The purpose of this lab is to practice multiplying ...



MAT 117 Application Assignment #1Answer the questions below. Use Equation Editor when writing or solving mathematical expressions or equations. First, save this file to your hard drive by selecting SAVE AS from the File menu. Click the white space below each question to maintain proper formatting.In order to receive credit, all work must be shown in the space provided. An answer alone will not be sufficient.The formulas that you will need are perimeter equals the sum of twice the length and twice the width (P=2l+2w), and area equals the product of the length and the width (A=lw). Using the given floor plan above, answer the following questions.Part 1: Using your knowledge of polynomial addition and subtraction (combining like terms), answer the following questions. Find the entire width of this two-bedroom apartment a (not counting the patio) in terms of x. (Be careful to examine the expressions that are given and use those to find the ones that are not.) The 2x+5 is on the left and the x-3 fills in to the top on the right.2x+5 + x-3= 3x+2 feetFind the entire length of this two-bedroom apartment in terms of x.All from the bottom:x + x+5 + x-1 + x + x+8Simplify:5x + 12 feetPart 2: Using your knowledge of the distributive property and polynomial addition and subtraction, answer the following questions. (Remember, P=2l+2w.) Find the perimeter of the entire 2-bedroom apartment (excluding the patio) in terms of x.P = 2L + 2W= 2(3x+2) + 2(5x+12)= 6x + 4 + 10x + 24= 16x + 28 feetFind the perimeter of the living room and dining room in terms of x. Width = 2x+5Length = x+x+5 = 2x + 5Perim = 2(2x + 5) + 2(2x + 5)= 4x + 10 + 4x + 10= 8x + 20 feetPart 3: Using your knowledge of solving linear equations, answer the following questions. If the perimeter of the living room and dining room is 68 feet, what is the value of x? Set the previous answer equal to 68:68 = 8x + 20Subtract 20:48 = 8xDivide by 8:x = 6 feetIf the length of the entire apartment is 52 feet, what is the value of x?Using the value from problem 2:52 = 5x + 12Subtract 12:40 = 5xDivide by 5:x = 8 feetPart 4: You have reviewed polynomial multiplication and division in this module, practice now. (Remember, A=lw) Find the equation that would represent the area of the entire living room/dining room in terms of x. L * W= (2x+5)(2x+5)Using the rule for perfect square trinomials:Area = 4x2 + 20x + 25 square feetFind the equation that would represent the area of the entire apartment (excluding the patio) in terms of x. Note: don't forget to subtract for the cutout area in the upper left corner.= L*W – Lsmall * Wsmall= (3x+2)(5x+12) – (x-3)(x-3)FOIL= 15x2 + 36x + 10x + 24 – (x2 – 6x + 9)Simplify:Area = 14x2 + 52x + 15 square feetIf the area of the kitchen was 2x-4, what would be the width? Write the expression or number for the width.Area = L*W2x-4 = (x-2)WFactor:2(x-2) = (x-2)WDivide out the x-2:W = 2 feetIf the area of the dining room and living room is 225 sq. ft., what is the equation that would be used to solve for x? Write the equation with zero on the right and then solve for x.Set that area to 225:4x2 + 20x + 25 = 225Subtract 225:4x2 + 20x – 200 = 0Divide by 4:x2 + 5x – 50 = 0Factor:(x+10)(x-5) = 0x = -10 or 5, but it can’t be negative, so:x = 5 feet ................
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