Calculate the value of x in each case

First taking small triangle,

Perpendicular(P') = 5cm

Base(B) = y (let)

Hypotenuse(H') = 12cm

so,

(H')² = (P')² + (B)²

(12)² = (5)² + (y)²

(y)² = 144 - 25

(y)² = 119

Now taking big triangle,

Perpendicular (P) = 12+5 = 17cm

Base (B) = y (already supposed)

Hypotenuse (H) = x

so,

(H)² = (P)² + (B)²

(x)² = (17)² + (y)²

(x)² = 289 + 119 = 408

x = √408

here is your mark brainliest

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt