Answer:
α² +β² = 3 4/9
Step-by-step explanation:
Assuming α and β are solutions to the equation, it can be factored as ...
(x -α)(x -β) = 0
Expanding this, we get ...
x² -(α +β)x +αβ = 0
Dividing the original equation by 3, we find ...
x² +(1/3)x -5/3 ≡ x² -(α+β)x +αβ ⇒ (α+β) = -1/3, αβ = -5/3
We know that the square (α+β)² can be expanded to ...
(α +β)² = α² +β² +2αβ
α² +β² = (α +β)² -2αβ . . . . . . subtract 2αβ
Substituting the values for (α+β) and αβ, we find the desired expression is ...
α² +β² = (-1/3)² -2(-5/3) = 1/9 +10/3 = 31/9
α² +β² = 3 4/9
Answer:
141 5/7
Step-by-step explanation:
8c + 10b ÷ 7a
Let c = 7, b = 12, and a = 5
8*7 + 10*12 ÷ 7*5
Multiply and divide from left to right
56+120 ÷7*5
56+ 600/7
Get a common denominator
392/7 + 600/7
992/7
Change from an improper fraction to a mixed number
141 5/7
(-6,-4)
If you dilate a point, (c,d) about (a,b) by a scale factor by k. You'll going to subtract each coordinates where the point will be dilated about (a,b) from the point (c,d) and then multiply them by k. This would be the formula if you want: (k(c -a), k(b -d))
Let's say F is the dilation of D about the origin or (0,0) then the x coordinate of F would be

This would be the y coordinate of F:

Thus the coordinates of F is (-6,-4)
If 6 oranges cost 3.60 than one orange costs .60. To find, divide total price by number of oranges.
3.60/6 = .60
There is no set of pound in a gallon because we do not know the substance. Different liquids weigh different amounts.
3.5 gallons is equal to 448 ounces. To find, multiply the number of gallons (3.5) by the amount of ounces in a gallon (128)
3.5 * 128 = 448
Pound and pints are like gallons and pound. Unless we know the substance we cannot solve.
.75 pints is equal to 12 ounces. To find that, we multiply the number of pints (.75) by the number of ounces in a pint (16)
.75 * 16 = 12
So first we assume that half is adult and have is student.
So
215 adult 215 student
Now since it said they were 70 less student tickets than adult tickets we subtract 70.
215 - 70 = 145
Now we add the 70 we subtracted from student tickets to the adult tickets.
215 + 70 = 285
So there were
285 adult tickets sold and 145 student tickets sold
I hope this helped. Have a great day!