Solve the equation for x, where x is a real number (5 points): -2x^2 + 6x + 4 = 5

1 answer:

6 0

Subtract 5 to both sides so that the equation becomes -2x^2 + 6x - 1 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
                                            x = [ -b ± √(b^2 - 4ac) ] / (2a)
                                            x = [ -6 ± √((6)^2 - 4(-2)(-1)) ] / ( 2(-2) )
                                            x = [-6 ± √(36 - (8) ) ] / ( -4 )
                                            x = [-6 ± √(28) ] / (-4)
                                            x = [-6 ± 2*sqrt(7) ] / (-4 )
                                            x =3/2 ± -sqrt(7)/ 2
The answers are 3/2 + sqrt(7)/2 and 3/2 - sqrt(7)/2.

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A quadrilateral WXYZ contains wxy where measure of wxy=92 degrees. Once rotated 270° about the origin and translated 2 units up,

Marianna [84]

Answer:

C. 92 degrees

Step-by-step explanation:

Given that the $\angle{wxy}=$ 92° which is one of the angles of the quadrilateral WXYZ

The quadrilateral is first rotated by 270° about the origin and then translated 2 units up, the new position of the quadrilateral is W'X'Y'Z'.

The shape of the quadrilateral is remained unchanged due to rotation and translation, so all the angles of the final quadrilateral W'X'Y'Z' is the same as the angles of the given quadrilateral WXYZ.

So, $\angle{w'x'y'}= \angle{wxy}$