True or false: (5.1 × 10^8)(2.1 × 10^8)=1.71×10^17 A true B false

The factors of x cube -10x square -53x-42

Verdich [7]

Answer:

$x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)$

Step-by-step explanation:

$x^3 - 10x^2 -53x - 42$

The factors of 42 : ±1 , ±2 , ±3 , ±6, ±7, ±14, ±21 , ±42

Using trial and error method we will find the first root of the polynomial.

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.

Now by long division or by using synthetic division we can find other factors.

Synthetic Division :

-1 | 1 -10 -53 - 42

| 0 - 1 11 42

|______________________

1 - 11 - 42 0

Therefore ,

$x^3 - 10 x^2 -53x -42 = ( x + 1)(x^2 - 11x +42)$ ------ ( 1 )

Next further factorize x² - 11x - 42

x² - 11x - 42

= x² - 14x + 3x - 42

=x(x - 14) + 3 (x - 14)

=(x + 3 )(x - 14)

Therefore ,

$x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)$

4 0

3 years ago

A dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population. She randomly assigns no

Darina [25.2K]

Answer:

is that hindi or something.

Step-by-step explanation:

7 0

3 years ago

A vegetable garden and a surrounding as a shaped like a square that together a 11 ft wide. The path is 2 feet wide. If one bag o

Alexxandr [17]

Answer:

$\displaystyle 4$

Step-by-step explanation:

we are given that A vegetable garden and a surrounding as a shaped like a square that together a 11 ft wide. The path is 2 feet wide.since together the width of Vegetable garden and path is 11 ft, the width of the vegetables garden will be the difference between the total width and the width of path Thus,

$\displaystyle \rm W _{ garden} = 11 - 2$

simplify substraction:

$\displaystyle \rm W _{ garden} = 9$

recall that, every single side of a square is equal to each other therefore the the area of the garden will be

$\displaystyle {9}^{2}$

simplify square:

$\displaystyle 81$

together the garden and path makes a square of every side length 11 ft saying that the area will be:

$\displaystyle {11}^{2}$

simplify square:

$\displaystyle 121$

the area of path will be the difference between the total area and the garden area therefore,

$\displaystyle 121 - 81$

simplify addition:

$\displaystyle 40$

to figure out how many bags are needed to cover the path. we just need to divide the area of the path by the area of a bag of gravel and that yields:

$\displaystyle \frac{40}{10}$

simplify division:

$\displaystyle \boxed{\rm4}$

hence,

4 bags are needed to cover the path.

7 0

3 years ago

How do you do this? Thanks for your time and effort!

V125BC [204]

Well first you have to simplify the denominators with x, by multiplying the denominator on the left times the top and bottom of the middle, and vice versa to get 10x/(4x^2-4x)-9(2x-2)/(4x^2-4x)=-1/4 and then you combine the fractions on the left to get 2(9-4x)/(4x^2-4x)=-1/4 and then you cross multiply the fractions to get 8(9-4x)=-4x^2+4x and then simplify to get 72-32x=-4x^2+4x and then 4x^2-36x+72=0 which then we can turn into 4(x-6)(x-3)=0 so x is 6 and 3

3 0

3 years ago

Could someone help me solve this step by step..thxx

jolli1 [7]

Answer:

Step-by-step explanation:

3^t=3^(1/5)

T=1/5

7 0

3 years ago

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