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love history [14]

3 years ago

6

What is the value of (-1/2)-4?

1 answer:

kykrilka [37]3 years ago

4 0

The answer would be A. -16

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2x^3-x^2-3x=210<br> the answer is 5 but I want to know why.

mel-nik [20]

Answer:

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

Step-by-step explanation:

1) Move all terms to one side.

$2x^{3} -x^{2} -3x-210=0$

2) Factor $2{x}^{3}-{x}^{2}-3x-210$ using Polynomial Division.

1 - Factor the following.

$2x^{3} -x^{2} -3x-210$

2 - First, find all factors of the constant term 210.

$1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210$

3) Try each factor above using the Remainder Theorem.

Substitute 1 into x. Since the result is not 0, x-1 is not a factor..

$2*1^{3} -1^{2} -3*1-210=-212$

Substitute -1 into x. Since the result is not 0, x+1 is not a factor..

$2(-1)^{3} -(-1)^{2} -3*-1-210=-210$

Substitute 2 into x. Since the result is not 0, x-2 is not a factor..

$2*2^{3} -2^{2} -3*2-210=-204$

Substitute -2 into x. Since the result is not 0, x+2 is not a factor..

$2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224$

Substitute 3 into x. Since the result is not 0, x-3 is not a factor..

$2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174$

Substitute -3 into x. Since the result is not 0, x+3 is not a factor..

$2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264$

Substitute 5 into x. Since the result is 0, x-5 is a factor..

$2\times {5}^{3}-{5}^{2}-3\times 5-210 =0$

------------------------------------------------------------------------------------------

⇒ $x-5$

4) Polynomial Division: Divide $2{x}^{3}-{x}^{2}-3x-210$ by $x-5$ .

$2x^{2}$ $9x$ $42$

-------------------------------------------------------------------------

$x-5$ | $2x^{3}$ $-x^{2}$ $-3x$ $-210$

$2x^{3}$ $-10x^{2}$

-----------------------------------------------------------------------

$9x^{2}$ $-3x$ $-210$

--------------------------------------------------------------------------

$42x$ $-210$

$42x$ $-210$

-------------------------------------------------------------------------

5) Rewrite the expression using the above.

$2x^2+9x+42$

$(2x^2+9x+42)(x-5)=0$

3) Solve for $x.$

$x=5$

4) Use the Quadratic Formula.

1 - In general, given $a{x}^{2}+bx+c=0$ , there exists two solutions where:

$x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}$

2 - In this case, $a=2,b=9$ and $c = 42.$

$x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}$

3 - Simplify.

$x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

5) Collect all solutions from the previous steps.

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

4 0

3 years ago

Read 2 more answers

Five times the sum of a number and 6 is 48

MissTica

5(n+6)=48

5n+30=48

5n=18

n=18/5

4 0

3 years ago

Find the value of x in the equation x⁄ 4 + x⁄14 + x⁄17 = 71

Morgarella [4.7K]

Hello from MrBillDoesMath!

Answer:

33769/181

Discussion:

Each term contains "x" so factoring it out gives

x( 1/4 + 1/14 + 1/17) = 71 (*)

Use common factor (17*14*4 = 952) as the denominator to combine terms:

1/4 = (17*14)/ 952 = 238/952

1/14 = (17*4)/952 = 68/952

1/17 = (14*4)/952 = 56/952

so 1/4 + 1/14 + 1/17 = (238 + 68 + 56)/ 952 = 362/952 = 181/476

Substituting in (*) gives

x ( 181/476) = 71 => multiply both sides by 476/181

x = (71 * 476)/181 => 71* 476 =33769

x = 33769/181

Thank you,

MrB

4 0

3 years ago

The table represents a linear function.

Alona [7]

Answer: -6

See attached picture

6 0

3 years ago

Figure ABCD is a parallelogram. What is the value of n?

Zigmanuir [339]

Answer

Find out the what is the value of n.

To prove

By using the parallelogram property .

In parallelogram opposite angels are congruent .

As shown in the figure .

∠B = ∠ D

As given

∠B = (2n + 32)°

∠D = (4n - 2)°

(2n + 32) = (4n - 2)

solving the above

4n -2n = 32 +2

2n = 34

$n = \frac{34}{2}$

n = 17

Therefore the value of n is 17 .

5 0

3 years ago

Read 2 more answers