Answer:
The length of AE is 20 units.
Step-by-step explanation:
Given two segments AD and BC intersect at point E to form two triangles ABE and DCE. Side AB is parallel to side DC. A E is labeled 2x+10. ED is labeled x+3. AB is 10 units long and DC is 4 units long.
we have to find the length of AE
AB||CD ⇒ ∠EAB=∠EDC and ∠EBA=∠ECD
In ΔABE and ΔDCE
∠EAB=∠EDC (∵Alternate angles)
∠EBA=∠ECD (∵Alternate angles)
By AA similarity, ΔABE ≈ ΔDCE
therefore, 
⇒ 
⇒ 
⇒ 
Hence, AE=2x+10=2(5)+10=20 units
The length of AE is 20 units.
Answer:
Step-by-step explanation:
So we have the expression:
And we wish to factor it.
First, let's make a substitution. Let's let u be equal to x². Therefore, our expression is now:
This is a technique called quadratic u-substitution. Now, we can factor in this form.
We can use the numbers -3 and -2. So:
For the first two terms, factor out a u.
For the last two terms, factor out a -3. So:
Grouping:
Now, substitute back the x² for u:
And this is the simplest form.
And we're done!
Answer:
62.8
Step-by-step explanation:
The formula for circumference is 2(pi)r
Let's plug in the values.
Well, we know the diameter, and since the radius is 1/2 the diameter, but then you multiply by 2 again, you don't have to change anything. Therefore, another formula is (pi)<em>d</em>
3.14 x 20
= 62.8 is your answer. And the answer is already rounded to the nearest tenth, so nothing is left to do!
<em>Hope this helps!</em>
Answer:
Downwards
Step-by-step explanation:
