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360° because angle subtend on centre of circle is always 360°

the positive factor of 28 is 1,2,4,7,14,28

1,2,4,7,14 and 28 are the positive factors

p + 4 = 1subtract 4 on both sidesp + 4 - 4 = 1 - 4p = -3

The zero of x+a is -a

Hence p(-a) is the remainder=-an+an=0.

Since the remainder is zero x+a is a factor

Area of square = (side length)² There are 12 squares whose sides are 12, 13, 14, ........ 23 so, area of square are 12² , 13² , 14² , .......23² we know, sum of square of natural number = n(n +1)(2n+1)/6 12² + 13² + ......23² = (1² + 2² + 3² + ..... + 23²) - (1² + 2² + ..... 11²)= S₂₃ - S₁₁= 23(23 + 1)(23 × 2 + 1)/6 - 11(11 + 1)(11 × 2 + 1)/6 = (23 x 24 x 47)/6 - (11 x 12 x 23)/6= 4324 - 506= 3818

105 is the square root of 11025

We know 11025 = 3 x 3 x 5 x 5 x 7 x 7 √1105 = √(3 x 3 x 5 x 5 x 7 x 7 )= 3 × 5 × 7= 105

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x=3&y=2

tq

4(x - 6 ) = 28

x- 6 = 28/4

x - 6 = 7

x = 7 + 6 = 13

4( x- 6 ) = 28=> x - 6 = 7=> x = 7+6 = 13

12y³ - 14y² - 10y

2y(6y² - 7y - 5)

2y( 6y² + 3y - 10y - 5)

2y ( 3y(2y + 1) - 5(2y + 1))

2y ( 3y - 5) (2y + 1)

Answer:c)14Explanation :

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(i) 14 is divisible by 2, but not by 4.(ii) 12 is divisible by 4, but not by 8.(iii) 24 is divisible by both 2 and 8, but not by 16.(iv) 30 is divisible by both 3 and 6, but not by 18.

1. 14 is divisible by 2 but not by 4.2. 12 is divisible by 4 but by 8.3. 24 is divisible by 2 and 8 but not by sixteen.4. 30 is divisible by 3 and 6 but not by 18.

-15,-12 they are divisible by 3

Tan π/8×180/πTan (180/8)=tan(22.5) Radiant

tan(π/8)= tan(π/4–π/8)

tan(π/8)=[1-tan(π\8)]/[1+tan(π/8]{I've skipped a step here}

Now, you get a quadratic eqn.

tan^2(π/8)+tan(π/8)-1=0

.°. tan(π/8)=(-2+2√2)/2{I’ve taken’ +’ because it's in the first quadrant}

=-1+√2

=0.414

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Use mathematical induction method to solve it. it's very easy

Use mathematical induction method to solve it. it's very easy

Solution: n = 1 ⇒ 9^(n + 1) - 8n - 9 = 9² - 8 - 9 = 81 - 17 = 64=1 x (64)

n = 2 ⇒9^(n + 1 )- 8n - 9 = 9³ - 8(2) - 9 = 729 – 16 - 9 = 704= 11 x (64)

From n = 3, 4, 5,....9^(n + 1) – 8n - 9 = 9^{(1 + 8)n }- 8n - 9

= 9 [nC0 + nC1 . 8 + nC2.8²+ ... nCn x 8^n] – 8n - 9

= 9[1 + 8^n + nC2.8²+ ... nCn x 8^n] –8n – 9

= 9 + 72n + 9. nC2. 8² + ... 9 x nCn x 8^n –8n - 9

= 8² [n + 9 (nC2 + nC3.8 +... nCn 8^(n-2))]

which is divisible by 64.

9^(n+1) - 8n - 9=9ⁿ×9 - 8n - 9= (1 + 8)ⁿ×9 - 8n - 9

Now, break (1+8)ⁿ by using binomial formula, (x + y)^n = nC0.x^n + nC1.x^(n-1)y + nC2.x^(n-2)y^2 + ........+nCn.y^n

(1+8)^n = nC0 + nC1(8) + nC2(8)² +....... + nCn(8)ⁿ use this above

= {nC0 + nC1.8 + nC2.8² + .....+ nCn.8ⁿ}×9 - 8n - 9

= (1 + 8n + nC2.8² + ......+nCn.8ⁿ)×9 - 8n - 9

= 9 + 72n + (nC2.8² +nC3.8³ +......+ nCn.8ⁿ)9 - 8n - 9

= (72n -8n) + 8²[nC2 + nC3.8 +.....+ nCn.8^(n-2)]

= 64n + 64[nC2 + nC3.8 +.....+nCn.8^(n-2)]

= 64 ×constant number

we obeserved that, 9^(n+1) - 8n -9 is divisible by 64

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a) (-3)+19=16c). 56+13+15=84e) (-16)+6-9-4=-23

1684-23 is the answer of the following

1684=-23 this is your answer

(a) (-3)-(-19)=(-3)+19=16

(a)

16,84,-23 is the correct answer of the given question

a)(-3)-(-19)=(-3)+19=16c)56-(-13)+15=56+13+15=84e)(-16)-(-6)+(-9)-4=(-16)+6-9-4=(-29)+6=(-23)

a) 16b) 84c)-23 is the answer

a)(-3)+19 = 16

b) 56 + 13 +15=84

c)(-16)+6 - 9 - 4 = -23

Let 0.235 bar be x

x = 0.2353535..... (1)

multiply (1) by 10

10x = 2.353535..... (2)

multiply (2) by 1000

1000x = 235.3535353..... (3)

eq(3) - eq(2)

990x = 233

x = 233/990

angle of depression is the answer.