False. This is because no matter what the number is, the properties of multiplication and division stay the same. So, if one odd and even number multiply/divide, then the answer will be negative. But, if two numbers of the same sign (both either negative or positive) are divided/multiplied, they will both be positive. Therefore, the result is not always the same sign as the starting integers
Hope this helped! :D
Answer:
<em>The sum of the two solutions to the given equation is 1/3.</em>
Step-by-step explanation:
<u>Nature of Roots of a Second-Degree Equation</u>
Given a quadratic equation:
![ax^2 + bx + c = 0](https://tex.z-dn.net/?f=ax%5E2%20%2B%20bx%20%2B%20c%20%3D%200)
The roots of the equation are:
![\displaystyle x_1=\frac{-b+ \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x_1%3D%5Cfrac%7B-b%2B%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
![\displaystyle x_2=\frac{-b- \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x_2%3D%5Cfrac%7B-b-%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
The sum of the roots is:
![\displaystyle x_1+x_2=-\frac{b}{a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x_1%2Bx_2%3D-%5Cfrac%7Bb%7D%7Ba%7D)
The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second term, divided by the leading coefficient.
We are given the equation:
![3x^2 - x = 4](https://tex.z-dn.net/?f=3x%5E2%20-%20x%20%3D%204)
Rearranging:
![3x^2 - x - 4=0](https://tex.z-dn.net/?f=3x%5E2%20-%20x%20-%204%3D0)
The coefficient b is b=-1, and the leading coefficient is a=3, thus the sum of the roots is:
![\displaystyle x_1+x_2=-\frac{-1}{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x_1%2Bx_2%3D-%5Cfrac%7B-1%7D%7B3%7D)
![\displaystyle x_1+x_2=\frac{1}{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x_1%2Bx_2%3D%5Cfrac%7B1%7D%7B3%7D)
The sum of the two solutions to the given equation is 1/3.
Answer: 20 students mow on Saturday, 3 of those sleep until noon. Those who don’t mow the lawns, 21 of them sleep until noon.
Step-by-step explanation: 40% of 50 is 20. 25% of 20 is 3. 50-20=30. 70% of 30 is 21
Answer:
i believe the answer would be 7
Step-by-step explanation:
3 + 20 ÷ 5 = 7