MATH - Speech or Presentation Example

PART I Answer the question and solve the problems below.  Make sure you show all your work so you can get partial credit even if you get the final answer wrong. 1. Determine whether the lines will be perpendicular when graphed.  3x  -  2y =    6  2x  +  3y =    6    Solution: First, the slope must be determined from each equation— Arranging to the form y = mx + b: The first equation becomes y = (3/2)*x - 3 whereas the second equation becomes y = (-2/3)*x + 2.

--- comparing the slopes, m1 = 3/2 and m2 = -2/3 are negative reciprocals of each other so this implies that the lines of the given equations are PERPENDICULAR. 2. Alice’s Restaurant has a total of 205 seats. The number of seats in the non-smoking section is 73 more than twice the number of seats in the smoking section. How many seats are in each section? Solution: Let x = the number of seats in the smoking section and 2x + 73 = the number of seats in the non-smoking section Since there are a total of 205 seats on both sections, then: x + 2x + 73 = 205 and combining like terms gives 3x = 132 then dividing each side by 3 --- x = 44 seats (smoking section) and 2(44) + 73 = 161 seats (non-smoking section)               3.

Solve the system of equations by the substitution method   x  + 3y =  32  -3x  + 2y =  3Solution:      Arranging the first equation makes x = 32 - 3y and substituting this into the second equation to replace the ‘x’ yields: -3 (32 - 3y) + 2y = 3 -96 + 9y + 2y = 3 --- 9y + 2y = 3 + 96 Then combining similar terms makes 11y = 99 and dividing by 11 (both sides) --- y = 9 plugging this into x = 32 - 3(9) --- x = 54.

Solve the system of equations x + y =  4 x - y =  -7Solution: By addition of the two given equations, 2x = -3 and dividing each side by 2 --- x = -3/2 And upon substitution to one of the original equations: -3/2 + y = 4 --- y = 4 + 3/2 --- y = 11/2             5. Ricks Paint Store sells a special shade of pink paint (Rickys Blush) which can be made from red paint and white paint.

The amount of red paint should be three times the amount of white paint. How much of each kind of paint is needed to make 264 gallons of Rickys Blush?Solution: Let x = the amount of white paint (in gallons) and 3x = the amount of red paint (in gallons) Since 264 gallons of paint are required for Ricky’s Blush of pink paint, Then x + 3x = 264 --- 4x = 264 and dividing by 4 (both sides) gives x = 66 gallons of white paint and 3(66) = 198 gallons of red paint               PART IICreate your system of linear equations then write a brief paper describing the system.

Is this a consistent system or inconsistent system?Application: My friend Edwin would like to put up a small store selling two kinds of peas – snap peas and snow peas. He estimates obtaining profit from each kg of snap peas worth $9.5 and from each kg of snow peas costing $8.7. If he desires to have 300 kgs of pea-mixture sold for $8.93 per kg, I wonder how much of each kind must be present in the mixture.Solution:Let x = the quantity of snap peas (in kg) and y = quantity of snow peas (in kg)Based on the given information, equations may be set up as:9.5x + 8.7y = (8.93)(300) --- equation (1)x + y = 300 --- equation (2)By applying substitution method (equation (2) into equation (1)):9.5x + 8.7 (300 – x) = (8.93)(300)9.5x + 2610 - 8.

7x = 26790.8x = 69Then dividing each side by 0.8, x = 86.25 kgs snap peasAnd 86.25 + y = 300 --- y = 213.75 kgs snow peas This is a CONSISTENT SYSTEM since there exists unique solution (86.25, 213.75).