Since the lengths of the segments AD=PD are equal that means that the triangle is an isosceles triangle. This also means that the angles A and P (in the triangle) are equal.
This also means that the angle P' (the one inside the quadrilateral) is equal to:
Now, if we extend the sides DP and CB we notice that the angles P' and Q
are equal
The only way that this angles can be equal is if the line segments DP and CB are parallel, this comes from the fact that two alternate interior angles are equal if and only if the lines are parallel.
Answer:
78
Step-by-step explanation:
angle ACD + angle DCB = 180 (Angles on straight line)
4x + 2 + 3x + 3 = 180
7x + 5 = 180
7x = 180-5
7x = 175
x = 175 / 7
x = 25
angle DCB = 3x +3 = 3*25 + 3 = 75 +3 = 78
For the first one it is, j<<span>−<span>13
Second one, </span></span>n<<span>−<span>8
</span></span>Third one, k><span>−<span>50</span></span><span>
</span>
Let x = the number of dimes
Let y = the number of pennies.
There are 8 coins, therefore
x + y = 8 (1)
The coins are worth 17 cents, therefore
10x + y = 17 (2)
Subtract equation (1) from equation (2).
10x + y - (x + y) = 17 - 8
9x = 9
x = 1
From (1), obtain
y = 8 -x = 8 - 1 = 7
Answer: 1 dime, 7 pennies.
First of all we have to arrange the data in ascending order as shown below:
28, 40, 43, 43, 45, 50, 50
Total number of values = 7
Since the number of values is odd, the median will be the middle value i.e. 4th value which is 43. Median divides the data in two halves:
1st Half = 28, 40, 43
2nd Half = 45, 50, 50
Q1 or the First Quartile is the middle value of the lower or 1st half which is 40.
Q3 or the Third Quartile is the middle value of the upper or second half, which is 50.
IQR or the Inter Quartile Range is the difference of Q3 and Q1.
So, IQR= Q3 – Q1 = 50 – 40 = 10
Thus, IQR for the given data is 10
