Sara is taking a test made up of multiple-choice and open-ended questions. The multiple-choice questions have a value of 4 points each, and the open-ended questions have a value of 5 points each. If Sara has already answered 10 multiple-choice questions correctly, which inequality best describes the amount of open-ended questions Sara must answer correctly to earn more than 70 points? x greater-than 6
x less-than 6
x greater-than 12
x less-than 12

To find this, you must find the total number of points Sara has scored already.  She has answered 10 multiple choice questions which are 4 points each.  This means that Sara has scored 40 points so far.

If Sara wants to score at least 70 points, she needs to score at least 30 more points.  To find how many open-ended questions she needs to answer, you need to divide the remaining number of points by the number of points an open-ended question is worth.  The number we get will be x.

30/5 = 6

This means Sara must complete at least 6 open-ended questions to score 70.  Now, all we have to do is figure out which inequality sign to use.  Since Sara wants to score more than 70 points, it should be the "greater than" sign.

Your answer is:  x>6  

Step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for