Which of the following best describes the set of complex numbers?
OA. The set of all numbers of the form a+bi, where a and bare any
real numbers and i equals -1
B. The set of all numbers of the form abi, where a and bare any real
numbers and i equals 1
C. The set of all numbers of the form a+bi, where a and b are any
real numbers and i equals √-1
OD. The set of all numbers of the form abi, where a and b are any real
numbers and / equals -1

Answer:

1.  x = 55°

2.  x = 11°

3.  x = 30°

4.  x = 19°

Step-by-step explanation:

Trigonometric Identities

[tex]\sin(x)=\cos(90^{\circ}-x)[/tex]

[tex]\cos(x)=\sin(90^{\circ}-x)[/tex]

Question 1

[tex]\begin{aligned}\implies \sin(35) & =\cos(90-35)\\ & = \cos(55)\end{aligned}[/tex]

[tex]\implies x=55^{\circ}[/tex]

Question 2

[tex]\begin{aligned}\implies \cos(79) & =\sin(90-79)\\ & = \sin(11)\end{aligned}[/tex]

[tex]\implies x=11^{\circ}[/tex]

Question 3

[tex]\begin{aligned}\cos(x)& =\sin(2x)\\\implies \cos(x)& =\sin(90^{\circ}-x)\\\\\implies 2x & = 90-x\\3x & = 90\\x & = 30^{\circ}\end{aligned}[/tex]

Question 4

[tex]\begin{aligned}\sin(x+4)& =\cos(4x-9)\\\implies \sin(\theta)& =\cos(90^{\circ}-\theta)\\\\\implies x+4 & = 90-(4x-9)\\x+4 & = 90-4x+9\\5x & = 95\\x & = 19^{\circ}\end{aligned}[/tex]

Answer:

ANSWER IS B

Step-by-step explanation:

NEXT TIME USE any graph website online

The expression of base area of box will be 4x + x²

The area of a a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. Basically, the area formula is the product of the rectangle's length and width.

Given,

Length = 4+x

width = x

height = x²+1

We have to find the expression of base area of box

Given the length, width, and height

The formula for area of rectangle is as follow:

Area of rectangle = length x width

Area of rectangle = (4+x) x (x)

Area of rectangle = 4x + x²

Hence the expression of base area of box will be 4x + x²

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Answer:

16П or approximately 50.3)

Step-by-step explanation:

The area of a circle is equal to П*r²

Since the circle is inside a rectangle with side that is equal to 8, we know that d = 8

2r = d

r = 8/2

r = 4

A = П*r²

A = П*16

А = 16П ( or 16*3.141592653589793238... = 50.26548... ≈ 50.3)

Answer:

area = 50.27 [tex]cm^2[/tex]

Step-by-step explanation:

In the diagram, we see that the diameter of the circle is 8cm. Therefore the radius of the circle is 8/2 = 4cm.

[tex]area \hspace{0.15cm}of \hspace{0.15cm}circle = $\pi$r^2[/tex]

                        = π [tex](4)^2[/tex]

                        = 50.27 [tex]cm^2[/tex]

The total surface area of the cone is 3π + 10 cm².

A cone is a three-dimensional object that consists of a circular base and a vertex.

Total surface area = πr (r + l)

Where:

π x 3 + (3 + 7)

3π + 10 cm²

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The length of the arc given in the question is; 4.1r

We are given;

Angle at which arc is subtended; θ = 235°

Formula for arc length subtended at an angle θ is;

Arc Length = (θ/360) * 2πr

where r is radius of circle.

Thus;

Arc Length = (235/360)  * 2πr

Arc Length = 4.1r

The complete question is;

Find the value of the length of an arc that subtends an angle of 235 degrees to the circle's center.

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Answer:

No. (-1/2) is not an integer

Integers involve all the no. +ve and -ve. which can be written without fraction. ie whole no. are counted as integers.

(-1/2) is a fraction

Opposite values are those values which on the number line has the same distance between them and zero. The temperature in each city is PoT=-PhT and PhT =+PoT.

