The value of c for which the considered trinomial becomes perfect square trinomial is: 20 or -20
<h3>What are perfect squares trinomials?</h3>
They are those expressions which are found by squaring binomial expressions.
Since the given trinomials are with degree 2, thus, if they are perfect square, the binomial which was used to make them must be linear.
Let the binomial term was ax + b(a linear expression is always writable in this form where a and b are constants and m is a variable), then we will obtain:
![(ax + b)^2 = a^2x^2 + b^2 + 2abx](https://tex.z-dn.net/?f=%28ax%20%2B%20b%29%5E2%20%3D%20a%5E2x%5E2%20%2B%20b%5E2%20%2B%202abx)
Comparing this expression with the expression we're provided with:
![x^2 + 10x + c](https://tex.z-dn.net/?f=x%5E2%20%2B%2010x%20%2B%20c)
we see that:
![a^2 = 1 \implies a = \pm 1\\b^2 = 10\\b = \pm 10\\2ab = c\\\pm2(10)1 = c\\c = \pm 20\\](https://tex.z-dn.net/?f=a%5E2%20%3D%201%20%5Cimplies%20a%20%3D%20%5Cpm%201%5C%5Cb%5E2%20%3D%2010%5C%5Cb%20%3D%20%5Cpm%2010%5C%5C2ab%20%3D%20c%5C%5C%5Cpm2%2810%291%20%3D%20c%5C%5Cc%20%3D%20%5Cpm%2020%5C%5C)
Thus, the value of c for which the considered trinomial becomes perfect square trinomial is: 20 or -20
Learn more about perfect square trinomials here:
brainly.com/question/88561
Answer:
-2+4i
Step-by-step explanation:
Simplify by combining the real and imaginary parts of each expression.
1 7/11 = 18/11
2 5/6 = 17/6
Product = 18/11 * 17/6
= 306 / 66 = 51/11 = 4 7/11 Answer
He should set up the refreshment stand on the incenter of the obtuse triangle. The incenter of a triangle is described as the intersection between the angle bisectors of a triangle. The inradius are the line segments from the incenter of the triangle to each of the three sides of the triangle which are all equal. The inradius is depicted as the radius of an inscribed circle in the triangle. Therefore, the shortest equal distance from his stand to each road is C. on the incenter.