345,000 ; 350,00 ; 300,000.
Solution:
we have been asked to find the solution of the equation
It can be solved using factoring as below:
![x^6 + 6x^3 + 5 = 0\\\\substitute, x^3=y\\\\y^2+6y+5=0\\\\y^2+5y+y+5=0\\\\y(y+5)+1(y+5)=0\\\\(y+5)(y+1)=0\\\\y=-1,-5\\\\\text{substitute back }y=x^3\\\\x^3=-1,-5\\\\x=-1,\sqrt[3]{-5} \\\\\text{These are the only real solutions}\\](https://tex.z-dn.net/?f=x%5E6%20%2B%206x%5E3%20%2B%205%20%3D%200%5C%5C%5C%5Csubstitute%2C%20x%5E3%3Dy%5C%5C%5C%5Cy%5E2%2B6y%2B5%3D0%5C%5C%5C%5Cy%5E2%2B5y%2By%2B5%3D0%5C%5C%5C%5Cy%28y%2B5%29%2B1%28y%2B5%29%3D0%5C%5C%5C%5C%28y%2B5%29%28y%2B1%29%3D0%5C%5C%5C%5Cy%3D-1%2C-5%5C%5C%5C%5C%5Ctext%7Bsubstitute%20back%20%7Dy%3Dx%5E3%5C%5C%5C%5Cx%5E3%3D-1%2C-5%5C%5C%5C%5Cx%3D-1%2C%5Csqrt%5B3%5D%7B-5%7D%20%5C%5C%5C%5C%5Ctext%7BThese%20are%20the%20only%20real%20solutions%7D%5C%5C)
(-10m^4n^7)(-3m^4n)
= -10*-3 m^4*m^4 * n^7* n^1
= 30m^8n^8
p(outcome) = (number of desired outcomes)/(total number of outcomes)
The total number of outcomes is the sum of the numbers of the marbles.
4 + 6 + 2 = 12
The desired outcome is selecting a red ball. There are 2 red balls, so the number of desired outcomes is 2.
p(red) = 2/12 = 1/6
Answer: The length of the rectangle is 37.5 inches and the width is 12.5 inches
Step-by-step explanation: The dimensions of the rectangle is not given but we have clues given. The length is given as three times it’s width which means if the width is W, then the length would be given as 3W (three times the width). Also the perimeter is given as 100 inches and the formula for the perimeter is;
Perimeter = 2(L + W)
We can now insert the known values as follows;
100 = 2(3W + W)
100 = 2(4W)
100 = 8W
Divide both sides of the equation by 8
12.5 = W
Having calculated the width as 12.5 inches, the length now becomes
L = 3W
L = 3 x 12.5
L = 37.5
Hence the length is 37.5 inches and the width is 12.5 inches