Opposite values are those values which on the number line has the same distance between them and zero. Although the sign on the values may be difference. For example if the first value is 4, then its opposite value is -4.

In general, the temperature equation for Portland, Maine is stated mathematically as

PoT=-PhT

As it is given in the question that the Portland, Maine and Phoenix, Arizona had opposite values. Also, the temperature in Portland is lower than in Phoenix. Therefore, the temperature in each city can be written as,

PoT=-PhT

PhT =+PoT

Hence, the temperature in each city is PoT=-PhT and PhT =+PoT.

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The Maximax decision is that Susan should build a very large gas station due to the largest value of row maximums.

A decision table can be defined as a type of table that is used for the graphical representation of the actions to perform, especially based on given conditions and business level rules.

The decision table for Susan’s problem is shown below:

Size            Good market   Fair market   Poor market    Row maximum

Small              50,000           20,000            -10,000           50,000

Medium          80,000           30,000            -20,000          80,000

Large              100,000          30,000            -40,000          100,000

Very large      300,000         25,000            -160,000         300,000

Thus, the Maximax decision is for Susan to build a very large gas station due to the largest value of row maximums.

For the Maximin decision, we have:

Size            Good market   Fair market   Poor market    Row minimum

Small              50,000           20,000            -10,000           -10,000

Medium          80,000           30,000            -20,000          -20,000

Large              100,000          30,000            -40,000          -40,000

Very large      300,000         25,000            -160,000         -160,000

Therefore, the Maximin decision is that Susan should build a small gas station due to the largest value of row minimums.

For the equally likely decision, we would find the row average:

Row 1 = (50,000 + 20,000 - 10,000)/3 = 20,000.

Row 2 = (80,000 + 30,000 - 20,000)/3 = 30,000.

Row 3 = (100,000 + 30,000 - 40,000)/3 = 30,000.

Row 4 = (300,000 + 25,000 - 160,000)/3 = 55,000.

Hence, the equally likely decision is that Susan should build a very large gas station due to the largest value of row average.

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Complete Question:

Even though independent gasoline stations have been having a difficult time, Susan has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline.  After a careful analysis, Susan developed the following table:

a. Develop a decision table for this problem

b. What is the maximax decision?

c. What is the maximin decision?

d. What is the equally likely decision?

Answer:

principal (p)=$1300

Interest (I) =$28.67

Time( T) = 1 year

R=?

we have,

R = I*100/T*R

The amount invested at each rate

Investment at 7% = $25000

Investment at 2%  = $11,000

Investment definition is an asset acquired or invested in to build wealth and save money from the hard earned income or appreciation.

Given:

Larry Mitchell invested = $36,000 at 7% annual simple interest

the rest at 2% annual simple interest.

Total investment = 36000

let the investment at 7% is x

then, invested at 2% = 36000 - x

Total interest earned = $1,970

Simple interest = principal * rate * time

Investment at 4%:

(x * 0.07) + [(36000 - x) * 0.02] = 1970

0.07x + 720 - 0.02x= 1970

0.05x = 1970-720

0.05x = 1250

x= 25000

Hence,

Investment at 7% = $25000

Investment at 2% = $36,000 - $25000 = $11,000

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Answer:

[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]

Step-by-step explanation:

To evaluate [tex]\displaystyle{f(x+1)}[/tex], substitute [tex]\displaystyle{x}[/tex] to [tex]\displaystyle{x+1}[/tex] so we should have:

[tex]\displaystyle{f(x+1) = |x+1-7|-4}[/tex]

Evaluate the expression and finally, we have:

[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]

Learn More

https://brainly.com/question/27923727 - How to find inverse and value of function

Step-by-step explanation:

let's write this properly :

f(x) = x³

g(x) = (x - 7)³ + 9

this translation means that every point of f(x) is shifted up by 9 units (by the "+ 9" term), and shifted right by 7 units (the " x - 7" term means that for every x the original result of x-7 happens, so, 7 units "later" or more to the right than originally).

so, the original (0, 0) point corresponds to (7, 9).

