Each pair of polygons is similar. Find the value of x.

The value of x is 1.5

Step-by-step explanation:

In similar figures, corresponding sides have the same ratio

In the given figure

∵ There are 2 similar polygons

∴ We must write their names with corresponding angles

∵ ∠A = ∠L, ∠B = ∠M, ∠C = ∠N, ∠D = ∠P

∴ Their names are ABCD and LMNP

→ By using the rule above

∴ Their corresponding sides have the same ratio

∴ =

∵ AB = 14 and LM = x + 9

∵ BC = 10 and MN = x + 6

→ Substitute them in the ratio up

∴ =

→ By using the cross multiplication

∵ 14 × (x + 6) = 10 × (x + 9)

∴ 14(x) + 14(6) = 10(x) + 10(9)

∴ 14x + 84 = 10x + 90

→ Subtract 10x from both sides

∵ 14x - 10x + 84 = 10x - 10x + 90

∴ 4x + 84 = 90

→ Subtract both sides by 84

∵ 4x + 84 - 84 = 90 - 84

∴ 4x = 6

→ Divide both sides by 4 to find x

∴ x = 1.5

∴ The value of x is 1.5

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.