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A complex number is a part of a number system that includes a real unit and an imaginary unit. All the statements are true except C and E.

A complex number is a part of a number system that includes the real numbers as well as a particular element labelled i, sometimes known as the imaginary unit, and which obeys the equation i² = 1.

As it is given that x=(a+bi), y=(c+di), and z=(f+gi), therefore, we need to plug in the values to check which all are true.

A.) x+y=y+x

[tex]x+y=y+x\\a+bi+c+di=c+di+a+bi[/tex]

As the two sides of the equation are equal, the equation is true.

B.) (x × y) × z = x × (y × z)

[tex](x \times y) \times z = x \times (y \times z)\\\\\ [ (a+bi) \times (c+di) ]\times (f+gi) = (a+bi) \times [(c+di) \times (f+gi)]\\\\(ac+adi+bci-bd) \times (f+gi)= (a+bi) \times (cf+cgi+fdi-dg)[/tex]

[tex](ac+adi+bci-bd) \times (f+gi)= (a+bi) \times (cf+cgi+fdi-dg)\\\\\\acf+adfi+bcfi-bdf+acgi-adg-bcg-bdgi = acf+acgi+afdi-adg + bcfi-bcg-bfd-bdgi[/tex]

As the two sides of the equation are equal, the equation is true.

C.) x−y=y−x

[tex]x-y=y-x\\\\(a+bi)-(c+di)=(c+di)-(a+bi)\\\\a+bi-c-di=c+di-a-bi[/tex]

As the two sides of the equation are not equal, the equation is not true.

D.) (x+y)+z=x+(y+z)

[tex](x+y)+z=x+(y+z)\\\\(a+bi+c+di)+f+gi = a+bi+(c+di+f+gi)\\\\a+bi+c+di+f+gi = a+bi+c+di+f+gi[/tex]

As the two sides of the equation are equal, the equation is true.

E.) (x−y)−z=x−(y−z)

[tex](x-y)-z=x-(y-z)\\\\(a+bi-c-di)-f-gi = a+bi-(c+di-f-gi)\\\\a+bi-c-di-f-gi =a+bi-c-di+f+gi)[/tex]

As the two sides of the equation are not equal, the equation is not true.

Hence, all the statements are true except C and E.

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Answer:

1000

Step-by-step explanation:

High school only - 1019 and round to the nearest thousand

Answer:

D. -7, 0, 6

Step-by-step explanation:

[tex]x^3+x^2-42x=0[/tex]

[tex]x(x^2+x-42)=0[/tex]

[tex]x(x^2-6x+7x-42)=0[/tex]

[tex]x(x-6)(x+7)=0[/tex]

ZEROS:

x = 0

x = 6

x = -7

Hope this helps!

Answer:

4370*10^2

437*10^3

43.7*10^4

Hope this helps :)

Answers:

This can be found by using the combinations and permutations formulas.

Combinations being the C equation and Permutations being the P equation.

21: [tex]C_{6}(21) = \left[\begin{array}{ccc}21\\6\end{array}\right] =\frac{21!}{6!(21-6)!}=\frac{21*20*19*18*17*16}{6*5*4*3*2*1} = 54264[/tex]

answer: 54264

22: [tex]C_{2}(n) = \left[\begin{array}{ccc}n\\2\end{array}\right] =\frac{n!}{2!(n-2)!}= answer[/tex]

answers:

  Art: 15

  Writing: 21

  Technology:  28

23: [tex]P(n,r)=\frac{6!}{(6-6)!}=720[/tex]

answer: 720

Explanation:

A permutation is an act of arranging the objects or numbers in order. Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter.

Step-by-step explanation:

Y is directly proportional to X" can be rewritten as a mathematical expression of the form Y = KX

"K" is the constant of proportionality and must be determined from the initial information.

If Y = 45 when X=140 means 45 = 140K

K = 45/140 = 0.32

Now that we know the value of K, we can use it to calculate the value of Y when X=70

Y = (0.32)(70) = 22.4

Answer:

Step-by-step explanation:

a) x<5 and x>−1

b)x<-1,x>5

c)x=5,x=-1

For the equation:  

y=-|x-2|+3 values of x for below cases are :

a) -|x-2|+3>0  , x ∈ (-1 , 5)

b) -|x-2|+3<0  ,   x ∈ R - [-1 , 5]  or x  ∈ (-∞ , - 1) U ( 5 , ∞)

c)-|x-2|+3=0    ,     x  ∈ {-1 , 5}

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Graph of the equation:  

⇒ y = -|x-2| + 3

To Find: Values of x in below cases:

a) -|x-2|+3>0

b) -|x-2|+3<0

c)-|x-2|+3=0

Solution:

a) -|x-2|+3>0

y=-|x-2|+3

⇒  y > 0

Hence, From the graph y > 0 when x ∈ (-1 , 5)

without using graph :

- |x - 2| + 3 > 0

3 > | x - 2|

| x - 2 | < 3

Case 1 : x - 2 > 0

x - 2 < 3

x < 5

Case2 : x - 2 < 0

x - 2 > - 3

x > - 1

b) -|x-2|+3<0

y=-|x-2|+3

 y < 0

From the graph y > 0 when x < - 1 or x > 5

x ∈ R - [-1 , 5]

or, x  ∈ (-∞ , - 1) U ( 5 , ∞)

without using graph :

-|x-2|+3<0

3 < | x - 2|

| x - 2 | > 3

case 1 : x - 2 > 0

x - 2 > 3

x > 5

case 2 : x - 2 < 0

x - 2 < - 3

x < - 1

a) -|x-2|+3=0

y=-|x-2|+3

y = 0

From the graph y = 0 when x = -1 and 5

x  ∈ {-1 , 5}

without using graph :

-|x-2|+3=0

3 = | x - 2|

| x - 2 | =  3

case 1 : x - 2 = 3

x = 5

case 2 : x - 2 = - 3

x =  - 1

Thus, For the equation:  y=-|x-2|+3 values of x for below cases are :

a) -|x-2|+3>0  , x ∈ (-1 , 5)

b) -|x-2|+3<0  ,   x ∈ R - [-1 , 5]  or x  ∈ (-∞ , - 1) U ( 5 , ∞)

c)-|x-2|+3=0    ,     x  ∈ {-1 , 5}

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Answer:

1,637.984

hope this helps

[tex]4\sqrt 3 - 7 \sqrt 3\\\\=(4-7) \sqrt 3\\\\=-3\sqrt 3[/tex]

Answer:

in the beginning bill have 8$

Step-by-step explanation:

8$

Answer:

w=√200 (or 14.14)

y=20

yea pretty simple its just the Pythagorean theorem and the fact that a triangle with equal base angles is isosceles triangle

Correlation coeffiencients is used to determine the relationships between data, Correlation coefficients can test two or more variable(s) at a time

This is a linear correlation between sets of data. This coefficient can only be between -1 and 1.

Positive values show a positive correlation while a negative value shows negative correlation.  A correlation coefficient of zero shows no relationship between variables.

Based on the explanation, we can conclude that Correlation coefficients can test two or more variable(s) at a time

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Answer:

-9²

81¹

They both are equal to 81.

Answer:

o

Step-by-step explanation:

because 6x is B and 2 is C so that means A 0

Answer:

A = 59 in²

Step-by-step explanation:

the area (A) of the shaded region is calculated as

A = area of outer triangle - area of inner triangle

  = [tex]\frac{1}{2}[/tex] bh - [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

  = [tex]\frac{1}{2}[/tex] × 13 × 14 - [tex]\frac{1}{2}[/tex] × 8 × 8

  = 91 - 32

  = 59 in²

Answer:

Native vegetable varieties are being organically cultivated by local farmers for hundreds of years. It is always recommended to regularly consume native vegetables where you belong to. Hybrids on the other hand are superior varieties of same vegetable species artificially crossed & developed by humans.

Step-by-step explanation:

Using proportions, it is found that each person consumes 3.57 times as many rice in Brazil and they do in the United States.

A proportion is a fraction of a total amount.

In this problem, we have that:

Hence, the rate between the consumption in Brazil and in the United States is given by:

[tex]r = \frac{5 \times 10^4}{1.4 \times 10^4} = 3.57[/tex]

Each person consumes 3.57 times as many rice in Brazil and they do in the United States.

