The solutions for the given system of equations are:
(3, 0), (-4, 7).
<h3>
How to solve the given system of equations:</h3>
Here we have the system:
x + y = 3
y = x² - 9
To solve this, we can replace the second equation into the first one, so we get:
x + (x² - 9) = 3
Now we can solve this quadratic equation for x, we need to solve:
x² + x - 12 = 0.
The solutions are given by Bhaskara's formula:
Then the two solutions are:
x = (-1 + 7)/2 = 3
x = (-1 - 7)/2 = -4
To get the y-values correspondent, we can evaluate the linear equation in these two values:
y = 3 - x.
For x = 3:
y = 3 - 3 = 0
For x = -4:
y = 3 + 4 = 7
Then the two solutions are: (3, 0), (-4, 7).
If you want to learn more about systems of equations:
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Both x and y are positive
Answer:
see attached for sketch of Empirical Rule
Step-by-step explanation:
The Empirical Rule (also known is the "68-95-99.7" rule) states that nearly all of the data will fall within three standard deviations of the mean.
Answer:
The prince's crown had a greater ratio of red gems to purple gems.
Step-by-step explanation:
KING = 5 red / 8 purple
PRINCE = 4 red / 5 purple
Times the ratio for the king by 5
5(5) / 8(5) = 25/40
Times the ratio for the prince by 8
4(8) / 5(8) = 32/40
The prince has a greater ratio of red gems
Hope this is right, and sorry if it is incorrect. Have a good day!
Answer:96
Step-by-step explanation: 4x8 = 32 so there will be 32 fluid ounces gone. subtract that from 128 to get 96.
