The two intersection points are (-2.79, -0.58) and (0.79, 6.58).
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How to find the points of intersection?</h3>
Here we want to solve the system of equations:
y = 2x + 5
x² + y² = 36
To solve this, we need to replace the first equation into the second one:
x² + (2x + 5)² = 36
Now we can solve this for x:
x² + 4x² + 10x + 25 = 36
5x² + 10x - 11 = 0
This is a quadratic equation, to solve it we use the general formula:

So we have two solutions for x:
x = (-10 - 17.9)/10 = -2.79
x = (-10 + 17.9)/10 = 0.79
To get the y-values of the solutions, we evaluate the linear equation in these values of x:
y = 2*(-2.79) + 5 = -0.58
y = 2*( 0.79) + 5 = 6.58
Then the two intersection points are (-2.79, -0.58) and (0.79, 6.58).
If you want to learn more about intersection points:
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3x - 15 = 105
3x = 120
x = 40
3(40) - 15 + y + 24 = 180
120 - 15 + y + 24 = 180
129 + y = 180
y = 51
For this case we have that the main function is given by:

We apply the following transformations:
Vertical expansions:
To graph y = a * f (x)
If a> 1, the graph of y = f (x) is expanded vertically by a factor a.
For a = 5 we have:

Vertical translations:
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
For k = 5 we have:

Answer:
The graph of g (x) is the graph of f (x) stretched vertically by a factor of 5 and translated up 5 units.
1) This is a combination, so use ⁴⁰C₂.
⁴⁰C₂ = 780
There are 780 handshakes in total.
2) I got my solution by using the combinations formula. Or another way you could do this is to add up... 39 + 38 + 37 + 36 + 35 + 34 + 33 + 32 + 31... +1. You will end up with 780 (I did this to double check my work).
3) The quickest way to figure this out if Drake invited 1,000 people is to use the natural numbers formula = n(n+ 1)/2.
Plug the numbers in: 999(1000)/2 = 499,500
If Drake invited 1,000 people, there would be 499,500 handshakes.
Answer:
what is the question. please provide a question.