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:
(x+3)( 3x^2 +5)
Step-by-step explanation:
3x^3+9x^2+5x+15
Split into two groups
3x^3+9x^2 +5x+15
Factor 3x^2 out of the first group and 5 out of the second group
3x^2 ( x+3) + 5(x+3)
Factor out x+3
(x+3)( 3x^2 +5)
Answer:
80
Step-by-step explanation:
There are four 4 by 3 rectangles, so I did 4x3 and got 12, then multiplied by 4 to get 48. There are also two 4 by 4 squares, so 4x4=16 and 16x2=32
32+48=80
Quotient is n over 7
difference is n-7
product is 7n
sum is n+7
Answer:
Option C, 488 square centimeters
Step-by-step explanation:
<u>Step 1: Determine the area of the rectangle</u>
<u>Step 2: Determine the area of the triangle</u>
<u>Step 3: Determine the total area</u>
Answer: Option C, 488 square centimeters
