Question

Plzzz answer ticked questions it's urgent

Answer 1

1. LHS = (5 + √5)(5 - √5)
we use the formula, (a - b)(a + b) = a² - b²
= (5)² - (√5)²
= 25 - 5 = 20 = rational number { A rational number is in the form of P/q and p , q are integers } = RHS
hence, proved//

2.(-12)³ + 7³ + 5³
Let a = -12 , b = 7 and c = 5
then, you can see , a + b + c = -12 + 7 + 5 = 0
so, we can apply the formula,
a³ + b³ + c³ = 3abc
(-12)³ + 7³ + 5³ = 3(-12)(7)(5) = -36 × 35 = -1260

3. angle POQ + angle QOR = 180°
x/2 + x/3 = 180°
5x/6 = 180°
x = 180 × 6/5 = 36 × 6 = 216°

hence, value of x = 216°

4. y = -5

5. Let the angle is x
x + 5x = 90°
6x = 90° => x = 15°

8. A-------------------C------B---------------------D
given,
AB = CD
you can see that ,
AB = AC + CB
CD = CB + BD
so, (AC + CB) = (CB + BD)
AC = BD

9. perimeter of isosceles triangle = 42
Let equal side length is x
then, base is 3x/2

now, x + x + 3x/2 = 42
7x/2 = 42 => x = 12 cm
hence, equal sides is 12 cm and third side is 18cm .
semi-perimeter of ∆ = 21 cm
now, use hero formula,
area of ∆ = √{s(s-a)(s-b)(s-c)}
= √{21 × (21-18) × (21 - 12) × (12 - 12)}
= √{ 21 × 3 × 9 × 9 }
= 27√7 cm²

10. collinear means slope of points are same .
A(-1,1) B(-3,3) and C(-5,5)
then, slope of AC = (3-1)/(-3+1) = 2/-2 = -1
slope of BC = (5-3)/(-5+3)
= 2/-2 = -1

slope of AC = slope of BC
hence, A,B,C are collinear

Answer 2

Required answer is in the attachment.