Answer:
Step-by-step explanation:
The equation is x^4 – 5x^2 – 36 = 0
We will break the middle term:
Firstly multiply the coefficient of x^4 by constant term of the equation:
1*36 = 36
Now find any two numbers whose product is 36 and their sum or difference is equal to 5
9*4 = 36
9-4 = 5
Now,
x^4 – 5x^2 – 36 = 0
x^4-9x^2+4x^2-36=0
Now take the common:
x^2(x^2-9)+4(x^2-9)=0
(x^2+4)(x^2-9)=0
x²+4=0,
x²= 0-4,
x²=-4,
Take root on both sides:
√x²=+/-√-4
+/-√-4 = +/-√-1 *√4
√-1 = i
Then +/-√-1 *√4 = √4 i
We know that the root of 4 is 2
Then we can write it as +/-2i
Thus x = 2i , -2i
Now (x^2-9)= 0
x²=0+9
x²=9
Take square root on both sides:
√x²=√9
x=+/-3
x= 3, -3
Therefore the values of x are 2i, -2i, 3 , -3 ....
Answer:
16
Step-by-step explanation:
Let's represent this with an equation, where x is the first number. The next number must be x+2, because it has to be even, not x+1, and the rest continue the same way:
x+(x+2)+(x+4)+(x+6)+(x+8) = 100
Solve for x.
5x+20 = 100
5x = 80
<u>x = 16</u>
Use pythagorena theorme
D=

NOTE: x1 and x2 means the first x and second x, not x^1 and x^2
points given are
(1,1)
(5,6)
x1=1
y1=1
x2=5
y2=6
D=

D=

D=

D=

6.403
answer is B
First find out how many times 3/4 yard goes into 9. 3/4 fits into 9 twelve times, so twelve puppets can be made.
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The binomial distribution is given by,
P(X=x) =

q = probability of failure = 1-0.2 = 0.8
n = 100
They have asked to find the probability <span>of obtaining a score less than or equal to 12.
</span>∴ P(X≤12) =

where, x = 0,1,2,3,4,5,6,7,8,9,10,11,12
∴ P(X≤12) =

+

+

+

+

+

+

Evaluating each term and adding them you will get,
P(X≤12) = 0.02532833572
This is the required probability.