Answer:
Option A)
![9x^2 - 36x + 35 = 0](https://tex.z-dn.net/?f=9x%5E2%20-%2036x%20%2B%2035%20%3D%200)
Step-by-step explanation:
We are given the following in the question:
Roots of quadratic equation are:
![\alpha = \dfrac{5}{3}, \beta = \dfrac{7}{3}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cdfrac%7B5%7D%7B3%7D%2C%20%5Cbeta%20%3D%20%5Cdfrac%7B7%7D%7B3%7D)
The sum of the roots and the product of the roots can be calculated as:
![\alpha + \beta = \dfrac{5+7}{3} = 4\\\\\alpha\beta = \dfrac{5}{3}\times \dfrac{7}{3} = \dfrac{5}{9}](https://tex.z-dn.net/?f=%5Calpha%20%2B%20%5Cbeta%20%3D%20%5Cdfrac%7B5%2B7%7D%7B3%7D%20%3D%204%5C%5C%5C%5C%5Calpha%5Cbeta%20%3D%20%5Cdfrac%7B5%7D%7B3%7D%5Ctimes%20%5Cdfrac%7B7%7D%7B3%7D%20%3D%20%5Cdfrac%7B5%7D%7B9%7D)
Standard form of quadratic equation:
![x^2-(\alpha + \beta)x+\alpha\beta = 0](https://tex.z-dn.net/?f=x%5E2-%28%5Calpha%20%2B%20%5Cbeta%29x%2B%5Calpha%5Cbeta%20%3D%200)
Putting values, we get,
![x^2 - 4x + \dfrac{35}{9} = 0\\\\9x^2 - 36x + 35 = 0](https://tex.z-dn.net/?f=x%5E2%20-%204x%20%2B%20%5Cdfrac%7B35%7D%7B9%7D%20%3D%200%5C%5C%5C%5C9x%5E2%20-%2036x%20%2B%2035%20%3D%200)
is the required quadratic equation.
Thus, the correct answer is
Option A)
![9x^2 - 36x + 35 = 0](https://tex.z-dn.net/?f=9x%5E2%20-%2036x%20%2B%2035%20%3D%200)
-20 because 40 is a positive and spent is negative
<h3>Answer: Approximately 6.4 units</h3>
==================================================
Explanation:
The origin is the point (0,0)
Use the distance formula to find the distance from (0, 0) to (4, -5)
Let
![(x_1,y_1) = (0,0)\\\\(x_2,y_2) = (4,-5)\\\\](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%280%2C0%29%5C%5C%5C%5C%28x_2%2Cy_2%29%20%3D%20%284%2C-5%29%5C%5C%5C%5C)
be our two points. Plug those values into the distance formula below and use a calculator to compute
![d = \sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}\\\\d = \sqrt{\left(0-4\right)^2+\left(0-(-5)\right)^2}\\\\d = \sqrt{\left(0-4\right)^2+\left(0+5\right)^2}\\\\d = \sqrt{\left(-4\right)^2+\left(5\right)^2}\\\\d = \sqrt{16+25}\\\\d = \sqrt{41} \ \text{ exact distance}\\\\d \approx 6.40312 \ \text{ approximate distance}\\\\d \approx 6.4\\\\](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%5Cleft%28x_1-x_2%5Cright%29%5E2%2B%5Cleft%28y_1-y_2%5Cright%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%5Cleft%280-4%5Cright%29%5E2%2B%5Cleft%280-%28-5%29%5Cright%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%5Cleft%280-4%5Cright%29%5E2%2B%5Cleft%280%2B5%5Cright%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%5Cleft%28-4%5Cright%29%5E2%2B%5Cleft%285%5Cright%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B16%2B25%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B41%7D%20%5C%20%5Ctext%7B%20exact%20distance%7D%5C%5C%5C%5Cd%20%5Capprox%206.40312%20%5C%20%5Ctext%7B%20approximate%20distance%7D%5C%5C%5C%5Cd%20%5Capprox%206.4%5C%5C%5C%5C)
The distance between the two points (0,0) and (4,-5) is approximately 6.4 units.
Step-by-step explanation:
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Answer:
Step 1:
✔ Cofunction identity
Step 5:
✔ Sine difference identity
Step 6:
✔ Cofunction Identity
Step 7:
✔ Cosine function is even, sine function is odd.
Step-by-step explanation: