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Answer: x² + 2xy + y² = 9

x² + 2xy + y² = (x + y)²

with x = 2 + 3i and y = [tex]\frac{3+i}{i}[/tex], we have:

[tex](x + y)^{2}=(2+3i+\frac{3+i}{i})^{2}\\\\=(\frac{2i+3i^{2}+3+i }{i})^{2}\\\\=(\frac{3i-3+3}{i})^{2} \\\\=(\frac{3i}{i})^{2}\\\\=3^{2}=9[/tex]

Step-by-step explanation:

Answer:

The standard deviation = 1.9

Step-by-step explanation:

standard deviation, ρ = sqrt ( [tex]\frac{sum(x_{i} - u)^{2} }{N}[/tex])

Where u is the mean of the data, [tex]x_{i}[/tex] each given value, and N is the number of data given.

Mean, u = [tex]\frac{6+5+2+5+8}{5}[/tex]

              = 5.2

So that;

[tex](6-5.2)^{2}[/tex]  = [tex](0.8)^{2}[/tex] = 0.64

[tex](5-5.2)^{2}[/tex] = [tex](-0.2)^{2}[/tex] = 0.04

[tex](2-5.2)^{2}[/tex]  = [tex](-3.2)^{2}[/tex] = 10.24

[tex](5-5.2)^{2}[/tex] = [tex](-0.2)^{2}[/tex] = 0.04

[tex](8-5.2)^{2}[/tex] = [tex](2.8)^{2}[/tex] = 7.84

Sum = 18.8

So that;

[tex]\sqrt{\frac{18.8}{5} }[/tex]  = [tex]\sqrt{3.76}[/tex]

          = 1.9391

          = 1.9

The standard deviation of the given data is 1.9

Answer:

12 feets below sea level

Step-by-step explanation:

Initial height = 25 feets above sea levwl

Total descent = 37 feets

Distance traveled below sea level = 37 feets - 25 feets = 12 feets

Hence, Sarah traveled 12 feets below sea level

Answer:

less than 1yd²:

2/3x3/5= 2/5

1/4x5/3= 5/12

1/2x9/10= 9/20

equal to 1yd²

1/4x4/1= 1

4/3x6/8= 1

more than 1yd²

2/3x5/3= 1.1

Step-by-step explanation:

2/3x3/5= 2/5

1/4x4/1= 1

2/3x5/3= 1.1

1/4x5/3= 5/12

1/2x9/10= 9/20

4/3x6/8= 1

Answer:

2..........3

--- x ---

3............5

Step-by-step explanation:

goes to area less than 1square yard

Answer:

slope is 6/0 which is undefined

Step-by-step explanation:

Answer:

Slope is -2

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

The Distributive property uses the number outside the parenthesis and combines it (using multiplication) with the ones inside.

So, the number 7 will be multiplied with the numbers inside the parenthesis.

7(11-7)

7 × 11 = 77

7 × -7 = -49 (It will just be the same way you multiply but with a added negative sign.)

77-49=

28

Answer:

Step-by-step explanation:

(-2 + 3)/(2 + 1) = 1/3 is the slope

Answer:

x>−7

Explanation:

Let's solve your inequality step-by-step.

−4x<28

Step 1: Divide both sides by -4.

−4x/−4 < 28/−4

x>−7

Answer: x>−7

Answer:

12

Step-by-step explanation:

6(3+5)/4 add number inside parentheses

6(8)/4 multiply 6 and 8

48/4 divide

12

Hope this helped you!

Answer:

If Y represents the number of green balls then it can have values from 0- 5

that is it can have all the value  0,1,2,3,4 and 5.

The probability of getting both balss green without replacement is 0.27778

Step-by-step explanation:

If the balls are not replaced then this is the dependent event .

The probability of getting the first ball is given be = 5/9

where 5 is the number of green balls and 9 is the total number of balls.

The probability of getting the second ball green given that first is also green is  = 5/9* 4/8= 20/72= 0.2778

If Y represents the number of green balls then it can have values from 0- 5

that is it can have all the value  0,1,2,3,4 and 5.

0 means there can be no green balls or white balls.

1 means there can be one green ball.

2 means there can be 2 green balls and so on.

In this exercise we have to use the knowledge of probability to calculate the chance of an event to occur, so you have to:

the chance of the event is 0.2778%

So organizing the information given in the statement is:

So with this information we can write that:

[tex]5/9* 4/8= 20/72= 0.2778[/tex]

See more about probability at brainly.com/question/795909

Answer:

Monday:

Cups of Sugar: 3

Tablespoon of Butter: 30

No. of Bananas: 75

Wednesday

Cups of Sugar: 1.12

Tablespoons of Butter: 11.2

No. of Bananas: 28

Answer:

-3/7

Step-by-step explanation:

find two lattice points

the ones I found are (-3, 3) and (4, 0)

use the slope formula

(0-3)/(4-(-3)) = -3/7

Answer:

x=10

Step-by-step explanation:

7x+70=16x-20

70=9x-20

9x=90

x=10

Answer:

0.9222222222222222/1

Step-by-step explanation:

Answer:

$105.45

Step-by-step explanation:

$7.40 x 14.25 = $105.45

She earns $105.45 after working for 14.25 hours.

Answer:

Measurements of this years garden are 10 meters and 6 metres.

Step-by-step explanation:

Width of a rectangular garden = 3 meters

Area of a rectangular garden = 10 square meters

Also,

Area of a rectangular garden = length × breadth

10 = length × 3

Length = [tex]\frac{10}{3}[/tex] meters

Mr. Petersons wants to make the garden three times as long and two times as wide.

New length = 3 (length) = [tex]3(\frac{10}{3} )=10[/tex] meters

New breadth = 2(width) = 2(3) = 6 meters.

Therefore,

Measurements of this years garden are 10 meters and 6 metres.

Answer:

8377

Step-by-step explanation:

Growth rate is exponential, so it is determined by the formula (1+growth rate)^n where n is years

1.035^15 = 1.675...

multiply by 5000, you get 8376.744....

Answer:

10=1x+25

slope=1

y-int-25

Thats all i know so far i will keep working on it

Step-by-step explanation:

Answer:

0.5 pounds per container.

Step-by-step explanation:

just divide 3 pound by 6 containers so it would be 3/6 which is equal to 1/2 which is the same as 0.5

There each container holds a number of pounds of flour which would be  0.5 pounds.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

If three pounds of flour are divided into 6 containers so that each container holds the same number of pounds of flour, we can find out how many pounds of flour each container holds by dividing the total amount of flour by the number of containers.

We can use the following equation to find out how many pounds of flour each container holds:

pounds of flour per container = total pounds of flour / number of containers

So, using this equation:

pounds of flour per container = 3 / 6

Apply the division operation, and we get

pounds of flour per container = 0.5

Each container holds 0.5 pounds of flour.

To learn more about the division operation click here :

brainly.com/question/25870256

#SPJ2

Answer:

(3, 4)

Step-by-step explanation:

Answer:

7/6

Step-by-step explanation:

U just need to multiply 7 x 1/6 = 7/6 = 1.16

Answer:

About 51.6 feet

Step-by-step explanation:

50^2+13^2

Square root of 2669 is 51.66236541

Step-by-step explanation:

11/4 then reduce

2 3/4

because 11/4 is just like saying 11 divided by 4

Answer:

2.75

Step-by-step explanation:

Make a division plane

Answer:

first: 8 in^2

second: 77 yd^2

third: 225 in^2   (assuming that the larger triangle base =50 in (25 x 2)

Step-by-step explanation:

area = 1/2 x base x height

first:

1/2 x 4 x 4 = 8 in^2

second:

1/2 x 14 x 11 = 77 yd^2

third:

(1/2 x 50 x 18) - ( 1/2 x 18 x 25) = 450 - 225 = 225 in^2

Answer:

d = [tex]\frac{11}{12}[/tex]

Step-by-step explanation:

1) To solve for d, isolate it in the equation. So, to get rid of the [tex]-\frac{1}{2}[/tex] with the d, add [tex]\frac{1}{2}[/tex] to both sides.

[tex]d-\frac{1}{2} = \frac{5}{12} \\d - \frac{1}{2} +\frac{1}{2} = \frac{5}{12} + \frac{6}{12} \\d = \frac{11}{12}[/tex]

Thus, d = [tex]\frac{11}{12}[/tex].

Answer:

(2x+3)(x+1)

Step-by-step explanation:

6x² + 2x + 9x +3

(6x² + 2x) + (9x +3)

2x (x+1) + 3 (x+1)

(2x+3)(x+1)

Answer:

(3x+1) ( 2x+3)

Step-by-step explanation:

6x² + 2x + 9x +3

Make the groups

6x² + 2x     +   9x +3

Factor 2x out of the first group  and 3 out of the second group

2x( 3x+1)   + 3(3 x+1)

Now factor out the common term inside the parentheses

(3x+1) ( 2x+3)

Answer: A We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

Step-by-step explanation:

Answer:

Blank 1: (-7,0)

Blank 2: (-1,0)

Step-by-step explanation:

Plug x=0 into the equation and solve the resulting equation y=7 for y

Plug y=0 into the equation and solve the resulting equation 0=(x+1)(x+7) for x