I assume that this is a system of equations so I'll use the substitution method.
Make one of the equations equal an isolated variable and since x is already isolated just add -3y on both sides.
x-3y=-24
+3y +3y
x=3y-24
Substitute that in for the first equation.
2(3y-24)+9y=27
6y-48+9y=27
15y-48=27
+48 +48
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15y=75
----- ----
15 15
y=5
Substitute y in the other equation and find x
x-3(5)=-24
x-15=-24
+15 +15
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x=-9
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There are 2 roots for this equation.
The discriminant is given by b²-4ac. This is what goes under the square root in the quadratic formula. Since we will be taking the square root of this, if the discriminant is less than 0, there are no real roots; you cannot have a real square root of a negative number.
If the discriminant is equal to 0, there is 1 real root; the square root of 0 is 0, so the quadratic formula would yield one answer.
If the discriminant is greater than 0, there are 2 real roots. This is because taking the square root of a positive number gives a positive and negative result.
b in our equation is -7, a is 3 and c is 4:
b²-4ac = (-7)²-4(3)(4) = 49 - 48 = 1
There is 1 real root.
You just add both fractions because you’re subtracting a negative.
Answer: 1/2
I got this wrong just to help you figure out the right answer. (I just did not answer and this is the final result)
For the initial 600 days the sun was shining for a total of 360 days. This can be found by converting the percentage to a decimal by dividing its value by 100 and then multiplying that value by the initial total number of days shining.
(60/100) x (600) = 360 days
She then observes the sun for an additional 200 days increasing the total amount of days from 600 to 800. As a result the percentage of sunny days drops from 60% to 50%. To help solve the problem you have to determine what 50% of the new total amount of days is.
(50/100) x 800 = 400 days
Lastly to determine how many of the days during the final 200 days were sunny subtract the number of sunny days from the first equation from the second.
400 days - 360 days = 40 days
This means that 40 of the final 200 days were sunny.
