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2 years ago

Solve by completing the square x^2-6x-4=0

Mathematics

1 answer:

Vesna [10]2 years ago

6 0

Answer:

x = 3 ± $\sqrt{13}$

Step-by-step explanation:

x² - 6x - 4 = 0 ( add 4 to both sides )

x² - 6x = 4

To complete the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 3)x + 9 = 4 + 9

(x - 3)² = 13 ( take square root of both sides )

x - 3 = ± $\sqrt{13}$ ( add 3 to both sides )

x = 3 ± $\sqrt{13}$

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In how many ways can a committee of 3 men and 4 boys be chosen from 7 men and 6 boys so as not to include the youngest boy if th

Ludmilka [50]

Answer:

There are 75 ways to form the committee.

Step-by-step explanation:

The order in which the people are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

Considering the eldest has to be there, 2 men from a set of 6 and 4 boys from a set of 5(excluding the youngest), so:

$T = C_{6,2}C_{5,4} = \frac{6!}{2!4!} \times \frac{5!}{1!4!} = 3*5*5 = 75$

There are 75 ways to form the committee.

6 0

2 years ago

Timed math quiz 6 <br> Please help

strojnjashka [21]

Answer:

6-2/-5-0

Step-by-step explanation:

the formula to calculate the slope is

y2-y1/x2-x1

where :point1(x1,y1)

and point2(x2,y2)

6 0

3 years ago

Please help, seriously confused

Rufina [12.5K]

Original height = original width = x mm

1. She made an enlarged copy...
height = 2x
width = 2x

2. She cut off a rectangle...
height = 2x
width = $\frac{2}{3} *2x= \frac{4}{3}x$

3.She doubled the width...
height = 2x
width = $2*\frac{4}{3}x = \frac{8}{3}x$

height * width = area

$2x * \frac{8}{3}x=139 \ 968 \\ \\ \frac{16}{3}x^2= 139 \ 968 \\\\ x^2=139 \ 968: \frac{16}{3}=139 \ 968 * \frac{3}{16}= 8 \ 748*3 = 26 \ 244 \\ \\ x= \sqrt{26 \ 244} = 162 \ mm$

Original height was 162 mm

6 0

3 years ago

The perimeter of a rectangle is 46 millimeters. The length of the rectangle can be represented by (3x+3), and its width can be r

Tamiku [17]

Answer:

The dimension of this rectangle = 2mm by 21mm

Where 2 mm = Width of the rectangle

21 mm = Length of the rectangle.

Step-by-step explanation:

The formula for the perimeter of a rectangle = 2(L + W)

= 2L + 2W

The perimeter = 46 mm

L = 3x + 3

W = x - 4

P = 2L + 2W

46mm = 2(3x + 3) + 2(x - 4)

46 = 6x + 6 + 2x - 8

Collect like terms

46 +8 -6 = 6x + 2x

48 = 8x

x = 48/8

x = 6

Since the Length = 3x + 3

= 3(6) + 3

= 18 + 3

= 21mm

Since the Width = x - 4

= 6 - 4

= 2mm

Therefore, the dimension of this rectangle = 2mm by 21mm

Where 2 mm = Width of the rectangle

21 mm = Length of the rectangle.

8 0

3 years ago

9 Acolle<br>mayurae<br>Kopo<br>ro

Lelechka [254]

Answer:

huh

Step-by-step explanation:

5 0

3 years ago