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 ,
9514 1404 393
Answer:
a) C x +x +x +3x +3x = 18
b) x = 2
c) 2 cm, 6 cm
Step-by-step explanation:
a) The sum of the lengths of the sides is equal to the length of the perimeter. The appropriate equation is ...
x +x +x +3x +3x = 18
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b) Simplifying, the equation becomes ...
9x = 18
x = 2 . . . . . divide by 9
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c) The shorter sides are x = 2 cm.
The longer sides are 3x = 6 cm.
Answer:
y= 1/2x-3
Step-by-step explanation:
2y - x = 8
First find the slope
2y = x+8
Divide by 2
2y/2 = x/2 +8/2
y = 1/2 x +4
The slope is 1/2 ( y=mx+b where m is the slope and b is the y intercept)
When lines are parallel they have the same slope)
Using y = mx+b
y =1/2x+b
Substituting the point (4,-1) into the equation
-1 =1/2(4)+b
-1 = 2+b
-3 =b
The equation of the line is
y= 1/2x-3
The answer is C.<span>consistent and independent</span>
Answer:
2.64
Step-by-step explanation:
0.9(x + 1.4) - 2.3 + 0.1x = 1.6
0.9x + 1.26 -2.3 + 0.1x - 1.6 = 0
(0.9x + 0.1x) + (1.26 - 2.3 - 1.6) = 0
x - 2.64 = 0
x = 2.64
