The solutions are
.
Solution:
Given equation:

Add
on both sides.

-------- (1)
(given) -------- (2)
Equate (1) and (2).

Add
on both sides.


Add 5 on both sides.


Divide by 5 on both sides, we get

Taking square root on both sides, we get

Substitute
in (1).



Substitute
in (1).



Therefore the solutions are
.
Option C is the correct answer.
Let's begin by breaking each number down into its prime factors: 4 = 2 x 2 5 = 5 6 = 2 x 3 Next, let's determine the Lowest Common Multiple (LCM) of the numbers 4, 5, and 6 by multiplying all common and unique prime factors of each number: common prime factors: 2 unique prime factors: 2,5,3 LCM = 2 x 2 x 5 x 3 = 60 Next, let's determine how many times 60 goes into 10,000 (excluding remainder): 10,000/60 = 166 and 2/3 Multiples of ALL 3 numbers (4,5,6) = 166 Next, let's determine the Lowest Common Multiple (LCM) of the numbers 4 and 5 by multiplying all common and unique prime factors of each number: common prime factors: none
unique prime factors: 2 x 2 x 5
LCM = 2 x 2 x 5 = 20 Next, let's determine how many times 20 goes into 10,000:
10,000/20 = 500
Multiples of BOTH numbers (4 and 5) = 500 Finally, let's subtract the multiples of ALL three numbers (4,5,6) from the multiples of BOTH numbers (4 and 5) to get our answer: Multiples of ONLY numbers 4 and 5 (excluding 6): 500 - 166 = <span>334</span>
The answer is Hx = ½ Wsin θ cos θ
The explanation for this is:
Analyzing the torques on the bar, with the hinge at the axis of rotation, the formula would be: ∑T = LT – (L/2 sin θ) W = 0
So, T = 1/2 W sin θ. Analyzing the force on the bar, we have: ∑fx = Hx – T cos θ = 0Then put T into the equation, we get:∑T = LT – (L/2 sin θ) W = 0
The answer would be 30in.
Reasoning: if the two figures are proportional, you would set it up in a proportion. It would be 36/x=12/10. Then cross multiply, so it would be 12x and 36(10). Afterwords you’ll have 12x=360, then divide both sides by 12 and you’ll end up with 30.

Factorization of the trinomial
3x^3 +6x^2 -24x
will be :-
taking common 3x
=>3x(x^2+2x-12)......1️⃣
now the factorization of (x^2+2x-12) will be
(x-2)(x+4).......2️⃣
so your answer from 1️⃣and 2️⃣ is (A) 3x(x-2)(x+4).
Hope it helped you.