Answer:
m(arc AC) = 72°
m(arc BD) = 108°
m∠DEB = 90°
Step-by-step explanation:
Ratio of the measure of arc AC, arc BC, arc BD and arc AD = 4 : 2 : 6 : 8
Since, m(arc AC) + m(arc CB) + m(arc BD) + m(arc AD) = 360°
By the property of ratio,
Measure of arc AC = 
= 
= 72°
Measure of arc BD = 
= 
= 108°
Measure of ∠DEB = 
= 
= 90°
Answer:
If its considered a triangle every unit inside a triangle is 90 square units
Step-by-step explanation:
Answer: The answer is 8.
Step-by-step explanation: The first step is to convert the expression into figures. We shall call the unknown number Y. So if we are told “the square of a number,” that means Y squared, or better still, Y^2. Further we are told “the difference between the square of a number and 40” and that can be written as;
Y^2 - 40.
Next we are told that this expression is equal to 3 times that number (that is 3Y). That can now be written out as follows,
Y^2 - 40 = 3Y
If we move all expressions to one side of the equation, what we would have is,
Y^2 - 3Y -40 = 0
(Remember that when a positive value crosses to the other side of an equation it becomes negative and vice versa)
We now have a quadratic equation
Y^2 -3Y - 40 = 0
By factorizing we now have
(Y -8) (Y + 5) = 0
Therefore Y - 8 = 0 or
Y + 5 = 0
Hence, Y = 8 or Y = -5
Since we are asked to calculate the positive solution, Y = 8
Answer:
c). y + x = 0
Step-by-step explanation:
The locus is a line perpendicular to the line connecting the 2 points and passing through the centre of the line.
The mid-point of the line connecting the given points is:
(a + b + a - b)/2 , (a - b + a + b) / 2
= (a, a)
It's slope = (a + b)- (a - b) / (a - b)- (a + b)
= 2b/ -2b
= -1
So the slope of the line we want is -1/(-1) = 1.
Using the point-slope form of a line:
y - y1 = m(x - x1)
y - a = 1(x - a)
y - a = x - a
x + y = 0
