As C is the mid-point of BD.
Therefore, BC=DC ...(i)
As AB ⊥ BD and ED ⊥ BD
So, ∠ABC= 90° and ∠EDC= 90°
Therefore, ∠ABC=∠EDC= 90° ...(ii)
As two line segments, AE and BD intersect at point C, so the vertically opposite angles are equal.
Therefore, ∠BCA=∠DCE ...(iii)
Now, in ΔABC and ΔEDC,
Angle, ∠BCA=∠DCE [ from equation (iii)]
Side, BC=DC [ from equation (i)]
Angle, ∠ABC=∠EDC [ from equation (ii)]
So, by ASA property of congruency, ΔABC and ΔEDC are congruent
Hence, ΔABC ≅ ΔEDC.
Hold on make a bigger pic
i believe the answer is a
Range
The range measures the spread of the dataset by calculating the difference between the largest and the smallest element. In your case, marks range from 6 to 10, so the range is 10-6=4.
How many students
The frequency tells you how many students got each mark. So, we know that 5 students got a mark of 6, 4 students got a mark of 7, 7 students got a mark of 8, 10 students got a mark of 9, 4 students got a mark of 10.
This implies that, in total, we have
students.
Mean
The mean is given by the sum of the marks, divided by the number of students. We already observed how many students got each mark, so the sum of all marks will be a weighted sum, where each mark counts once per student:
![5\cdot 6 + 4\cdot 7 + 7\cdot 8+ 10\cdot 9 + 4\cdot 10 = 244](https://tex.z-dn.net/?f=5%5Ccdot%206%20%2B%204%5Ccdot%207%20%2B%207%5Ccdot%208%2B%2010%5Ccdot%209%20%2B%204%5Ccdot%2010%20%3D%20244)
Now we divide this sum by the number of students to get
![\dfrac{244}{30}=8.1\overline{3}](https://tex.z-dn.net/?f=%5Cdfrac%7B244%7D%7B30%7D%3D8.1%5Coverline%7B3%7D)
So, the average mark is about 8.
Answer:x= 36 y= 67 and z=77
Step-by-step explanation: we have to write the equations from the data give in the exercise, this means :
First of all, x,y and z correspònd to the first, second and third angles, respectively.
The sum of the measures of the angles of a triangle is 180
can be written as x+y+z=180
The sum of the measures of the second and third angles is four times the measure of the first angle.
It can be written by: x+y=4z
The third angle is 10 more than the second
It can be written as z=y+10
By solving the equations systems the above values can be determined.
x+y+z=180
x+y=4z
z=y+10