Answer:
10.3
Step-by-step explanation:
Let the given points be the endpoints of a right triangle. The horizontal change in x is from 4 to -5 and is negative 9; the vertical change in y is from -2 to+ 3 and is +5.
The desired distance is found using the Pythagorean theorem:
d = √(9² + 5²) = √106, or 10.3 (to the nearest tength)
<h3>
Answer: x = 40</h3>
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Work Shown:
A+B+C = 180 ..... three angles of any triangle add to 180
(2x+10)+(x)+(2x-30) = 180
5x-20 = 180
5x = 180+20 .... adding 20 to both sides
5x = 200
x = 200/5 ... dividing both sides by 5
x = 40
This is the measure of angle B
We can stop here.
If you need to know the values of the other angles, then,
- angle A = 2x+10 = 2*40+10 = 90
- angle C = 2x-30 = 2*40-30 = 50
Then note how A+B+C = 90+40+50 = 90+90 = 180 which helps confirm our answer.
Answer:
ED = 4 units
Step-by-step explanation:
Observing the figure given to us, we can deduce the following:
=>CE = EA (because point E is the midpoint of CA)
Therefore, if CE = EA = x unit, CA = 2x
=>Also, CD = DB (because point D is the midpoint of CB)
Therefore, if CD = DB = y, CB = 2y
Thus, CA/CE = CB/CD = 2 (2x/x = 2y/y)
Going by the above ration we got comparing the ratio of the corresponding sides of ∆CAB and ∆CED (2:1), we can conclude that ∆CAB ~ ∆CED
Using the ratio of the corresponding sides of ∆CAB to ∆CED = (2:1), measure of segment ED is calculated below:
AB/ED = 2/1
8/ED = 2/1
Cross multiply
8 × 1 = 2 × ED
Divide both sides by 2
8/2 = ED
ED = 4 units
