Find the value of x in the isosceles triangle shown below.

Step-by-step explanation:

We know that this is an isosceles triangle from the given information. We are also given that its height, or altitude, is 8. The height/altitude to the base of an isosceles triangle is also the median to the base. A median is a line segment that bisects another line segment, or splits it into two equal parts. Therefore, we know that the vertical line segment in the diagram splits the base into two equal parts, each measuring units.

Now, we know that the altitude of a line segment is perpendicular to it, or forms a ° angle with it. Therefore, the vertical segment divides the larger isosceles triangle into 2 congruent right triangles with legs of 8 and and hypotenuse of . We can use the Pythagorean Theorem ( where and are the legs and is the hypotenuse of the right triangle) to solve for . Substituting the values for , , and into the Pythagorean Theorem equation, we get:

(Substitute values for , , and )

(Simplify)

(Subtract 64 from both sides)

(Simplify)

(Multiply both sides of the equation by 4)

(Simplify)

(Take the square root of both sides of the equation)

(Simplify)

is an extraneous solution because a triangle cannot have negative side lengths. Thus, our final answer is . Hope this helps!

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

step-by-step explanation: