If you have 1,478 squares, can you make a stair-like structure using all of the squares?

Answer:

Step-by-step explanation:

Given the following complex numbers, we are to expressed them in the form of a+bi where a is the real part and b is the imaginary part of the complex number.

1) (2-6i)+(4+2i)

open the parenthesis

= 2-6i+4+2i

collect like terms

= 2+4-6i+2i

= 6-4i

2)  (6+5i)(9-2i)

= 6(9)-6(2i)+9(5i)-5i(2i)

= 54-12i+45i-10i²

= 54+33i-10i²

In complex number i² = -1

= 54+33i-10(-1)

= 54+33i+10

= 54+10+33i

= 64+33i

3) For the complex number 2/(3-9i), we will rationalize by multiplying by the conjugate of the denominator i.e 3+9i

= 2/3-9i*3+9i/3+9i

=2(3+9i)/(3-9i)(3+9i)

= 6+18i/9-27i+27i-81i²

= 6+18i/9-81(-1)

= 6+18i/9+81

= 6+18i/90

= 6/90 + 18i/90

= 1/15+1/5 i

4) For (3 − 5i)(7 − 2i)

open the parenthesis

= 3(7)-3(2i)-7(5i)-5i(-2i)

= 21-6i-35i+10i²

= 21-6i-35i+10(-1)

= 21-41i-10

= 11-41i

  Simplified form of the given expressions will be,

1). 6 - 4i

2). 64 + 33i

3). [tex]\frac{1}{15}+\frac{1}{5}i[/tex]

4). [tex]\frac{31}{53}-\frac{31}{53}i[/tex]

1). In a complex number (a + bi),

    a = Real part of the complex number

   bi = Imaginary part

     Expression given in the question → (2 - 6i) + (4 + 2i)

Rule to solve the given expression,

"Add real part and imaginary part of two complex numbers separately"

(2 - 6i) + (4 + 2i) = (2 + 4) + (-6i + 2i)

                         = 6 + (-4i)

                         = 6 - 4i

  Therefore, simplified form of the given expression will be (6 - 4i).

2). Given expression → (6 + 5i)(9 - 2i)

Rule to solve the expression → i² = -1

(6 + 5i)(9 - 2i) = 6(9 - 2i) + 5i(9 - 2i)

                       = 54 - 12i + 45i - 10i²

                       = 54 - 12i + 45i + 10 [Since, i² = -1]

                       = (54 + 10) + (45i - 12i)

                       = 64 + 33i

     Therefore, simplified form of the given expression will be (64 + 33i).

3). Given expression → [tex]\frac{2}{3-9i}[/tex]

Multiply numerator and denominator with the conjugate of (3 - 9i) to convert the expression into (a + bi).

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

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

       [tex]=\frac{6+18i}{9-81(-1)}[/tex]

       [tex]=\frac{6+18i}{9+81}[/tex]

       [tex]=\frac{6+18i}{90}[/tex]

       [tex]=\frac{6(1+3i)}{90}[/tex]

       [tex]=\frac{1}{15}+\frac{1}{5}i[/tex]

    Therefore, simplified form of the given expression will be [tex]\frac{1}{15}+\frac{1}{5}i[/tex]

4). Given expression → [tex]\frac{(3-5i)}{(7-2i)}[/tex]

Multiply numerator and denominator with the conjugate of the denominator.

[tex]\frac{(3-5i)}{(7-2i)}=\frac{(3-5i)(7+2i)}{(7-2i)(7+2i)}[/tex]

         [tex]=\frac{3(7+2i)-5i(7+2i)}{7^2-(2i)^2}[/tex]

         [tex]=\frac{21+4i-35i-10i^2}{49-4(-1)}[/tex]

         [tex]=\frac{21-31i+10}{53}[/tex]

         [tex]=\frac{31-31i}{53}[/tex]

         [tex]=\frac{31}{53}-\frac{31}{53}i[/tex]

  Therefore, simplified form of the given expression will be [tex]\frac{31}{53}-\frac{31}{53}i[/tex].

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Answer:

n^2/4

Step-by-step explanation:

If n is the number, squared is n^2

Quotient if this number and four is

n^2/4

The quotient of a number squared and four will be n² / 4.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

The square of a number is the multiplication of that number with itself.

Let the number be n.

Then the square of the number n will be given as,

⇒ n²

The quotient of a number squared and four will be given as,

⇒ n² / 4

Thus, the quotient of a number squared and four will be n² / 4.

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Answer:

The circumference is pi times larger than the diameter of a circle.

Step-by-step explanation:

The formula of the circumference of a circle is

C = 2(pi)r = (pi)d

C = (pi)d

To find the ratio of the circumference to the diameter, divide both sides of the equation by d.

C/d = pi

The circumference is pi times larger than the diameter of a circle.

Negotiating in trade means you are coming to an agreement on an item's value option (A) is correct.

The goal of negotiation is to obtain an agreement on one or more contentious issues between two or more parties.

As we know,

On the other hand, trade negotiation is a procedure whereby countries come together to talk about the potential for trade with the aim of arriving at a trade agreement.

When you bargain in trade, you're settling on a price for a product.

Thus, negotiating in trade means you are coming to an agreement on an item's value option (A) is correct.

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Answer:

Step-by-step explanation:

2x + 5y = 7 ......... Equation 1

x = 2 - 4y .......... Equation 2

Substitute x that's equation 2 into equation 1 and solve for y

That's

2( 2 - 4y ) + 5y = 7

4 - 8y + 5y = 7

- 3y + 4 = 7

- 3y = 7 - 4

- 3y = 3

Divide both sides by - 3

y = - 1

Substitute the value of y into equation 1

That's

x = 2 - 4(-1)

x = 2 + 4

x = 6

Therefore the solutions are

Hope this helps you

Answer:

plz show the pic so I can understand

Answer:

  divide by 5: x = 13/5 = 2.6

Step-by-step explanation:

Make use of the properties of the multiplicative inverse and the multiplication identity element. Multiplying both sides of the equation by the multiplicative inverse of the coefficient of x makes the result be 1x on the left side.

  (1/5)(5x) = (1/5)(13)

  1x = 13/5

The multiplicative identity element (1) does not change the value of what it multiplies, so this simplifies to ...

  x = 13/5

_____

Effectively, we divide (both sides) by 5.

Answer:

A

Step-by-step explanation:

5 X 60 = $300

she only needs to sell 60 bracelets, but sell up to 100

60 ≤ (must sell 60) x (number of bracelets she sells) ≤ 100 (number of bracelets she can sell)

hope this helps! sorry for being a bit late!

Answer:

4 to the 5th power

Step-by-step explanation:

since 4 is being multiplied by itself 5 times, then 5 becomes the exponent :)

The exponential form of the expression is [tex]4^5[/tex].

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

4 x 4 x 4 x 4 x 4

There are five 4's.

So,

= [tex]4^5[/tex]

Thus,

The exponential form is [tex]4^5[/tex].

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that is correct because 37/ one and 37×1

this is the correct answer

Answer:

c

Step-by-step explanation:

choice A means

[tex]11 - 2 {m}^{3} [/tex]

choice B means

[tex]2m - 11[/tex]

choice C means which is the answer

[tex] {2m}^{3} - 11[/tex]

choice D means

[tex] {(2m)}^{3} - 11[/tex]

hope it helps ❤❤❤

For any question comment me

Answer:

i cant see it

Step-by-step explanation:

umm

Answer:

970 cm

Step-by-step explanation:

Given that:

Size of brick :

25cm × 16cm × 10cm

Number of bricks = 4700

Dimension of wall = 20 m long × 20 cm wide

Let the height = h

Hence, dimension of wall (length and height)

2000 cm × h

Dimension of window = 2m × 1.5m = 200cm × 150cm

Number of windows = 2

Total area covered by windows = 2 * (L * B)

= 2(200 * 150) = 60,000cm

Brick = (25 * 16) * 4700 = 1, 880, 000 cm ( length and height)

Wall = 2000 * height - 60,000 = 1880000

2000height - 60,000 = 1880000

2000height = 1880000 + 60,000

2000height = 1940000

Height = 1940000 / 2000

Height of wall = 970 cm

Ansewern

I think you forgot the stament and please add it so i can helpyou out with it.

Step-by-step explanation:

Answer:

im sorry

Step-by-step explanation:

Answer:

____________________

68% of 56000 is 38080.

I guess that'd be the amount of people that recovered.

____________________

Answer:

8ft and 16ft

Step-by-step explanation:

you guess and check till you reach the answer

1+23         5+19

2+22        6+18

3+21         7+17

4+20        8+16

Answer:

LM = 28 units

Step-by-step explanation:

Length of segment KL = (4x + 7) units

Length of segment LM = (5x - 12) units

Length of LM = 67 units

Since length of KM = length of KL + length of LM

By substituting the given values in the expression,

67 = (4x + 7) + (5x - 12)

67 = (4x + 5x) + (7 - 12)

67 = 9x - 5

9x = 67 + 5

x = [tex]\frac{72}{9}[/tex]

x = 8

Therefore,

LM = (5x - 12)

     = (5×8) - 12

     = 40 - 12

     = 28

Length of segment KM is 28 units.

Answer:

5x280=1400

Step-by-step explanation:

$1400

if he works on the weekends then add 580

s0 $1980

Answer:

3.5

Step-by-step explanation:

these are being decided by 4 everytime, so you can just continue the sequence. 3584,896,224,56,14,3.5

Answer:

[tex]m=\frac{n}{3} -7[/tex]

Answer:

22/3

Step-by-step explanation:

First, I multiplied 7 and 3 because 7 is the whole number and 3 is the denominator of the fraction.

7*3=21

Then, I added 21 to 1 because 1 is the numerator in the fraction.

21+1=22

Finally, I made it 22/3 because the denominator of the fraction is 3.

So, your final answer is 22/3.

[tex]$7\frac{1}{3}[/tex] as a improper fraction can be written as 22/3.

Given is to write 7 1/3 as a improper fraction.

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. We can write that for a fraction {x/y} to be improper, the following conditions should be fulfilled -

{x} > {y}

or

{x} ≥ {y}

We can write 7 1/3 as a improper fraction as -

[tex]$7\frac{1}{3}[/tex] = [tex](3\times7+1)/3[/tex] = [tex]$\frac{22}{3}[/tex]

Therefore, [tex]$7\frac{1}{3}[/tex] as a improper fraction can be written as [tex]$\frac{22}{3}[/tex].

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Answer:

55 mph

Because he drives to new york to boston in 4 hours and its 220 miles so 220 is the miles and you divide by the hours so 4 hours so he drove 55 mph

Answer:

Multiplying integers is very similar to multiplying whole numbers. ... A positive number times a positive number equals a positive number. A positive number times a negative number equals a negative number. A negative number times a negative number equals a positive number.

Answer:

integers are whole numbers

Answer:

D. 2.7

Step-by-step explanation:

Given

[tex]Mean = 8.0[/tex]

[tex]n = 20[/tex]

[tex]Range = 2.5\ to\ 12.0[/tex]

Required

Estimate the standard deviation

Since, the given data has incomplete parameters, we can apply the range rule to estimate the standard deviation;

This is done as follows;

[tex]S.D = \frac{1}{4}(Max - Min)[/tex]

In this case:

[tex]Max = 12.0[/tex]

[tex]Min = 2.5[/tex]

So:

[tex]S.D = \frac{1}{4}(Max - Min)[/tex]

[tex]S.D = \frac{1}{4}(12.0 - 2.5)[/tex]

[tex]S.D = \frac{1}{4}(9.5)[/tex]

[tex]S.D = 2.375[/tex]

From the list of given option, the closest to 2.375 is 2.7;

Hence, the best estimate is 2.7

The correct option is D. 2.7

Given that,

The standard deviation should be

[tex]= \frac{1}{4} (12 - 2.5)\\\\ = \frac{1}{4} (9.5)[/tex]

= 2.375

= 2.7

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Answer:

Line UM.

Step-by-step explanation: you can name a line by naming at least two points on it.

Line l can be called line UM, line LM, and line UL because line l is contained in plane S.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

m is the ratio of the line,

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases.

It is given that:

A plane S contains a line l.

It is possible to give a name for line l in different ways.

The line l can be called:

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.

Thus, line l can be called line UM, line LM, and line UL because line l is contained in plane S.

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Answer:

(2,3) and (7,10)

Step-by-step explanation:

Use the slope 5/7 to get to a new point by moving up 5 units and moving to the right 7 units.

If the coordinate point is (x, y) then the coordinate of the other point will be (x + 5, y + 7).

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

The slope is the ratio of the rise or fall and run.

The slope is 5/7. The rise is 5 and the run is 7.

If the coordinate point is (x, y) then the coordinate of the other point will be (x + 5, y + 7).

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Steps to solve:

(3x - 10) = 149

~Add 10 to both sides

3x = 159

~Divide 3 to both sides

x = 53

Best of Luck!

Answer:

1080 seconds

Step-by-step explanation:

We need to multiply the 0.3 hours by 3600 to convert it to seconds.

0.3*3600=1080

Answer:

1200 sec

Step-by-step explanation:

.30 hours is equal to 20 minutes

60 sec in 1 min

60x20

6x2=12

1200