If I’m not mistaken I think this is what you’re asking for?
The two intersection points are (-2.79, -0.58) and (0.79, 6.58).
<h3>
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:
brainly.com/question/17206319
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Using the distributive property is done by multiplying the factor (outside the parentheses) to each term within it. In this case, 8(3 + 4), we multiply the 8 by 3, and then add it to the product of 8 x 4:
8(3 + 4) = 8 x 3 + 8 x 4 = 24 + 32
If we need to simplify further, this adds up to 56.
Answer:
<em>Beck actually caught 45 fish</em>
Step-by-step explanation:
<u>System of Equations</u>
We call the following variables:
x = number of fish Ally caught
y = number of fish Beck caught
They caught a total of 75 fish, thus:
x + y = 75 [1]
If Ally had caught twice as much fish as she actually did, and Beck had caught three times as many fish as he actually did, then Ally would have caught 75 fewer fish than Beck, thus:
3y = 2x + 75 [2]
From [1]:
x = 75 - y [3]
Substituting in [2]:
3y = 2(75 - y) + 75
Operating:
3y = 150 - 2y + 75
Simplifying:
5y = 225
Dividing by 5:
y = 45
Beck actually caught 45 fish
Answer: 8/33
Step-by-step explanation:
So the probability of picking a purple marble is 8/12, after that there are 11 marbles left in the box
Now the probability of picking a green marble without placing the first marble back is 4/11
So the probability of doing both is 8/12 x 4/11 = 8/33
