Please help asap, thank you!

x ≈ 2.1

y ≈ 5.4

w = 5

Step-by-step explanation:

The given parameters are;

Segment AC = 13

Segment BC = y

Segment AD = 12

Segment CD = w

Segment BD = x

By Pythagoras's theorem, for the right triangle ΔACD, we have;

² = ²  + ²

∴ 13² = 12² + w²

w² = 13² - 12² = 25

w = √(25) = 5

w = 5

By, Pythagoras's theorem similarly, in the right triangle ΔBCD we have;

y² = x² + w²

∴ y² = x² + 5² = x² + 25

y² = x² + 25

In the right triangle ΔABC we have;

² = ²  + ²

∴ (12 + x)² = 13² + y² = 13² + (x² + 25)

(12 + x)² = 13² + (x² + 25)

144 + 24·x + x² = 13² + x² + 25

24·x = 13² + 25 - 144 = 50

x = 50/24 ≈ 2.1

x ≈ 2.1

y² = x² + 25

∴ y = √(x² + 25) = √((50/24)² + 25) = 65/12 ≈ 5.4

y ≈ 5.4

, 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

so what is the problem what are they asking you to solve

step-by-step explanation:

so what is the problem what are they asking you to solve