Mr. jared asked his math students to compute the numerical value of(a++6)for a particular positive value of a ruby accidentally copied the expression as(a+3)a+6,so even though she used the correct value for a and did all computations correctly, she got the wrong answer. similarly, amber mistakenly wrote the expression as a+3.(a+6)and obtained an incorrect answer, despite making no other mistakes. curiously, ruby and amber ended up with the same wrong answer! what was the correct answer to mr. jared'squestion?

The correct answer is 70.

Step-by-step explanation:

Since they got the same answer we have the equation:

(a + 3)a + 6 = a + 3(a + 6)

a^2 + 3a + 6 = a + 3a + 18

a^2 + 3a - 3a -a + 6 - 18 = 0

a^2 - a - 12 = 0

(a - 4)(a + 3) = 0

So a = 4 or -3.

As a is given as positive we take a = 4.

The correct numerical value =

(4 + 3)( 4 + 6)

= 70.

the solution is the point

step-by-step explanation:

we have

> equation a

> equation b

adds equation a and equation b

substitute the value of x in equation b to find the value of y

the solution is the point

, 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