Roberta has $4.00 in dimes and quarters. She has 5 more dimes than quarters. Write a system of equations that you could use to f
1 answer:
Answer:
Step-by-step explanation:
Let x be the number of quaters and y be the number of dimes Roberta has.
1. Quater is equal to 25 cents, then x quaters is equal to 25x cents. Dime is equal to 10 cents, then y dimes is equal to 10y cents. $4.00=400 cents, then
25x+10y=400.
2. Roberta has 5 more dimes than quarters, then
y=x+5.
3. The system of equations is
Substitute second equation into the first one:
10 quaters and 15 dimes
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Answer with Step-by-step explanation:
Let Z be a set of integers
We have to prove that is odd for all value of x
Z.
There are two cases
1.When x is an odd integer number
2.when x is even integer number
1.When x is an odd integer number
When x is positive odd integer
Then is positive odd number (because square of odd positive number is always positive an odd number )
5x is also odd number
-5x -1 = -even number
Suppose x=3
Then -15-1=-16
Odd number - even number=Odd number
Hence , is an odd number .
When x is negative odd number
Then x square is positive odd number and 5x is negative odd term term
Therefore,odd number + odd number -1=Even number -1=Odd number
Hence is an odd number.
2.When x is an even number
When x is positive even number
x square is positive even number and 5x is positive even number
Even number -Even number -1 =Even number -odd number =Odd number
Suppose x=4
=16-20-1=-5=Odd number
When x is negative even number
Then x square is positive even number and 5x is negative even number
=Even number +Even number -1=Even number -1=Odd number
Hence, for all elements of Zis odd.
Answer:
Step-by-step explanation:
Let v be the speed after the collision of both the cars.
Now, momentum is given by: mass × velocity, then by equating the total momentum before and after the collision of the two cars, we get
⇒
⇒
⇒
Thus, they are moving at the velocity of