Answer:
(x +(-2) ) and ( x+3)
The factors of a given cubic polynomial function are
( x-1) (x -2 ) and (x +3)
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that x³ - 7x + 6=0
f(x) = x³ - 7x + 6=0
put x=1
f(1) = 1 -7 +6 =0
(x -1 ) is one factor of given polynomial
By using synthetic division
x³ x² x constant
x=1 ║ 1 0 -7 6
<u>║ 0 1 1 -6</u>
<u> 1 1 -6 0</u>
The polynomial ( x² + x - 6) =0
<u><em>Step(ii):-</em></u>
The factors of
x² + x - 6=0
x² + 3x -2x - 6=0
x ( x +3 ) - 2( x +3) =0
(x -2 ) ( x+3 ) =0
x = 2 and x =-3
<u><em>Final answer:-</em></u>
The factors of a given cubic polynomial function are
( x-1) (x -2 ) and (x +3)
20 is the answer:
The shortest collection time in the after would be the minimum. This is 25.
The shortest collection time for before would also be the minimum. This is 45.
45 - 25 = 20
Answer:the mode is b
Step-by-step explanation:
B
If you want to convert a number to a percentage, you must multiply the number by 100%.
If you want to convert a percentage to a number (a fraction), you must divide the percentage by 100.
![p\%=\dfrac{p}{100}\to p=(p)(100)\%\\\\81=(81)(100)\%=8,100\%\\\\81\%=\dfrac{81}{100}](https://tex.z-dn.net/?f=p%5C%25%3D%5Cdfrac%7Bp%7D%7B100%7D%5Cto%20p%3D%28p%29%28100%29%5C%25%5C%5C%5C%5C81%3D%2881%29%28100%29%5C%25%3D8%2C100%5C%25%5C%5C%5C%5C81%5C%25%3D%5Cdfrac%7B81%7D%7B100%7D)
(-3, 0) is a solution to given equation
(-6, -1) is a solution to given equation
<em><u>Solution:</u></em>
<em><u>Given that equation is:</u></em>
![y = \frac{1}{3}x + 1](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B3%7Dx%20%2B%201)
<h3><em><u>
Option 1</u></em></h3>
(-3, 0)
Substitute x = -3 and y = 0 in given equation
![0 = \frac{1}{3} \times -3 + 1\\\\0 = -1 + 1\\\\0 = 0](https://tex.z-dn.net/?f=0%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20-3%20%2B%201%5C%5C%5C%5C0%20%3D%20-1%20%2B%201%5C%5C%5C%5C0%20%3D%200)
Thus (-3, 0) is a solution to given equation
<h3><em><u>
Option 2</u></em></h3>
(-9, -1)
Substitute x = -9 and y = -1 in given equation
![-1 = \frac{1}{3} \times -9 + 1\\\\-1 = -3 + 1\\\\-1 \neq -2](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20-9%20%2B%201%5C%5C%5C%5C-1%20%3D%20-3%20%2B%201%5C%5C%5C%5C-1%20%5Cneq%20%20-2)
Thus (-9, -1) is not a solution to given equation
<h3><em><u>
Option 3</u></em></h3>
(-6, -1)
Substitute x = -6 and y = -1 in given equation
![-1 = \frac{1}{3} \times - 6 + 1\\\\-1 = -2 + 1\\\\-1 = -1](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20-%206%20%2B%201%5C%5C%5C%5C-1%20%3D%20-2%20%2B%201%5C%5C%5C%5C-1%20%3D%20-1)
Thus (-6, -1) is a solution to given equation