Answer: 8:12,8to12
Step-by-step explanation:
Answer:
A) JK and LM will be parallel to each other.
Step-by-step explanation:
On reflection on
line the x co-ordinate changes with y co-ordinate and y co-ordinate changes with x co-ordinate
![(x,y)\rightarrow (y,x)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%20%28y%2Cx%29)
Points on line EF
![(0,6) , (-5,-2)](https://tex.z-dn.net/?f=%280%2C6%29%20%2C%20%28-5%2C-2%29)
On reflection of this line on
the new points we get for line JK are
![(6,0),(-2,-5)](https://tex.z-dn.net/?f=%286%2C0%29%2C%28-2%2C-5%29)
Points on line GH
![(-4,9),(-9,1)](https://tex.z-dn.net/?f=%28-4%2C9%29%2C%28-9%2C1%29)
On reflection on y=x line the new points we get for line LM are
![(9,-4),(1,-9)](https://tex.z-dn.net/?f=%289%2C-4%29%2C%281%2C-9%29)
Slope of line JK
![m=\frac{y_2-y_1}{x2-x1}\\m=\frac{(-5)-0}{(-2)-6} \\m=\frac{-5}{-8}=\frac{5}{8}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx2-x1%7D%5C%5Cm%3D%5Cfrac%7B%28-5%29-0%7D%7B%28-2%29-6%7D%20%5C%5Cm%3D%5Cfrac%7B-5%7D%7B-8%7D%3D%5Cfrac%7B5%7D%7B8%7D)
Slope of line LM
![m=\frac{y_2-y_1}{x2-x1}\\m=\frac{(-9)-(-4)}{1-9} \\m=\frac{-9+4}{-8}=\frac{-5}{-8}\\m=\frac{5}{8}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx2-x1%7D%5C%5Cm%3D%5Cfrac%7B%28-9%29-%28-4%29%7D%7B1-9%7D%20%5C%5Cm%3D%5Cfrac%7B-9%2B4%7D%7B-8%7D%3D%5Cfrac%7B-5%7D%7B-8%7D%5C%5Cm%3D%5Cfrac%7B5%7D%7B8%7D)
For two line to be parallel, their slopes will be same.
![m_{JK} =\frac{5}{8} , m_{LM}=\frac{5}{8}](https://tex.z-dn.net/?f=m_%7BJK%7D%20%3D%5Cfrac%7B5%7D%7B8%7D%20%2C%20m_%7BLM%7D%3D%5Cfrac%7B5%7D%7B8%7D)
Since slopes of lines JK and LM are same therefore we can say that these are parallel to each other.
Four-ounce bag of pork rinds offers eight grams of protein, he said, adding that Small Batch pork rinds are also gluten-free and lower in ...
Answer:
15.13cm
Step-by-step explanation:
From that above question:
We are told that:
Lateral surface area of a right circular cone : πr√r² + h²
We are give the following parameters:
Lateral surface area = 236.64cm²
Radius = 4.75cm
We are to find the height
Making h the subject of the formula
h = √[(A/r)² - πr²]/π
h = √[(236.64/4.75)²- π ×4.75²]/π
h = 15.12975 cm
Approximately to the nearest hundredth = 15.13cm
For this case we have the following quadratic equation:
![-3x ^ 2 + x-4 = 0](https://tex.z-dn.net/?f=-3x%20%5E%202%20%2B%20x-4%20%3D%200)
Where:
![a = -3\\b = 1\\c = -4](https://tex.z-dn.net/?f=a%20%3D%20-3%5C%5Cb%20%3D%201%5C%5Cc%20%3D%20-4)
By definition, the discriminant of a quadratic equation is given by:
![d = b ^ 2-4 (a) (c)](https://tex.z-dn.net/?f=d%20%3D%20b%20%5E%202-4%20%28a%29%20%28c%29)
We have to:
Two different real roots
Two different complex roots
Two equal real roots
Substituting the values we have:
![d = 1 ^ 2-4 (-3) (- 4)\\d = 1-48\\d = -47](https://tex.z-dn.net/?f=d%20%3D%201%20%5E%202-4%20%28-3%29%20%28-%204%29%5C%5Cd%20%3D%201-48%5C%5Cd%20%3D%20-47)
So, we have two different complex roots
Answer:
Two different complex roots