Given:
The given system of equations is:
To find:
The solution to this system of equations by graphing.
Solution:
We have,
The table of values for first equation is:
x y
0 1
1 -1
Plot the points (0,1) and (1,-1) on a coordinate plane and connect them a straight line.
The table of values for second equation is:
x y
0 -4
2 -3
Plot the points (0,-4) and (2,-3) on a coordinate plane and connect them a straight line.
The graphs of given equations are shown in the below figure.
From the below figure, it is clear that the lines intersect each other at point (2,-3). So, the solution of the given system of equations is (2,-3).
Therefore, the solution to this system of equations is:
x-coordinate: 2
y-coordinate: -3
Answer:
or 2.738
Step-by-step explanation:
Let’s just look at the triangle on the top with the 
on the top and x on the bottom. (Basically the top half to the equilateral triangle)
There is a small square in the bottom right corner, which indicates that this triangle is a right triangle. This means that we can use the Pythagorean Theorem: 
We know that \sqrt{10} is our hypotenuse, and therefore our c in our equation. Let’s say that x=a in our equation. Therefore we are left to find b. However, b is half the length of the side of the original equilateral triangle. An equilateral triangle means that all three sides are the same length. Therefore our side would also be \sqrt{10} units long. However we know that b is half of that value, so b=
or 
Plugging these values into the equation:
x^2+ (\frac{\sqrt{10} }{2})^{2}=\sqrt{10} ^{2}
This approximately equals 2.738
Let X be the number of boys in n selected births. Let p be the probability of getting baby boy on selected birth.
Here n=10. Also the male and female births are equally likely it means chance of baby boy or girl is 1/2
P(Boy) = P(girl) =0.5
p =0.5
From given information we have n =10 fixed number of trials, p is probability of success which is constant for each trial . And each trial is independent of each other.
So X follows Binomial distribution with n=10 and p=0.5
The probability function of Binomial distribution for k number of success, x=k is given as
P(X=k) = 
We have to find probability of getting 8 boys in n=10 births
P(X=8) = 
= 45 * 0.0039 * 0.25
P(X = 8) = 0.0438
The probability of getting exactly 8 boys in selected 10 births is 0.044
A the slope of the line is 1
to calculate the slope m , use the ' gradient formula '
m = ( y₂ - y₁ ) /( x₂ - x₁ )
where (x₁, y₁ ) = 6, 3) and (x₂, y₂ ) = (9, 6)
m = 
= 
= 1
The correct answer is that there are 5 terms in this problem
