Answer:
1 1/3
Step-by-step explanation:
2/3 x 2/1 = 4/3 = 1 1/3
A quadratic equation that has 2 roots that are equal means that the discriminant of the equation is 0. The value of k that makes the equation have 2 real and equal roots is ![k = \frac{5}{6}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B5%7D%7B6%7D)
Given that:
![(2k + 1)x^2 + 2x = 10x - 6](https://tex.z-dn.net/?f=%282k%20%2B%201%29x%5E2%20%2B%202x%20%3D%2010x%20-%206)
Rewrite as:
![(2k + 1)x^2 + 2x - 10x + 6 = 0](https://tex.z-dn.net/?f=%282k%20%2B%201%29x%5E2%20%2B%202x%20-%2010x%20%2B%206%20%3D%200)
![(2k + 1)x^2 - 8x + 6 = 0](https://tex.z-dn.net/?f=%282k%20%2B%201%29x%5E2%20-%208x%20%2B%206%20%3D%200)
A quadratic equation is represented as:
![ax^2 + bx + c = 0](https://tex.z-dn.net/?f=ax%5E2%20%2B%20bx%20%2B%20c%20%3D%200)
By comparison:
![a=2k+1\\ b =-8\\\ c =6](https://tex.z-dn.net/?f=a%3D2k%2B1%5C%5C%20b%20%3D-8%5C%5C%5C%20c%20%3D6)
If an equation has 2 real and equal roots, then:
![b^2 = 4ac](https://tex.z-dn.net/?f=b%5E2%20%3D%204ac)
So, we have:
![(-8)^2 = 4 \times (2k + 1) \times 6](https://tex.z-dn.net/?f=%28-8%29%5E2%20%3D%204%20%5Ctimes%20%282k%20%2B%201%29%20%5Ctimes%206)
![64 = 4 \times (2k + 1) \times 6](https://tex.z-dn.net/?f=64%20%3D%204%20%5Ctimes%20%282k%20%2B%201%29%20%5Ctimes%206)
Divide by 4
![16 = (2k + 1) \times 6](https://tex.z-dn.net/?f=16%20%3D%20%282k%20%2B%201%29%20%5Ctimes%206)
Divide by 6
![\frac{16}{6} = (2k + 1)](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B6%7D%20%3D%20%282k%20%2B%201%29)
![\frac{8}{3} = 2k + 1](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B3%7D%20%3D%202k%20%2B%201)
Subtract 2 from both sides
![2k = \frac{8}{3} -1](https://tex.z-dn.net/?f=2k%20%3D%20%5Cfrac%7B8%7D%7B3%7D%20-1)
Take LCM
![2k = \frac{8-3}{3}](https://tex.z-dn.net/?f=2k%20%3D%20%5Cfrac%7B8-3%7D%7B3%7D)
![2k = \frac{5}{3}](https://tex.z-dn.net/?f=2k%20%3D%20%5Cfrac%7B5%7D%7B3%7D)
Divide by 2
![k = \frac{5}{6}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B5%7D%7B6%7D)
Hence, the value of k that makes the equation have 2 real and equal roots is ![k = \frac{5}{6}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B5%7D%7B6%7D)
Read more about real and equal roots at:
brainly.com/question/2535040
-2(y-3)=22
-2y+6=22
-2y=16
y=-8
Answer: The only difference between the six functions depends on the sides we use.
Step-by-step explanation:
The primary trigonometry ratio are
Sine (sin)
Cosine (cos)
Tangent (tan)
The reciprocal ratio are derived from the three primary functions. Because they can easily be derived, calculators and spreadsheets do not usually have them. These are:
Secant (sec)
Cosecant (csc)
Cotangent (cot)
Please find the attached files for more explanation