23% is maybe the percentage but if not then it maybe a little higher or lower
Dodecahedron is a 3D shape, usually when it ends with hedron it is 3D.
If the initial time was 60 seconds and 18 seconds have passed,
There would be 42 seconds left.
Explanation:
The Law of Sines is your friend, as is the Pythagorean theorem.
Label the unmarked slanted segments "a" and "b" with "b" being the hypotenuse of the right triangle, and "a" being the common segment between the 45° and 60° angles.
Then we have from the Pythagorean theorem ...
b² = 4² +(2√2)² = 24
b = √24
From the Law of Sines, we know that ...
b/sin(60°) = a/sin(θ)
y/sin(45°) = a/sin(φ)
Solving the first of these equations for "a" and the second for "y", we get ...
a = b·sin(θ)/sin(60°)
and ...
y = a·sin(45°)/sin(φ)
Substituting for "a" into the second equation, we get ...
y = b·sin(θ)/sin(60°)·sin(45°)/sin(φ) = (b·sin(45°)/sin(60°))·sin(θ)/sin(φ)
So, we need to find the value of the coefficient ...
b·sin(45°)/sin(60°) = (√24·(√2)/2)/((√3)/2)
= √(24·2/3) = √16 = 4
and that completes the development:
y = 4·sin(θ)/sin(φ)
Add 3 to both sides so that the equation becomes 2x^2 + 7x - 6 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ -7 ± √(7^2 - 4(2)(-6)) ] / ( 2(2) )
x = [ -7 ± √(49 - (-48) ) ] / ( 4 )
x = [ -7 ± √(97) ] / ( 4)
x = [ -7 ± sqrt(97) ] / ( 4 )
x = -7/4 ± sqrt(97)/4
The answers are -7/4 + sqrt(97)/4 and -7/4 - sqrt(97)/4.
