Are the equations 4-5x=24 and 5x=20 equivalent?
1 answer:
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Answer:
The answer is and
Step-by-step explanation:
Given:
-4x-2y=14
-10x+7y=-24
Now, to solve it by elimination:
......(1)
......(2)
So, we multiply the equation (1) by 7 we get:
And, we multiply the equation (2) by 2 we get:
Now, adding both the new equations:
<em>Dividing both the sides by -8 we get:</em>
Now, putting the value of in equation (1):
<em>Subtracting both sides by 25 we get:</em>
<em>Dividing both sides by -2 we get:</em>
Therefore, the answer is and
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.
