In the Itty Bitty High School, there are 85 students. There are 27 students who take French, 51 who take Geometry and 38 who take History. There are 10 that take Geometry and French, 7 that take History and French and 15 that take Geometry and History. There are 2 students who take all 3 and 5 that take none of these subjects.

58 students

Step-by-step explanation:

Given

Required

Students that take only 1 subjects

The attached image illustrates the question.

For French only (x), we have:

Collect like terms

For Geometry only (y), we have:

Collect like terms

For History only (z), we have:

Collect like terms

Students with one subject is then calculated as:

∠cbe and ∠deb are same-side interior angles.

i took the test

, 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