ok 3 questions
A. Is a polygon a plane figure (Always,sometimes,never) answer one of three
B.find value of x X(squared) +x amd X(squared) + 4
C. Find x. X(squared) + 2x + 40
and x(squared) - x +190
If someone could show me how to do those that would be great
Sure! Let's go through each question step by step:
A. Is a polygon a plane figure (Always, sometimes, never)?
To answer this question, let's first understand the definitions:
- A polygon is a closed plane figure with straight sides.
- A plane figure is any flat shape that can be drawn on a piece of paper.
From these definitions, we can conclude that a polygon is always a plane figure. The answer is "Always."
B. Find the value of x: x² + x and x² + 4.
To find the value of x, we need to solve the given equations separately:
1. x² + x
Since we have only one equation without any specific values, we can't solve for the exact value of x. However, we can factor out the common term "x" and rewrite the equation as:
x(x + 1)
So, the value of x is either 0 or -1.
2. x² + 4
Similar to the previous equation, we can't find the exact value of x unless we have additional information. However, we can factor out this equation as well:
x² + 4 = (x + 2)(x - 2)
So, the possible values of x are 2 or -2.
C. Find x: x² + 2x + 40 and x² - x + 190.
Let's solve each equation separately:
1. x² + 2x + 40
To find x, we need to set the equation equal to zero:
x² + 2x + 40 = 0
Since this equation cannot be easily factored, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
For our equation, a = 1, b = 2, and c = 40. Plugging these values into the quadratic formula, we get:
x = (-2 ± √(2² - 4(1)(40))) / (2(1))
Simplifying further:
x = (-2 ± √(-156)) / 2
Since we have a negative value under the square root, there are no real solutions to this equation.
2. x² - x + 190
Again, we set the equation equal to zero:
x² - x + 190 = 0
This equation cannot be easily factored either, so we'll use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
For this equation, a = 1, b = -1, and c = 190. Plugging these values into the quadratic formula, we get:
x = (-(-1) ± √((-1)² - 4(1)(190))) / (2(1))
Simplifying further:
x = (1 ± √(1 + 760)) / 2
x = (1 ± √761) / 2
Thus, the values of x are approximately (1 + √761)/2 and (1 - √761)/2.
I hope this helps! If you have any further questions, feel free to ask.