Answer:
Equation -3x² - x + 3 = -3x² can not be solved using quadratic formula.
Step-by-step explanation:
1. -3x² - x + 3 = -3x²
Simplify above equation,
-3x² + 3x² - x + 3 = 0
or -x + 3 = 0 , Sine x² terms cancelled each other.
Hence this equation can not be solved using quadratic formula.
2. 0 =x² , yes here we can use quadratic formula
3. 0 = 2x²-1
Simplifying the above equation,
0 = 2x² - 1
1 = 2x²
x² =
Hence we can use quadratic formula here.
4. x²+3x-2 = 4x²- 5x - 1
Simplifying given equation,
x²+3x-2 = 4x²- 5x - 1
or x² - 4x² +3x +5x -2 + 1 = 0
or -3x² + 8x - 1 = 0
since x² term is here, hence we can solve this using quadratic formula.
If two pentagons are similar, then their sides are proportional. To find PT, we'll need to set up a proportion.
AE / PT = AB / PQ
---There are many ways to set up this proportion, it just depends on what side lengths you have and ensuring that they match up on both shapes.
6 / x = 5 / 12.5
5x = 75
x = 15
Length of PT = 15 cm
Option C
Hope this helps!
Answer:
9 hours 43 mins 0 seconds
Step-by-step explanation:
4 (2h 25mins 45s)
8h + 100mins + 180s
- 8h
- 100mins → 1h 40min
- 180s → 3 mins
Part of the value of sin(u) is cut off; I suspect it should be either sin(u) = -5/13 or sin(u) = -12/13, since (5, 12, 13) is a Pythagorean triple. I'll assume -5/13.
Expand the tan expression using the angle sum identities for sin and cos :
tan(u + v) = sin(u + v) / cos(u + v)
tan(u + v) = [sin(u) cos(v) + cos(u) sin(v)] / [cos(u) cos(v) - sin(u) sin(v)]
Since both u and v are in Quadrant III, we know that each of sin(u), cos(u), sin(v), and cos(v) are negative.
Recall that for all x,
cos²(x) + sin²(x) = 1
and it follows that
cos(u) = - √(1 - sin²(u)) = -12/13
sin(v) = - √(1 - cos²(v)) = -3/5
Then putting everything together, we have
tan(u + v)
= [(-5/13) • (-4/5) + (-12/13) • (-3/5)] / [(-12/13) • (-4/5) - (-5/13) • (-3/5)]
= 56/33
(or, if sin(u) = -12/13, then tan(u + v) = -63/16)