Determine whether a triangle with the given vertices is a right triangle.
1 answer:
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Our function f(x) can be rewritten if we factor out a common x^2 from each term:
Now inside the parentheses we have a polynomial of the form a^2 - b^2, or the difference of two perfect squares, which can be factored as (a+b)(a-b) so we have:
Setting our function equal to zero gives us the roots x = 0, x = 4, and x = -4.
The multiplicity of the root zero is two since it occurs twice, and the others are one since they occur only once. If you graph the function you can see that it will only touch the x-axis at x = 0, but will cross the x-axis at x = 4 and x = -4.
Now inside the parentheses we have a polynomial of the form a^2 - b^2, or the difference of two perfect squares, which can be factored as (a+b)(a-b) so we have:
Setting our function equal to zero gives us the roots x = 0, x = 4, and x = -4.
The multiplicity of the root zero is two since it occurs twice, and the others are one since they occur only once. If you graph the function you can see that it will only touch the x-axis at x = 0, but will cross the x-axis at x = 4 and x = -4.
Answer:
Equation of line u in slope-intercept form is:
Step-by-step explanation:
Equation of line t : y = -2x + 9.
We need to find equation of line u, which is perpendicular to line t and passes through point (-10,4)
The equation must be in slope-intercept form.
The general equation of slope-intercept form is: where m is slope and b is y-intercept
Finding Slope:
If two lines are perpendicular, their slopes are opposite i.e
Slope of line t: y=-2x+9 we get m =-2 (Comparing with general form y=mx+b, we get m =-2)
Slope of line u:
So, we get Slope of line u: m=
Finding y-intercept:
Using slope m= and point(-10,4) we can find y-intercept
Equation of line u:
So, equation of line u, having slope m= and y-intercept b=9, we get:
So, Equation of line u in slope-intercept form is: