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:
Height of the antenna = 28 ft (Approx)
Given:
Length of base = 300 ft
Angle of elevation to the building = 40°
Angle of elevation to the antenna = 43°
Find:
Height of the antenna
Computation:
Using trigonometry function:
Tan40° = Height of building / Length of base
Height of building = 251.73 ft
Tan43° = [Height of building + Height of the antenna] / Length of base
0.9325 = [251.73 + Height of the antenna] / 300
Height of the antenna = 28.02 ft
Height of the antenna = 28 ft (Approx)
Answer:
On Friday he did not make any bracelets He makes 8 more bracelets each day from Tuesday through Thursday
Step-by-step explanation:
He made 12 bracelets on Monday
For 3 days (from Tuesday to Thursday) he added 8 more each day)
8*3=24
24+12 = 36
M =12
T= 20 (12+8)
W=28(20+8)
Th=36(28+8)
F=36 (still has 36 because on Friday he did not make 8 more bracelets)
8*3=24
24+12 = 36
