. Draw a diagram that uses areas of rectangle to illustrate that 5X + 10 and 5(X+2) are equivalent. **
 * 5M **
 * X 2M **
 * 5(X+2) **
 * 5(2+2) **
 * 10 + 10 **
 * = 20 **
 * 5X + 10 **
 * 5*2 + 10 **
 * 10 + 10 **
 * = 20 **
 * 2B. Make a table or graph to show that 5X + 10 and 5(X+2) is equivalent. **
 * 3. Write the expression in expanded form that is equivalent to the given expression. **
 * 3A. ** 1.5(4+X) = 6+ 1.5X
 * 4. Write the expression in factored form that is equivalent to the given expression. **
 * 4A. ** 27 + 36X = 9(3+4X)
 * 5. Express the area of the purple rectangle in both factored and expanded form. **
 * || [[image:file:///C:/Users/Adit/AppData/Local/Temp/msohtmlclip1/01/clip_image003.gif width="267" height="101"]] ||
 * || [[image:file:///C:/Users/Adit/AppData/Local/Temp/msohtmlclip1/01/clip_image003.gif width="267" height="101"]] ||

**X** X2 + 3X X(X+3)
 * X 3M **
 * 6A. Draw a rectangle whose area is represented by the expression X(5+X) **
 * || [[image:file:///C:/Users/Adit/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif width="299" height="132"]] ||
 * || [[image:file:///C:/Users/Adit/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif width="299" height="132"]] ||

**X** **5M X** 5X + X2 **7A. Use what you learned to write some expressions that are equivalent to 4X + 6.** 2(2X+3) **7B. Use what you learned to write some expressions that are equivalent to X2+4X** X(X+4) **7C. What general rules have you discovered that can help you write equivalent equations?** You can combine like terms to make expanded form into factored form. If you want to go from factored form to expanded form, you do the multiplication and then combine like terms. If you have numbers that have a common factor, you put it in factored form with the common factor and then use one of the methods above.
 * 6B. Write an expression in expanded form that is equivalent to X(5+X) **