More can be learned about proportions at https://brainly.com/question/24372153

Answer: 1/2

Step-by-step explanation:

I took the ixl and I put 1/3 but it was actually 1/2

The fraction of books which had 200 or fewer pages is given by A = 1/2

A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary.

A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.

It is used when showing the distribution of data points across a selected measure and if the box in a box plot is stretched in one direction or the other, then the data is skewed in that direction.

Given data ,

Isabelle kept track of the number of pages in each book she read last summer

Now , let the box plot be represented as A

Now , the first and third quartile along with the median is given below ;

So , the fraction of books which had 200 or fewer books is given by A = 1/2

Hence , the box plot is solved and the fraction is A = 1/2

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x = 7

hope it helps...!!!

Answer:

the region occupied in a plane is called area

Answer:

n(A) = 5 and n(B) = 9

Step-by-step explanation:

It should be 5 in A and 9 in B

Answer:

x=2

Step-by-step explanation:

1) -13 on each side (7x=14)

2) Divide by 7 on each side (x=2)

3) x=2

Answer:

Your Answer is 11 inches by 2 inches

Step-by-step explanation:

Area of Rectangle: Area = Length * Width

Given information:

Put that into the Formula.

Area = Length * Width

22 in^2 = (2x - 1) * (x - 4)

Solve.

22 in^2 = (2x - 1) * (x - 4)

[tex]22 = (2x^2 - 9x + 4)\\2x^2 - 9x - 18 = 0[/tex]

Factor it.

(2x^2 - 9x - 18) = 0

(2x + 3)(x-6) = 0

[tex]x=-\frac{3}{2} ,6[/tex]

Plug that into the Length and Width to find the actually Length and Width.

Length:

[tex]2x - 1\\2*-\frac{3}{2}-1\\ -3-1\\-4\\[/tex]

Width:

[tex]x - 4\\-\frac{3}{2}-4\\ -\frac{11}{2}[/tex]

Area = Length * Width

Area = - 4* -11/2

Area = 22

Length:

[tex]2x - 1\\2*6-1\\ 12-1\\11\\[/tex]

Width:

[tex]x- 4\\6-4\\ 2[/tex]

Area = Length * Width

Area = 11 * 2

Area = 22 in^2

Answer:

zack ran 17 more miles per week than antonio

Step-by-step explanation:

Statements:

1. m<DHF = m<EHG

2. m<1 = m<1

3. m<2 + m<1 = m<DHE

m<3+ m<1 = m<EHG

4. m<2 + m<1 = m<3 + m<1

5. m<2 = m<3

Reasons:

1. Given

2. reflective property

3. Angle addition postulate

4. substitution

5. subtraction property of equality

Hey there!

3/4

= 3 ÷ 4

= 0.75

= 75%

Option A.
12/16

= 12 ÷ 2 / 16 ÷ 2

= 6 / 8

= 6 ÷ 8

= 0.75

= 75%

Thus, this statement is: TRUE

Option B.
6/8

= 6 ÷ 2 / 8 ÷ 2

= 3 / 4

= 3 ÷ 4

= 0.75

= 75%
Thus, this statement is: TRUE

Option C.
15/20

= 15 ÷ 5 / 20 ÷ 5

= 3 / 4

= 3 ÷ 4

= 0.75

= 75%

Thus, this statement is: TRUE

Option D.
20/28

= 20 ÷ 2 / 28 ÷ 2

= 10 / 14

= 10 ÷ 2 / 14 ÷ 2

= 5 / 7

= 0.714286

= 71.4286%

Thus, this statement is: FALSE

Option E.
24/32

= 24 ÷ 2 / 32 ÷ 2

= 12 / 16

= 12 ÷ 4 / 16 ÷ 4

= 3 / 4

= 3 ÷ 4

= 0.75

= 75%
Thus, this statement is: TRUE

Therefore, your answers are

• Option A. 12/16
• Option B. 6/8
• Option C. 15/20
• Option E. 24/32

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

575 if your asking for the area

Step-by-step explanation: