Sophia Milestone 2 College Algebra Questions with Correct answers. Latest 2022.For the equation 1.75n = 7, what is the value of
... [Show More] n?
0.25
6
4
5.25
RATIONALE
To find the value of n, we need to isolate it to one side of the equation. We do this by performing inverse operations to both sides of the equation. Since n
is being multiplied by 1.75, we will divide both sides by 1.75, because division is the inverse of multiplication.
On the left side, n will become isolated once we divide by 1.75. On the right side, we have 7 divided by 1.75.
7 divided by 1.75 is equal to 4. The solution to the equation is n = 4.
CONCEPT
Solving single-step equations
2
Edgar opened a deposit account. In the first month, he made an initial deposit of $3200, and plans to contribute an additional $175 every month. The account does not pay
any interest.
After how many months will he have a total of $6000?
15 months
17 months
18 months
14 months
RATIONALE
The amount in Edgar's deposit account can be modeled using the formula for an arithmetic sequence. The term is the value after n
months, is the initial balance, d is the common difference (or steady monthly deposits), and n is the number of months. Use the
information provided to find each value.
The initial deposit, , is $3200. Edgar deposits $175 each month, which is the difference, d. We want to know how many months, n, it will
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take for the balance to reach $6000, which is the value for . Next, substitute each value in for , d, and .
Once each known value is substituted, we can solve for n. First, distribute 175 into (n – 1).
175(n – 1) is equivalent to 175n – 175. Next, combine like terms on the right side.
3200 minus 175 is equal to 3025. Subtract this value from both sides to isolate the n term.
6000 minus 3025 equals 2975. Finally divide both sides by 175.
2975 divided by 175 is equal to 17. It will take 17 months for the balance to reach $6,000.
CONCEPT
Introduction to Arithmetic Sequences
3
Rationalize the denominator and simplify the following expression:
RATIONALE
When working with radicals, we want to avoid having a radical in the denominator. The first step in the process is to rationalize the denominator.
To do this, multiply the numerator and denominator by the conjugate of the denominator. The conjugate is a binomial with the opposite sign
between its term, or .
Use FOIL to expand numerator and denominator. Since we used the conjugate of the denominator, you will notice the denominator will just be the
difference of squares (and it is now rational!).
In the numerator, we multiplied the first terms to get ; multiplied the outside terms to get -3; multiplied the inside terms to get -2; and
multiplied the last terms to get . The denominator is the difference of squares, or . Next, we can combine like terms in the
numerator.
In the numerator, combine the radical terms to get and combine the constant terms to get -5. Next, evaluate the exponents in the denominator.
In the denominator, is 4 and is just 3. Next, we can subtract these two values.
4 minus 3 is 1. The expression is equivalent to .
CONCEPT
Rationalizing the Denominator
4
The number of employees who will be able to perform a specific task is given by the equation , where N is the number of people who are able to perform the
task, and t is time (in days).
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How long will it take until 100 employees are able to perform the task?
4 days
16 days
8 days
20 days
RATIONALE
The number of employees who can perform the task is modeled by this equation. To find how long it will take until 100 employees can perform the task, we
will substitute this value for N and solve for t.
Once N is replaced, we can solve for t. First, divide both sides by 25 to undo 25 multiplied by the square root of t.
On the left, 100 divided by 25 is 4. To undo the square root of t on the right, square both sides.
On the left, 4 squared is 16. It will take 16 days for 100 employees to be able to perform the task. [Show Less]