I want the answer the the problem

The length of the segment GI is 30.5 units

Step-by-step explanation:

In any triangle, the line segment joining the mid-points of two sides is parallel to the third side and equal to half its length

In ΔFHJ

∵ G is the mid-point of the side FH

∵ I is the mid-point of the side JH

∵ FJ is the 3rd side of the triangle

→ From the rule above

∴ GI // FJ

∴ GI = FJ

∵ FJ = 61 units

∴ GI = (61)

∴ GI = 30.5

∴ The length of the segment GI is 30.5 units

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.

, 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