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77julia77 [94]
4 years ago
9

Use synthetic division to show that the number given to the right of the equation is a solution of the equation. Then solve the

polynomial equation.
2x^(3)+x^(2)-8x-4=0; 2

Mathematics
1 answer:
AysviL [449]4 years ago
8 0

Answer:

x = 2 \: or \: x =  - 2 \: or \: x =  -  \frac{1}{2}

Step-by-step explanation:

The given polynomial equation is

2 {x}^{3}  +  {x}^{2}  - 8x - 4 = 0

We perform the synthetic division as shown in the attachment by dividing by x-2.

This gives a remainder of 0 and a quotient of

2 {x}^{2}  + 5x + 2

This means the polynomial equation becomes:

(x - 2)(2 {x}^{2}  + 5x + 2) = 0

We factor the quadratic term by splitting the middle term;

(x - 2)(2 {x}^{2}  + 4x +x +  2) = 0

(x - 2)(2 x(x+ 2) +1(x +  2) )= 0

Collect common factors again:

(x - 2)((x+ 2)(2x +  1) = 0

The solution is:

x = 2 \: or \: x =  - 2 \: or \: x =  -  \frac{1}{2}

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if two circles have circumference of 12 pi inches and 18 pi inches,find the ratio between their radii
djverab [1.8K]
The formula for the circumference is:
2\pi r
So to find first radius:
2\pi r = 12\pi \\  \\ \pi r = 6\pi \\  \\ r = 6
Second radius:
2\pi r = 18\pi \\  \\ \pi r = 9\pi \\  \\ r = 9
The ratio between them is:
\frac{6}{9}  =  \frac{2}{3}  = 0.66667
8 0
3 years ago
Which table represents a function? A 2-column table with 4 rows. The first column is labeled x with entries negative 3, 0, negat
tangare [24]

Answer:

This is a many-to-one function as the value of y = -1 corresponds to two values of x:

\begin{array}{|c|c|}\cline{1-2} x & y\\\cline{1-2} -3 & -1\\\cline{1-2} 0 & 0\\\cline{1-2} -2 & -1\\\cline{1-2} 8 & 1\\\cline{1-2}\end{array}

Step-by-step explanation:

<u>Function</u>

A special relationship where each input (x-value) has a single output (y-value).

A function is <u>one-to-one</u> if each value in the range (y-values) corresponds to exactly one value in the domain (x-values).

A function is <u>many-to-one</u> if some values in the range (y-values) correspond to more than one (many) value in the domain (x-values).

This is a many-to-one function as the value of y = -1 corresponds to two values of x:

\begin{array}{|c|c|}\cline{1-2} x & y\\\cline{1-2} -3 & -1\\\cline{1-2} 0 & 0\\\cline{1-2} -2 & -1\\\cline{1-2} 8 & 1\\\cline{1-2}\end{array}

This is not a function as the value of x = -5 corresponds to two values of y:

\begin{array}{|c|c|}\cline{1-2} x & y\\\cline{1-2} -5 & -5\\\cline{1-2} 0 & 0\\\cline{1-2} -5 & 5\\\cline{1-2} 6 & -6\\\cline{1-2}\end{array}

This is not a function as the value of x = -2 corresponds to two values of y:

\begin{array}{|c|c|}\cline{1-2} x & y\\\cline{1-2} -4 & 8\\\cline{1-2} -2 & 2\\\cline{1-2} -2 & 4\\\cline{1-2} 0 & 2\\\cline{1-2}\end{array}

This is not a function as the value of x = -4 corresponds to two values of y:

\begin{array}{|c|c|}\cline{1-2} x & y\\\cline{1-2} -4 & 2\\\cline{1-2} 3 & 5\\\cline{1-2} 1 & 3\\\cline{1-2} -4 & 0\\\cline{1-2}\end{array}

8 0
2 years ago
Name two things we can measure on a 2-D Object
hram777 [196]
I'm going to give you 4 but it is width, length, area and perimeter

i hope this helps  
8 0
3 years ago
A force of 3 pounds is required to hold a spring stretched 0.6 feet beyond its natural length. how much work (in foot-pounds) is
ioda

The work done (in foot-pounds) in stretching the spring from its natural length to 0.7 feet beyond its natural length is 1.23 foot-pound

<h3>Data obtained from the question</h3>

From the question given above, the following data were obtained:

  • Force (F) = 3 pounds
  • Extension (e) = 0.6 feet
  • Work done (Wd) =?

<h3>How to determine the spring constant</h3>
  • Force (F) = 3 pounds
  • Extension (e) = 0.6 feet
  • Spring constant (K) =?

F = Ke

Divide both sides by e

K = F/ e

K = 3 / 0.6

K = 5 pound/foot

Thus, the spring constant of the spring is 5 pound/foot

<h3>How to determine the work done</h3>
  • Spring constant (K) = 5 pound/foot
  • Extention (e) = 0.7 feet
  • Work done (Wd) =?

Wd = ½Ke²

Wd = ½ × 5 × 0.7²

Wd = 2.5 × 0.49

Wd = 1.23 foot-pound

Therefore, the work done in stretching the spring 0.7 feet is 1.23 foot-pound

Learn more about spring constant:

brainly.com/question/9199238

#SPJ1

5 0
1 year ago
Which is shorter 96in or 12ft
sammy [17]
96 inches is shorter than 12 feet. This is because 12 feet in inches is 144 inches, which is greater than 96. 

Hope this helps! :D

~PutarPotato
5 0
3 years ago
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