Answer:
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Step-by-step explanation:
The factors of 42 : ±1 , ±2 , ±3 , ±6, ±7, ±14, ±21 , ±42
<u>Using trial and error method we will find the first root of the polynomial.</u>
1 : ( 1 )³ - 10 ( 1 )² - 53 ( 1 ) - 42
1 - 10 - 53 - 42 ≠ 0
Therefore 1 is not a root
-1 : ( -1 )³ - 10 (- 1 )² - 53 (- 1 ) - 42
- 1 - 10 + 53 - 42
53 - 53 = 0
Therefore - 1 is a root of the polynomial.
Therefore ( x + 1) is a factor.
<u>Now by long division or by using synthetic division we can find other factors.</u>
<u>Synthetic Division :</u>
-1 | 1 -10 -53 - 42
| 0 - 1 11 42
|______________________
1 - 11 - 42 0
Therefore ,
------ ( 1 )
<u>Next further factorize x² - 11x - 42</u>
x² - 11x - 42
= x² - 14x + 3x - 42
=x(x - 14) + 3 (x - 14)
=(x + 3 )(x - 14)
Therefore ,
F=\dfrac{9}{5}C+32\\\\A.\\\dfrac{9}{5}C+32=F\ \ \ |-32\\\\\dfrac{9}{5}C=F-32\ \ \ |\cdot\dfrac{5}{9}\\\\C=\dfrac{5}{9}(F-32)
B.\\F=212\to C=\dfrac{5}{9}(212-32)=\dfrac{5}{9}\cdot180=100\\\\212^oF=100^oC
C.\\F=80\to C=\dfrac{5}{9}(80-32)=\dfrac{5}{9}\cdot48\approx26.7\\\\80^oF\approx26.7^oC
Answer:
(2, 1 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( , )
Here (x₁, y₁ ) = (7, 3) and (x₂, y₂ ) = (- 3, - 1) , then
midpoint = ( , ) = ( , ) = (2, 1 )