1.) In solving the equation (x + 1)(x - 2) = 4, Eric stated that the solution would be x + 1 = 4 => x = 3 or (x - 2) = 4 => x = 6. 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 330 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 - 10t + 330, 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.
3x^2 + 6x - 5 = 0

Solution Preview

1. Eric should be making use of the Zero Product Theorem, but for that to work the product of his two factors must be 0. Here is the correct solution.

x^2 - x ...

Solution Summary

The expert solves an equation. The nearest hundredths place are provided.

solving equations and graph the functions. Find all real or imaginary solutions to each equation. ... 3. x - 1 = 2x - 3 4. (w2- 1)2 + 2(w2- 1) = 15 x + 2 x + 4. ...

... 9. How do I solve the following system of equations: 3y+1=2(x+8) AND 3Y+5=2X-4. ... 9. How do I solve the following system of equations: 3y+1=2(x+8) AND 3Y+5=2X-4. ...

... Radical Expressions and Linear Equations and Inequalities are investigated. The solution is detailed and well presented. ... 5x(x + 1)(x 1) > 0. 5− 2 x 24. ...

... To solve this system, we plug in the first equation to the second one and get 3(3 y ... y = 3 So x = 3 y − 4 = 3 × 3 − 4 = 5 . So the solution is x = 5, y ...

...x sin( 2 x) 1). Given the differential equation for y ... y ′′ + 2by ′ + b 2 y = e −bx / x 2 , x > 0 ; a ... the complementary solution of (1) by solving L[ y ...

...solve the system of equations: y = 2x 6 y=x5. By substituting, we will get. 2x 6 = x 5 2x x = -5 + 6 = 1 x=1. y = 2x 6 = 2 6 = -4 The ...

... the slope of any line perpendicular to the line through points (6, 3) and (7, 7). 7. Match the graph with one of the equations. ...x = -8 9. Solve the following ...

... 0) = 0 and ∂t boundary conditions u (0, y, t ) = u (1, y, t ) = u ( x,0, t ) = u ( x,1, t ) = 0. 2. Solve the two-dimensional wave equation for a ...