Answer:
The measure of angle A is: m∠A = 96
Therefore, option A is true.
Step-by-step explanation:
Given
m∠C = 3x
m∠D = x+52
We know that the opposite angles of a parallelogram are also equal.
Determining m∠A
It is clear that A is the opposite angle of C.
i.e.
m∠A = m∠C
as m∠C = 3x
so m∠A = 3x
Determining m∠B
It is also clear that B is the opposite angle of D.
i.e.
m∠B = m∠D
as m∠D = x+52
so m∠B = x+52
We know that the sum of the angles of a parallelogram is 360°.
so
m∠A + m∠B + m∠C + m∠D = 360°
3x + (x+52) + 3x + (x+52) = 360°
Group like terms
Subtract 104 on both sides
Simplify
Divide both sides by 8
Simplify
Thus,
The measure of the angle A is:
m∠A = 3x
substitute x = 32
m∠A = 3(32)
m∠A = 96
Hence, the measure of angle A is: m∠A = 96
Therefore, option A is true.
Answer:
B and E
Step-by-step explanation:
∠ ECD = ∠ ACB ( vertically opposite angles are congruent ) , then
12x - 9 = 6x + 27 ( subtract 6x from both sides )
6x - 9 = 27 ( add 9 to both sides )
6x = 36 ( divide both sides by 6 )
x = 6 → B
Then
∠ ACB = 6x + 27 = 6(6) + 27 = 36 + 27 = 63° → E
Suppose, we are given
two points as
F as (x1, y1)
H as (x2, y2)
assume it divides in m/n
we can use formula
now, we are given points as
F=(x1, y1)=(4,8)
H=(x2, y2)=(10,12)
so,
now, we can find
so, point is
.................Answer
The best approximation for the median is 3.6.
An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).
For the given density curve, the area under the density curve is
A=(1/2)×5×(1/2)=5/4
now, for the median, the area on the left and the area on the right of the median.
Let the median be x, then
The area criteria we get
(1/2)x(x/10)=(5/4)/2
⇒x²=5*20/4=25/2
So, we get x=5/()=3.5 ≈ 3.6
Hence the required answer is option 3.6
Learn more about density curves here-
brainly.com/question/18345488
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