Is the expression 4x − 3(5x − 1) is equivalent to the expression 3 + 9x. True False
2 answers:
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Answer: The quotient is (2x+1)
Step-by-step explanation:
Here, the dividend =
Divisor =
By the long division method for finding the quotient we will follow the following steps,
Steps 1 : Write dividend inside the division sign and divisor outside the division sign,
Step 2: Multiply the divisor by 2x and subtract the result by the dividend,
Step 3: Now, again multiply the divisor by 1,
Step 4: Subtract the result by the remaining dividend,
Since, further division is not possible,
Hence, the sum of all terms that are multiplied = 2x+1
Which is our quotient.
The smallest such number is 1055.
We want to find such that
The moduli are not coprime, so we expand the system as follows in preparation for using the Chinese remainder theorem.
Taking everything together, we end up with the system
Now the moduli are coprime and we can apply the CRT.
We start with
Then taken modulo 2, 3, 5, and 7, all but the first, second, third, or last (respectively) terms will vanish.
Taken modulo 2, we end up with
which means the first term is fine and doesn't require adjustment.
Taken modulo 3, we have
We want a remainder of 2, so we just need to multiply the second term by 2.
Taken modulo 5, we have
We want a remainder of 0, so we can just multiply this term by 0.
Taken modulo 7, we have
We want a remainder of 5, so we multiply by the inverse of 2 modulo 7, then by 5. Since , the inverse of 2 is 4.
So, we have to adjust to
and from the CRT we find
so that the general solution for all integers
.
We want a 4 digit solution, so we want
which gives .
The table in Part A represents y as a function of x. This means that the value of Y is dependent on the value of X. The table can be represented by an equation that describes the relation of X and Y:
or 
By substituting any value of X, you get a specific value of Y based from the given relationship, thus Y is a function of X.
For Part B, the value of f(150) is $470 and it represents the total cost for borrowing a rowboat for 150 hours. By substituting the value of x = 150 into the function, you get the total cost:
By substituting any value of X, you get a specific value of Y based from the given relationship, thus Y is a function of X.
For Part B, the value of f(150) is $470 and it represents the total cost for borrowing a rowboat for 150 hours. By substituting the value of x = 150 into the function, you get the total cost: