The answer is 4a^2.
2a2
The height of an equilateral triangle is √3/2 x side_length. So for an equilateral triangle of side length 2a, the area is: area = 1/2 x base x height 1/2 x (2a) x (√3/2 x 2a) = √3 a2
144a2b
The quadratic formula originated from the concept of completing the square. let's take ax2 + bx + c = 0. To complete the square, solve for x. Subtract c. ax2 + bx = -c. Then divide by a [notice- if there is no a value, then a=1]. x2 + bx/a = -c/a. Add (b/2a)2 to both sides. x2 + bx/a + b2/4a2 = -c/a + b2/4a2 Factor/Reformat. (x + b/2a)2 = (b2-4ac) / 4a2 (x + b/2a)2 = [(b2-4ac) / 2a]2 Square-root both sides. x + b/2a = ± √(b2-4ac) / 2a Subtract b/2a. x = -b/2a ± √(b2-4ac) / 2a Combine terms. x = [-b ± √(b2-4ac)] / 2a
The answer is 4a^2.
20 = 1Consider what is the value of 2a ÷ 2a? Any number divided by itself is 1. Thus:2a ÷ 2a = 1The law of indices says that when dividing, they are subtracted, for example:25 ÷ 22 = (2 x 2 x 2 x 2 x 2) ÷ (2 x 2) = 2 x 2 x 2 = 23 = 25-2So 2a ÷ 2a is (also):2a ÷ 2a = 2a-a = 20Since any number subtracted from itself is 0 (= a - a). This must have the same value as before, thus:20 = 1The 2 above can be replaced by any number x which means that any number to the power 0 is 1:x0 = 1
The height of an equilateral triangle is √3/2 x side_length. So for an equilateral triangle of side length 2a, the area is: area = 1/2 x base x height 1/2 x (2a) x (√3/2 x 2a) = √3 a2
4a
Factor them. 2 x 2 x a = 4a 2 x 5 x a x a = 10a2 Select the common factors. 2 x a = 2a, the GCF.
144a2b
2a - a = a
a x a means that a is multiplied by a. 2a means that a is multiplied by 2. Unless a happens to be 2, a x a will give a different result.The difference is a x (a-2). for example if a = 2, then the difference is zero. If a = 3, the difference is 3The operators are different: 2a = a + a (addition).
4aa-bb fits the special type of polynomial in the form of x**2-y**2 which can be rewritten as (x-y)(x+y) sqrt(4aa) = 2a sqrt(bb) = b (2a-b)(2a+b)
x + 2a
2x^2 - 21x + c = 0 x^2 - 21x/2 + c/2 = 0 (x + a)(x + 2a)= x^2 - 21x/2 + c/2 x^2 + 3a + 2a^2 3a = -21/2 ------> a = -7/2 2a^2 = c/2 ---> 49/2 = c/2 ---> c = 49
The quadratic formula originated from the concept of completing the square. let's take ax2 + bx + c = 0. To complete the square, solve for x. Subtract c. ax2 + bx = -c. Then divide by a [notice- if there is no a value, then a=1]. x2 + bx/a = -c/a. Add (b/2a)2 to both sides. x2 + bx/a + b2/4a2 = -c/a + b2/4a2 Factor/Reformat. (x + b/2a)2 = (b2-4ac) / 4a2 (x + b/2a)2 = [(b2-4ac) / 2a]2 Square-root both sides. x + b/2a = ± √(b2-4ac) / 2a Subtract b/2a. x = -b/2a ± √(b2-4ac) / 2a Combine terms. x = [-b ± √(b2-4ac)] / 2a