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2 years ago

Rewrite the equation by completing the square. 4 x^{2} +20x +25 =0

Mathematics

2 answers:

Ede4ka [16]2 years ago

8 0

Answer:

(x+5/2)^2 = 0

Step-by-step explanation:

4 x^{2} +20x +25 =0

Divide by 4

4/4 x^{2} +20/4x +25/4 =0

x^2 +5x +25/4 =0

Subtract 25/4 from each side

x^2 +5x +25/4 -25/4 =-25/4

x^2 +5x =-25/4

Take the coefficent of x

Divide by 2

5/2

Square it

25/4

Add it to each side

x^2 +5x +25/4 =-25/4+25/4

(x+5/2)^2 = 0

Take the square root of each side

x+5/2 = 0

x = -5/2

sukhopar [10]2 years ago

6 0

Answer:

(2x + 5)² = 0

Step-by-step explanation:

4x² + 20x + 25 = 0

4x² + 10x + 10x + 25 = 0

2x(2x + 5) + 5(2x + 5) = 0

(2x + 5)(2x + 5) = 0

(2x + 5)² = 0

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Eighteen telephones have just been received at an authorized service center. Six of these telephones are cellular, six are cordl

Karo-lina-s [1.5K]

Full Question

Eighteen telephones have just been received at an authorized service center. Six of these telephones are cellular, six are cordless, and the other six are corded phones. Suppose that these components are randomly allocated the numbers 1, 2, . . . , 18 to establish the order in which they will be serviced.

What is the probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced?

What is the probability that two phones of each type are among the first six serviced?

Answer:

a. 0.149

b. 0.182

Step-by-step explanation:

Given

Number of telephone= 18

Number of cellular= 6

Number of cordless = 6

Number of corded = 6

There are 18C6 ways of choosing 6 phones

18C6 = 18564

From the Question, there are 3 types of telephone (cordless, Corded and cellular)

There are 3C2 ways of choosing 2 out of 3 types of television

3C2 = 3

There are 12C6 ways of choosing last 6 phones from just 2 types (2 types = 6 + 6 = 12)

12C6 = 924

There are 2 * 6C6 * 6C0 ways of choosing none from any of these two types of phones

2 * 6C6 * 6C0 = 2 * 1 * 1 = 2.

So, the probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced is

3 * (924 - 2) / 18564

= 3 * 922/18564

= 2766/18564

= 0.149

There are 6C2 * 6C2 * 6C2 ways of choosing 2 cellular, 2 cordless, 2 corded phones

= (6C2)³

= 3375

So, the probability that two phones of each type are among the first six serviced is

= 3375/18564

= 0.182

5 0

2 years ago

What is the relationship between the ratios? 48 72 and 6 9 Drag and drop to complete the statement. The ratios are . proportiona

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You mean 6 9 or 69 ....

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3 years ago

Read 2 more answers

F(x) = -x - 3 Find f(-4) f(-4) = -(-4) -3

skelet666 [1.2K]

Answer:

$\boxed{ \bold{ \boxed{ \sf{f( - 4) = 1}}}}$

Step-by-step explanation:

Given, f ( x ) = - x - 3

Let's find the value of f ( - 4 )

$\sf{f( - 4) = - ( - 4) - 3}$

We know that , $( - ) \times ( - ) = ( + )$

⇒ $\sf{ 4 - 3}$

Subtract 3 from 4

⇒ $\sf{1}$

Hope I helped!

Best regards!!

5 0

2 years ago

Please help me with this question

Elden [556K]

Answer:

Step-by-step explanation:

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R is 21.2 km due South-East of S

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4 0

3 years ago

Solve for x in the equation.

labwork [276]

Answer:

The solution is $\displaystyle x=1\pm \sqrt{47}$ . Fourth option

Explanation:

Solve for x:

$2x^2+3x-7=x^2+5x+39$

Move all the terms from the right to the left side of the equation, a zero in the right side:

$2x^2+3x-7-x^2-5x-39=0$

Join all like terms:

$x^2-2x-46=0$

The general form of the quadratic equation is:

$ax^2+bx+c=0$

Solve the quadratic equation by using the formula:

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

In our equation: a=1, b=-2, c=-46

Substituting into the formula:

$\displaystyle x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(-46)}}{2(1)}$

$\displaystyle x=\frac{2\pm \sqrt{4+184}}{2}$

$\displaystyle x=\frac{2\pm \sqrt{188}}{2}$

Since 188=4*47

$\displaystyle x=\frac{2\pm \sqrt{4*47}}{2}$

Take the square root of 4:

$\displaystyle x=\frac{2\pm 2\sqrt{47}}{2}$

Divide by 2:

$\displaystyle x=1\pm \sqrt{47}$

First option: Incorrect. The answer does not match

Second option: Incorrect. The answer does not match

Third option: Incorrect. The answer does not match

Fourth option: Correct. The answer matches exactly this option

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2 years ago