Answer:
x = 4
Step-by-step explanation:
A trapezium is a quadrilateral (has four sides and four angles) with one pair of parallel sides. A trapezium is said to be isosceles if the bases are parallel, the two other sides known as the legs are equal and diagonals of the trapezium are equal to each other.
In trapezoid ABCD, BC and AD are the diagonals.
Hence BC = AD (property of isosceles trapezoid)
9x + 1 = 12x - 11
Simplifying:
12x - 9x = 1 + 11
3x = 12
Dividing both sides by 2:
x = 4
The discriminant is
which is 0.
Since the discriminant is 0, there is only one real solution.
Step-by-step explanation:
for triangle HLM
180-2x
180-(3x+6)
H
2x=3x-10
x=10°
180-36=144°
36-20=16°
H=2x
H= 180-144-16= 20°
1) slope = (y₂-y₁)/(x₂-x₁)
Let A and B be A(4,-6) and B(0,2) ;
m = [2-(-6)]/[0-4) = (2+6)/(-4) → m = -2
2) Midpoint = value of x of the midpoint = (x₁+x₂)/2
value of y of the midpoint = (y₁+y₂)/2
x(midpoint) = (4+0)/2 → x= 2
y(midpoint) = (-6+2)/2 → y= - 2, so Midpoint M(2,-2)
3) Slope of the perpendicular bisector to AB:
The slope of AB = m = -2
Any perpendicular to AB will have a slope m' so that m*m' = -1 (or in other term, the slope of one is inverse reciprocal of the second, then if m =-2, then m' = +1/2 ; Proof [ (-2)(1/2) = -1]
4) Note that the perpendicular bisector of AB passes through the midpoint of AB or M(2,-2). Moreover we know that the slope of the bisector is m'= 1/2
The equation of the linear function is :
y = m'x + b or y = (1/2)x + b. To calculate b, replace x and y by their respective values [in M(-2,2)]
2= (1/2).(-2) + b → 2 = -1 + b → and b= 3, hence the equation is:
y = (1/2)x + 3
