For the answer to the question above, when you carry your jewelry box or your phone 3 floors down
and 2 miles to the left, the angles and side lengths don't change,
and it still looks exactly the same as it did before you picked it up
and moved it.
Translation can't change angles or lengths. And if those don't
change, then the later shape is congruent to the earlier shape.
Your x values are 1.24 and -0.404.
First you need to make the equation equal 0, and you can do this simply by subtracting 5x, so you get
6x² - 3 - 5x = 0
The quadratic formula is (-b +- √b² - 4ac)/2a, where a is the x², b is the x, and c is the value. This means we can just substitute it in.
You find the value of the part inside the square root, which is -5² - 4 × 6 × -3 = 97. Now we can use this to substitute in to (5 +- √97)/12. We can do it with the plus sign, and get 1.24, and then with the subtract sign and get -0.404.
I hope this helps!
Let's calculate the value of angle A and B
sin(A) =-4/5 → sin⁻¹(- 4/5) = A → A = - 53.13
cos(B) = -5/13 → cos⁻¹ (- 5/13) = B → B = 112.62
tan (A+B) = sin(A+B)/cos(A+B) with A+B = -53.13 + 112.62 = 59.49
tan (A+B) = sin(59.49)/cos(59.49) = 0.86154/0.507688 = 1.6969.
(Answer H = 56/33 = 1.6969)
