Answer: option C is the correct answer
Step-by-step explanation:
The system of linear equations is
10x + 7y = 12 - - - - - - - 1
8x + 7y = 18 - - - - - - - 2
Since the coefficient of y is the same in equation 1 and equation 2, we will eliminate y by subtracting equation 2 from equation 1, it becomes
10x - 8x + 7y - 7y = 12 - 18
2x = -6
x = - 6/2 = - 3
Substituting x = - 3 into equation 1, it becomes
10×-3 + 7y = 12
-30 + 7y = 12
Let the constants be on the right hand side and the term containing y be on the left hand side. It becomes
7y = 12 + 30
7y = 42
y = 42/7
y = 6
C) (−3, 6)
Short AnswerThere are two numbers
x1 = -0.25 + 0.9682i <<<<
answer 1x2 = - 0.25 - 0.9582i <<<<
answer 2 I take it there are two such numbers.
Let one number = x
Let one number = y
x + y = -0.5
y = - 0.5 - x (1)
xy = 1 (2)
Put equation 1 into equation 2
xy = 1
x(-0.5 - x) = 1
-0.5x - x^2 = 1 Subtract 1 from both sides.
-0.5x - x^2 - 1 = 0 Order these by powers
-x^2 - 0.5x -1 = 0 Multiply though by - 1
x^2 + 0.5x + 1 = 0 Use the quadratic formula to solve this.

a = 1
b = 0.5
c = 1

x = [-0.5 +/- sqrt(0.25 - 4)] / 2
x = [-0.5 +/- sqrt(-3.75)] / 2
x = [-0.25 +/- 0.9682i
x1 = -0.25 + 0.9682 i
x2 = -0.25 - 0.9682 i
These two are conjugates. They will add as x1 + x2 = -0.25 - 0.25 = - 0.50.
The complex parts cancel out. Getting them to multiply to 1 will be a little more difficult. I'll do that under the check.
Check(-0.25 - 0.9682i)(-0.25 + 0.9682i)
Use FOIL
F:-0.25 * -0.25 = 0.0625
O: -0.25*0.9682i
I: +0.25*0.9682i
L: -0.9682i*0.9682i = - 0.9375 i^2 = 0.9375
NoticeThe two middle terms (labled "O" and "I" ) cancel out. They are of opposite signs.
The final result is 0.9375 and 0.0625 add up to 1
The answer is 29.5
Okkkkkkkkrrrrrrrr It is a long division just use calculator
The probability of getting the correct order in the spelling bee is 1 chance in 362,880.
This is a permutation problem. Our goals is to find the total number of ways that the 9 students can be ordered.
For the first spot there are 9 choices, then 8 choices, then 7 choices....
We need to evaluate:
9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880
Another way to write this is: 9!