A)
Because the sum of angles in a triangle must equal 180° we can say:
62+α+90=180
α+152=180
α=28°
b)
Since all sides have equal length, all angles must have equal measure. (This is an equilateral triangle). And again, because the sum of the angle must be 180° we can say:
b+b+b=180
3b=180
b=60°
Answer:
The last answer is correct. (x: 1,2,3,4 ; y: -5,0,5,10)
Step-by-step explanation:
In a linear function, the rate of increase/decrease is constant (the same). For the last answer, since for every x increase, y increases by 5, it is linear and has a constant rate of change.
Given:
Let x be the whole amount inherited.
1/2 * x - invested with Bernie Madoff
1/3 * x - lost due to identity theft
1/8 * x - lost in casino
40,000 - remainder
x - x/2 - x/3 - x/8 = 40,000
LCM:
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
3: 3, 6, 9, 12, 15, 18, 21, 24
8: 8, 16, 24,
x * 24/24 = 24x / 24
x/2 * 12/12 = 12x / 24
x/3 * 8/8 = 8x / 24
x/8 * 3/3 = 3x / 24
40,000 * 24/24 = 960,000 / 24
24x/24 - 12x/24 - 8x/24 - 3x/24 = 960,000/24
(24x - 12x - 8x - 3x)/24 = 960,000/24
x/24 = 960,000/24
24 * x/24 = 24 * 960,000/24
x = 960,000
x = 960,000 initial inheritance
x/2 = 960,000/2 = 480,000 invested with Bernie Madoff
x/3 = 960,000/3 = 320,000 lost due to identity theft
x/8 = 960,000/8 = 120,000 lost in the casino
40,000 - remaining amount.
960k - 480k - 320k - 120k = 40k
40k = 40k
Because the polynomial has degree 2, we can assume that there are 2 solutions (roots), whether real or imaginary.
You can subtract 60 in order to put this in standard form
48x^2+44x-60 = 0
From there, just put a,b, and c into the quadratic formula and you're good to solve for your answers.
(-b+-sqrt(b^2-4ac))/2a
(-44+-sqrt(44^2-4(48)(-60)))/2(48)
Then solve.
There is probably a better way, but this should give you the two roots/solutions.