Answer:

which p? there isn't any p in above equation

Answer:

.0032 .032 .32 3299

Step-by-step explanation:

0.32% =.0032

3.2% = .032

.32

3299

Answer:

49 + 28 = 7(7 + 4)

Step-by-step explanation:

49 bags of soil one week

28 bags of soil the next week

49 + 28 bags of soil purchased in total

Find the GCF (Greatest Common Factor) of 49 and 28.

49/7 = 7

28/7 = 4 (GCF is 7 since it is the largest number that can divide both 49 and 28 equally)

Factor out the GCF + rewrite division above (optional for visualization)

49/7 = 7 -> 49 = 7 * 7

28/7 = 4 -> 28 = 7 * 4

49 + 28 = 7(7 + 4)

Let me know if you have any questions!

As per the question each row must have 6 seats more than the row before it. And there are 11 seats in the first row.

So, the first row has 11 seats

2nd row has 11+6 seats

3rd row has 11+2*6=11+12=23

4th row has 11+3*6=11+18=29

and so on...

We know that the difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. Arithmetic progression can be calculated as

aₙ = a₁ + (n - 1)d,

where aₙ is the nth and a₁ is the first term of this progression respectively and d is the common difference between terms.

So, we can observe the trend and develop the equation for the problem.

There are 11+(n-1)*6 seats in the n-th row.

So, there is 11+(18-1)*6=11+17*6=113 seats in the 18th row.

Therefore, there are 113 seats in the 18th row.

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Numerical Expression

The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols.

find the common denominator and thin combine the numerators over the common denominator trhin simplify each term thin simplify by adding subtracing  thin the result can be shown in multiple forms

exact form 19/2

decimal form 9.5

mixed number form 9 1/2

Answer:

x = - 5/2

Step-by-step explanation:

Using the law of indices

. a^-n = 1/a^n

. (a^4)^5 = a^5×4 = a^20

Note : When two base are equal , we equate the Exponents.

3^4x-5 = (1/27)^2x+10

= 3^4x-5 = (27^-1)^2x+10

= 3^4x-5 = (3^-3)^2x+10

= 3^4x-5 = 3^ -3(2x+10)

= 3^4x-5 = 3^ -6x-30

The two base are 3 so we equate the exponents.

= 4x - 5 = -6x - 30

= 4x + 6x = -30+5

= 10x = -25

= 10x/10 = -25/10

x = -25/10

x = - 5/2

X is -5/2

The value of DG is 4x + 45

From the question, we are to determine the value of DG

From the given information,

DE = 2x + 17

EF = 8

FG = 2x + 20

Then,

DG = DE + EF + FG

DG = 2x + 17 + 8 + 2x + 20

DG = 4x + 45

Hence, the value of DG is 4x + 45

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[tex]x^2+72x=8\\x^2+72x+1296=1304\\(x+36)^2=1304\\x+36=\sqrt{1304} \vee x+36=-\sqrt{1304} \\x=-36+2\sqrt{326} \vee x=-36-2\sqrt{326}[/tex]

Answer:

I think its x = 7

I belive it is

Answer:

whats the question? please explain

should i create the world problem with 12 3 and 9?

Based on the amount being taxed, the period of taxation, and the tax, the annual percentage of tax is 19.96%.

Assuming this rate was x, the following formula would apply:

Annual rate/ 365 days a year x number of days x amount to be taxed = Tax amount

Solving gives:

x/365 x 32 x 8,000 = 140

701.369863x = 140

x = 140 / 701.369863

= 19.96%

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Step-by-step explanation:

1. True

2. False

3. True

5. Falsw

6.True

7.True

8.False

10.True

15. always

17. always

Part 1

[tex](f\circ g)(x)=f(g(x))=\frac{\frac{1}{x}}{\frac{1}{x}-3}[/tex]

Multiplying the numerator and denominator by x,

[tex](f\circ g)(x)=\boxed{\frac{1}{1-3x}}[/tex]

Part 2

The domain for this function is all values of x except for when the denominator equals 0 (because then, it would be undefined).

The denominator is equal to 0 when x=1/3, so the domain is [tex]\boxed{x \neq \frac{1}{3}}[/tex]