Given x = {15, 22, 33, 44, 89, 165, 1025} and y = {-5, 15, 33, 88, 99, 150, 160, 1025}, which of the following statements is false?
x u y = {-5, 15, 22, 33, 44, 89, 99, 150, 160, 165, 1025}
x ∩ y = {15, 33, 1025}
øc (x u y)

XUY is the false statement.

Step-by-step explanation:

Given X = {15, 22, 33, 44, 89, 165, 1025}

and Y = {-5, 15, 33, 88, 99, 150, 160, 1025}

1). XUY = All elements or terms of both the sets.

XUY = {-5, 15, 22, 33, 44, 88, 89, 99, 150, 160, 165, 1025}

But the in the given option 88 is missing. Therefore, this statement is False.

2). X∩Y = common terms of both the sets.

X∩Y = {15, 33, 1025}

Matches the given option, so true.

3). ∅ ⊂ (XUY)

Since empty set is a subset of every set so this option is also true.

Therefore, XUY is the false statement.

y = i/2 xtnop + (3i/2 tnop+ 1)

step-by-step explanation:

the picture is the step by step explanation.

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9