3.3 % chance that will randomly pick tallest
Answer: There’s a .35 % chance that the marble will be green. When drawing all 3, the chance is .04%
Step-by-step explanation:
Answer:
m∠DEC = 78°
Step-by-step explanation:
Given information: AC = AD, AB⊥BD, m∠DAC = 44° and CE bisects ∠ACD.
If two sides of a triangles are congruent then the opposite angles of congruent sides are congruent.
AC = AD (Given)
According to the angle sum property, the sum of interior angles of a triangle is 180°.
Divide both sides by 2.
CE bisects ∠ACD.
Use angle sum property in triangle CDE,
Subtract 102 from both sides.
Therefore, the measure of angle DEC is 78°.
Answer:
x = -2, x = 3 − i√8, and x = 3 + i√8
Step-by-step explanation:
g(x) = x³ − 4x² − x + 22
This is a cubic equation, so it must have either 1 or 3 real roots.
Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.
g(-1) = 18
g(1) = 18
g(-2) = 0
g(2) = 12
g(-11) = 1782
g(11) = 858
g(-22) = -12540
g(22) = 8712
We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.
g(x) = x³ − 4x² − 12x + 11x + 22
g(x) = x (x² − 4x − 12) + 11 (x + 2)
g(x) = x (x − 6) (x + 2) + 11 (x + 2)
g(x) = (x (x − 6) + 11) (x + 2)
g(x) = (x² − 6x + 11) (x + 2)
x² − 6x + 11 = 0
Quadratic formula:
x = [ 6 ± √(36 − 4(1)(11)) ] / 2
x = (6 ± 2i√8) / 2
x = 3 ± i√8
The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.
Slope = rise/run
slope = 3/12
slope = 1/4
answer is
<span>1/4</span>
