John ate 40% of the candies in a bag. If John ate 20 candies , how many candies were total in the bag ?
2 answers:
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Answer:
<h2>There are 13 quarters, 5 nickels and 20 dimes.</h2>Step-by-step explanation:
Givens
- Max has $5.50.
- He has eight more quarters than he does nickels.
- He had four times as many dimes as he has nickels.
From these statements, we can deduce algebraical expressions to solve the problem. Let's call quarters,
nickels and
dimes.
(8 more quarters than nickels)
(he has four times as many dimes as he has nickels).
(Max has a total of $5.50, one quartes is $0.25, one nickel is $0.05 and one dime is $0.10).
Let's replace the first two expressions into the third equation
There are 5 nickels.
Now, we use this value to find the number of quarters
There are 13 quarters.
Also,
There are 20 dimes.
Therefore, there are 13 quarters, 5 nickels and 20 dimes.
Answer:
Given :
ABC is a right triangle in which ∠ABC = 90°,
Also, Legs AB and CB are extended past point B to points D and E,
Such that,
To prove :
Proof :
In triangles AEC and EBA,
∠EAC= ∠ABE ( right angles )
∠CEA = ∠AEB ( common angles )
By AA similarity postulate,
,
Similarly,
Now, In triangles ADC and CBD,
∠ACD = ∠CBD ( right angles )
∠ADC= ∠BDC ( common angles )
By AA similarity postulate,
,
Similarly,
From equations (1) and (2),
The corresponding sides of similar triangles are in same proportion,
Hence, proved....
