Aquadratic equation is shown below:

x2 − 14x + 41 = 0

which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers? (5 points)

a: add 8 to both sides of the equation
b: add 9 to both sides of the equation
c: subtract 8 from both sides of the equation
d: subtract 9 from both sides of the equation

What is the vertex form of f(x) = x2 + 6x + 3

The length of a rectangle is x times the square root of 100. the width is one-half y more than three-halves x. given that the area of the rectangle is 125 cm2, which equation could represent the rectangle in terms of x and y? a) 5xy − 15x = 125 b) 5xy + 15x = 125 c) 15x2 − 5xy = 125 d) 15x2 + 5xy = 125

Each person in an it department of 25 people works on at least one of 3 major projects: system security, program implementation, platform development. 10 people work on system security, 13 work on program implementation, and 12 work on platform development. 4 people work on system security and platform development, 5 people work on program implementation and platform development, and 2 people work on all three projects. how many people work on system security and program implementation?