Answer:
The length = 35 ; The width = 12
Step-by-step explanation:
Perimeter = 2L + 2W
Length = x
Width = x - 23
94 = 2(x) + 2(x - 23)
94 = 2x + 2x - 46
94 = 4x - 46
94 + 46 = 4x
140 = 4x
140/4 = x
35 = x The length = 35; The width = (35 - 23) = 12
Answer:
Let's do an example first and then summerize what are the techniques to complete the square for quadratic equation in order to solve for x. -2x^2 + 5x + 12 = 0 -2x^2 + 5x = -12 -2 (x^2 - 5/2 x) = -12 so 2ab = 5/2 x ("2ab" refers to the formula (a+b)^2 = a^2 + 2ab + b^2 or (a+b)^2 = a^2 - 2ab + b^2 ) Since a=1 (because x^2 is the a^2 in the formula), we get 2*1*b = 2b = 5/2 x, so b = 5/4 That means to complete the square we will add "b^2" (which is (5/4)^2 here) and then subtract (5/4)^2 in the parenthesis: -2 [ x^2 - 5/2 x + (5/4)^2 - (5/4)^2 ] = -12 Now that is same as -2 (x - 5/4 )^2 + (-2) * (-5/4)^2 = -12 To simplify it we follow these steps: -2 (x - 5/4 )^2 + 2 * 25/16 = -12 -2 (x - 5/4 )^2 + 25/8 = -12 Multiply both sides of the equation by 8 we get this: -16 (x-5/4)^2 +25 = -96 then -16 (x-5/4)^2 = -121 Techniques summerization: To complete the square for quadratic equation in order to solve for x, first we need to move the terms without x (which is "c" in the "ax^2+bx+c=0" form) to the right side of the equation. Then we divide both sides of the equation by "a" in the "ax^2+bx+c=0" equation. Through the formula (a+b)^2 = a^2 + 2ab + b^2 or (a+b)^2 = a^2 - 2ab + b^2 we will then figure out the value of "b", so then we know what is the b^2 we need to add then subtract. Finally just simplify the equation. Hope this helps.
Step-by-step explanation:
Answer:
A rectangle has rotational symmetry of order 2.
Step-by-step explanation:
The rotational symmetry involves rotation.
The rotational symmetry of order is the number of times a shape is mapped onto itself during a 360° rotation.
A rectangle has rotational symmetry of order 2.
When a rectangle is rotated on 180° or 360° it is mapped onto itself.
Answer:
(2x+3)(x+1)
Step-by-step explanation:
