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Answer:

  B. cos(pi/2) +i·sin(pi/2)

Step-by-step explanation:

You can convert to rectangular and back, or you can use the trig function relations directly.

  w = 4·cis(π/2) = 4i

  z = 3·cis(3π/2) = -3i

Then the sum is ...

  w +z = 4i -3i = i = cis(π/2) . . . . matches choice B

__

An alternative representation of z is ...

  z = -3·cis(π/2)

Then ...

  w +z = 4·cis(π/2) -3·cis(π/2) = cis(π/2)

_____

Additional comment

In the above, we have used cis(α) to represent (cos(α) +i·sin(α)).

Answer:

D

Step-by-step explanation:

It says that f(1/3x)=g(x), so scale factor is 1/3 and it is across the y axis because f(x) is basically y.

The correct statement is that the graph of function f is compressed horizontally by a scale factor of 1/3 to create the graph of function g.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Let us take the function g(x) as f(1/3 x).

This means that g(x) takes the value of f at  1/3 of x's value.

If f(2) = 4, then g(6) = f(1/3×6) = f(2) = 4.

When we replace x with 3x, we are compressing the graph of f horizontally by a factor of 1/3.

This is because every point on the graph of f now has 1/3 of its original x-coordinate.

The point (2, 4) was on the graph of f, it is now on the graph of g as (6, 4).

The scale factor is less than 1 because we are compressing the graph horizontally, which means the x-values are getting smaller.

Therefore, the correct statement is that the graph of function f is compressed horizontally by a scale factor of 1/3 to create the graph of function g.

To learn more on Graph click:

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Answer: The answer is 12q-1/2

Step-by-step explanation:

Answer:

yes, the question is proportional. if you multiply 9.50 by 2 you get 19 and so on and so forth. the constant rate is 9.50

y=0.2x

#0

[tex]\\ \sf\longmapsto y=0.2(0)=0[/tex]

#5

[tex]\\ \sf\longmapsto y=0.2(5)=1[/tex]

#10

[tex]\\ \sf\longmapsto y=0.2(10)=2[/tex]

#15

[tex]\\ \sf\longmapsto y=15(0.2)=3[/tex]

#20

[tex]\\ \sf\longmapsto y=0.2(20)=4[/tex]

Step-by-step explanation:

The given Eqⁿ is, [tex]{ \purple{ \sf{y = 0.2x}}}[/tex]

[tex]{ \star}[/tex]Put x = 0, then

[tex]{ \purple{ \sf{y = 0.2(0) = 0}}}[/tex]

[tex]{ \boxed{ \red{ \sf{(x, \: y )\: = (0,0)}}}}[/tex]

[tex]{ \star}[/tex]Put x = 5, then

[tex]{ \purple{ \sf{y = 0.2(5) = 1}}}[/tex]

[tex]{ \boxed{ \red{ \sf{(x, \: y) \: = (5,1)}}}}[/tex]

[tex]{ \star}[/tex]Put x = 10, then

[tex]{ \purple{ \sf{y = 0.2(10) = 2}}}[/tex]

[tex]{ \boxed{ \red{ \sf{(x ,\: y) \: = (10,2)}}}}[/tex]

[tex]{ \star}[/tex]Put x = 15, then

[tex]{ \purple{ \sf{y = 0.2(15) = 3}}}[/tex]

[tex]{ \boxed{ \red{ \sf{(x, \: y) \: = (15,3)}}}}[/tex]

[tex]{ \star}[/tex]Put x = 20, then

[tex]{ \purple{ \sf{y = 0.2(20) = 4}}}[/tex]

[tex]{ \boxed{ \red{ \sf{(x, \: y) \: = (20,4)}}}}[/tex]

Answer:

252.21m

Step-by-step explanation:

Times it by 3 and that should give you the answer you are looking for. Please mark it as brainliest

1) True

2) True

3) False

4) False

5) False

6) True

7) True

8) False

Answer:

So for the 9's facts, we can use a 10's fact, and then just subtract one group. For example, for 9×3, first do 10×3 to make 30, and then subtract one group of 3 to make 27. For 9×7, first do 10×7 to make 70, and then subtract one group of 7 to make 63.

Answer:

32

Step-by-step explanation:

The shape in image is an equilateral triangle which means all of it's angles has equal measurements:

2x - 4 = 5y and that is equal to 60 degrees

2x - 4 = 60 add 4 to both sides

2x = 64 divide both sides by 2

x = 32

15% of $18 is $2.70...........

Answer:

-2

Step-by-step explanation:

rise over run is 2/1 and y is decreasing as x is increasing so its negative

Hello! :)

x+12=20

Move all numbers to the right, using the opposite operation:

x=20-12

x=8

Therefore, x=8

Hope it helps. Enjoy your day! :)

Do ask me if you have any question.

