  by Lori
(WASHINGTON)

I have a lot troubles understanding word problems on where to start the solving process. Please help I need answers by tomorrow please show all work to help me understand the how.

1. In solving the equation (x + 1)(x – 2) = 54, Eric stated that the solution would be
x + 1 = 54 => x = 53 or (x – 2) = 54 => x = 56
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.

2. If a stone is tossed from the top of a 190 meter building, the height of the stone as a function of time is given by h(t)=-9.8t^2-10t+190, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer.

3. Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
8x^2+2x+4=0

a)Two different irrational solutions
b)Two different imaginary solutions
c)Exactly one rational solution
d)Two different rational solutions

4. Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.
18x + 6y = 78
12x + 54y = -48

5. Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
14x+18y =-54
-4x-14y = 42

Thank you,
Lori

 Sep 10, 2011 Quadratic & Simultaneous Equations by: Staff --------------------------------------------------------------------Part IVthe discriminant isΔ = (b² - 4ac)Δ = (2² - 4*8*4)Δ = (4 - 128)Δ = -124Choice b): There are two imaginary solutions since √(b² - 4ac) = √(-124) ≈ ±11.1355 i--------------------------------------------------4. Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.18x + 6y = 7812x + 54y = -48 You can simplify the second equation by dividing each side of the equation by 6(12x + 54y)/6 = (-48)/612x/6 + 54y/6 = (-48)/6(12/6)*x + (54/6)*y = (-48)/6(2)*x + (9)*y = -82x + 9y = -8You can simplify the first equation by dividing each side of the equation by 6(18x + 6y)/6 = (78)/618x/6 + 6y/6 = 78/6(18/6)*x + (6/6)*y = 78/6(3)*x + (1)*y = 133x + y = 13Solve the simplified version of the 1st equation for y3x + y = 133x - 3x + y = 13 - 3x0 + y = 13 - 3xy = 13 - 3xSUBSTITUTE the SOLUTION of y in the 2nd equationy = 13 - 3x (is the solution for y from the 1st equation) 2x + 9y = -8 (this is the simplified version of the 2nd equation)Substitute 13 - 3x for y in simplified version of the 2nd equation2x + 9y = -82x + 9(13 - 3x) = -8Solve for xEliminate the parentheses on the left side of the equation using the distributive law2x + 9(13 - 3x) = -82x + (9)*(13) + (9)*(-3x) = -8Combine like terms2x + 117 - 27x = -82x - 27x + 117 = -8(2x - 27x) + 117 = -8(-25x) + 117 = -8Add 25x to each side of the equation-25x + 117 = -8-25x + 25x + 117 = -8 + 25x(-25x + 25x) + 117 = -8 + 25x0 + 117 = -8 + 25x117 = -8 + 25xAdd 8 to each side of the equation117 + 8 = -8 + 25x + 8125 = -8 + 25x + 8125 = -8 + 8 + 25x 125 = (-8 + 8) + 25x 125 = 0 + 25x 125 = 25x Divide each side of the equation by 25125 / 25 = 25x / 255 = 25x / 255 = x * (25 / 25)5 = x * (1)5 = x x = 5Now that you know that x = 5, substitute the number 5 wherever x appears in either of the equations.3x + y = 13 (this is the simplified version of the 1st equation) x = 53 * 5 + y = 13 15 + y = 13 Solve for y15 + y = 13 15 + y - 15 = 13 - 15 15 - 15 + y = 13 - 15 (15 - 15) + y = 13 - 15 0 + y = 13 - 15 y = 13 - 15 y = -2 the final answer to problem 4 is: x = 5, y = -2 check the solution by substituting the numerical values of x and y into both original equations1st equation (original): 18x + 6y = 78x = 5, y = -218x + 6y = 7818 * 5 + 6 * (-2) = 7890 - 12 = 7878 = 78, OK2nd equation (original): 12x + 54y = -48x = 5, y = -212x + 54y = -4812 * 5 + 54 * (-2) = -4860 + 54 * (-2) = -4860 - 108 = -48-48 = -48, OKsince both equations are in balance for the values x = 5 and y = -2, x and y are valid solutions --------------------------------------------------------------------