2x2-5x-18=0
Two solutions were found :
x = -2
x = 9/2 = 4.500
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(2x2 - 5x) - 18 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2-5x-18
The first term is, 2x2 its coefficient is 2 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -18
Step-1 : Multiply the coefficient of the first term by the constant 2 • -18 = -36
Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -5 .
-36 + 1 = -35
-18 + 2 = -16
-12 + 3 = -9
-9 + 4 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 4
2x2 - 9x + 4x - 18
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-9)
Add up the last 2 terms, pulling out common factors :
2 • (2x-9)
Step-5 : Add up the four terms of step 4 :
(x+2) • (2x-9)
Which is the desired factorization
Equation at the end of step 2 :
(2x - 9) • (x + 2) = 0
Step 3 :
Theory - Roots of a product :
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Answer:
1/2%
Step-by-step explanation:
Answer:
a) 0.1558
b) 0.7983
c) 0.1478
Step-by-step explanation:
If we suppose that small aircraft arrive at the airport according to a <em>Poisson process</em> <em>at the rate of 5.5 per hour</em> and if X is the random variable that measures the number of arrivals in one hour, then the probability of k arrivals in one hour is given by:
(a) What is the probability that exactly 4 small aircraft arrive during a 1-hour period?
(b) What is the probability that at least 4 arrive during a 1-hour period?
(c) If we define a working day as 12 hours, what is the probability that at least 75 small aircraft arrive during a working day?
If we redefine the time interval as 12 hours instead of one hour, then the rate changes from 5.5 per hour to 12*5.5 = 66 per working day, and the pdf is now
and we want <em>P(X ≥ 75) = 1-P(X<75)</em>. But
hence
P(X ≥ 75) = 1-0.852 = 0.1478
Answer:
B: (x-6)^2=0
Step-by-step explanation:
Answer:
x ≈ 46.7°
Step-by-step explanation:
Using the sine ratio in the right triangle
sin x = 
= 
= 
, then
x = 
( ) ≈ 46.7° ( to the nearest tenth )