~An excited gal

[tex]MagicalNature[/tex] here to help

Answer:

b

Step-by-step explanation:

If you multiple each side by 3 then they will equal the numbers that b has

Answer:

[tex]\implies \footnotesize \text{ Average Speed} = \dfrac{ \text{Total Distance}}{ \text{Total time}} \\ [/tex]

[tex]\implies \footnotesize \text{ Average Speed} = \dfrac{ 6.7 \: km}{ \frac{1}{2} \: hr }[/tex]

[tex]\implies \footnotesize \text{ Average Speed} = 6.7 \times 2 \: km/h[/tex]

[tex]\implies \footnotesize \textbf{ Average Speed = 13.4 \: km/h}[/tex]

His rate is 13.4km/ hour

Data;

To solve this problem, we have to convert his speed from km/min to km/h

[tex]60min =1 hour\\[/tex]

Since his rate is 6.7kmin 30 minutes, let's convert it to hour

[tex]6.7km = 30min\\x km = 1min\\x = \frac{6.7}{30} \\x = 0.223km/min[/tex]

But to convert minutes to hours, we have to divide the time by 60

[tex]0.223\frac{km}{min}*60/1 = 13.4[/tex]

From the calculation above, his rate is 13.4km/ hour

Learn more on conversion from minutes to hours here;

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Answer:

12

Step-by-step explanation:

Answer:

16 players can be brought to the tournament. The equation is written within my step-by-step explanation.

Step-by-step explanation:

Variable p = number of players

Set up an equation:

974.50 + 60.75p = 1946.50

Isolate variable p:

60.75p = 972

Divide:

p = 16

Check your work:

974.50 + 60.75(16) = 1946.50

974.50 + 972 = 1946.50

1946.50 = 1946.50

Answer:

Step-by-step explanation:

can you upload diagram?

Answer:

y = 5x - 32

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

y = 5x - 2 ← is in slope- intercept form

with slope m = 5

Parallel lines have equal slopes, then

y = 5x + b ← is the partial equation

To find b substitute (6, - 2 ) into the partial equation

- 2 = 30 + b ⇒ b = - 2 - 30 = - 32

y = 5x - 32 ← equation of parallel line

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:  

Z  < − 6

Interval Notation:

( − ∞ , − 6 )

Step-by-step explanation:

Answer:

z<-6

Step-by-step explanation:

4-5Z>34

-5z>34-4

-5z>30

z<-6

Answer:

£3.9

Step-by-step explanation:

Philip went to the shop with £9.60

spent £5.70

Money left = £9.60 -£ 5.70

                  =£3.9

Hence,

He came home with £3.9

Answer:

see below for answer

Step-by-step explanation:

(4p^2+32p)/(p-2)=(4p(p+8))/p-2

(p^2+p-6)/(2p^3+16p^2)=(p+3)(p-2)/(2p^2)(p+8)

(4p(p+8)/(p-2))*((p+3)(p-2)/((2p^2)(p+8)))=2(p+3)/p

I hope you have your answer now

Answer:

52$

Step-by-step explanation:

13 (75% off) so 13 is 1/4 the price.

13x4 = 52

Answer:

the topic of a piece of informational writing: C. the subject or focus

The topic of an informative piece is the writer's feelings about the subject which is the correct answer that would be an option (B).

Informational writing is a piece of writing that is truthful and aims to educate or explain a topic to the reader. This teaches primary school students how to write realistic, insightful essays on a variety of topics.

It gives the reader fundamental information about a certain issue, which serves to inform the reader. Informational writing, unlike other types of writing, does not aim to influence the reader's opinion or inspire them to take action.

The informational writing is straightforward and succinct. It does not include any superfluous words, flamboyant notions that might confuse the readers or too detailed terminology.

Therefore, the correct answer would be option (B).

Learn more about the Information writing to click here:

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Answer:

88 sides

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides, then

180° (n - 2) = 15480° ( divide both sides by 180° )

n - 2 = 86 ( add 2 to both sides )

n = 88

Answer:

Consecutive interior angles

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

v=l*w*h so 2^3=8

Answer:

Step-by-step explanation:

1. There are only 4 numbers including 5 that follow the "five or more" requirment, and the probability of spinning it once is 4/8, or 1/2. (The total sections is 8) Then we multiply 1/2 and 1/2 together to get the "two times in a row" requirement done. (1/2)*(1/2)= 1/4 is the probability.

2. There are two values on the spinner that are a multiple of 3, 3 itself and 6. Again, the total amount of numbers/sections is 8, so the probability of spinning a multiple of three is 2/8 or 1/4. The probability of spinning an odd number is 4/8 or 1/2. (1/2)*(1/4)=1/8 is the probability.

3. The probability of spinning one odd number is 1/2, and so we multiply 1/2 by itself four times. (1/2)*(1/2)*(1/2)*(1/2)=1/16 is the probability.

4. There are 6 numbers greater than two on the number wheel not including two itself. So the probability of that is 6/8, or 3/4. Then we multiply 3/4 by itself 3 times as it asks. (3/4)*(3/4)*(3/4)*(3/4)=81/256 is the probability.

Note that I am not really sure about the answer myself, but I hope that this can help in some way. Good luck! :)

Answer:

The answer is C.

Step-by-step explanation:

Answer:

Step-by-step explanation:

All pentagons angles = 540

540 - 107 - 100 - 96 - 119 = 118

Hope it helped!

Kavitha

Answer:

The answer above is in fact correct

Step-by-step explanation:

107+100+96+119+118=540