Match the vocabulary word to its correct definition.

1. complex conjugate the sum of a real number and an imaginary number: a + bi, where a is a real number and b is the imaginary part
2. complex number the part of a complex that is multiplied by i; so, the imaginary part of the complex number a + bi is b; the imaginary part of a complex number is a real number
3. i the part of a complex that is not multiplied by i. So, the real part of the complex number a + bi is a; the real part of a complex number is a real number
4. imaginary number a number defined with the property that 12 = -1, so that
5. imaginary part of a complex number the inverse of a complex number a + bi is a complex number c + di such that the product of these two numbers equals 1
6. multiplicative inverse any nonzero multiple of i; this is the same as the square root of any negative real number
7. real part of a complex number the conjugate of a complex number has the opposite imaginary part. So, the conjugate of a + bi is a - bi. Likewise, the conjugate of a - bi is a + bi. So, complex conjugates always occur in pairs

Answer:

1.

(a) The Domain is the set of inputs of the function.

Considering that the function takes a period of 3 weeks (21 days), the domain is [0, 21], once we can't evaluate what happens after the 21st day.

[tex]\text{Domain is } [0, 21][/tex]

Otherwise, it could be [tex][0, \infty)[/tex]

Note: We include 0 and 21.

Once the greatest balance was $400, it will not exceed $400, either it doesn't show negative values.

[tex]\text{Range is } [0, 400][/tex]    

Note: We include 0 and 400.

(b)

Once the greatest balance was $400, when x=0, it seems that the y-value is half of $400, therefore, approximately $200. It also represents the initial value, the amount of money when she opened the account.

(c)

[tex]f(x)=B(d)[/tex]

[tex]B(12)=0[/tex]

(d)

It is in segment 4.

The balance equal to zero means that the y-value of the graph is zero, therefore in the x-axis.

Answer:

both angles are the same, so you can use it interchangeably in proving.

But i suggest you to mantain only one, because it's easier to understand and it looks better.

Answer:

b

Step-by-step explanation:

If a negative number times another number is positive, that means that the other number is also negative because multiplying two negative numbers gives you a positive number. Therefore, a - b must be negative. In order for the difference of two numbers to be negative, the number being subtracted must be bigger than the number it's being subtracted from. For example, in 2 - 7, 7 > 2 but 2 - 7 is negative, the same goes for 3 - 8, 4 - 10, etc. Therefore, b must be greater.

Step-by-step explanation:

Hello, there!!!

Let's simply work with it,

Firslty let's assume the whole cake, when you assume the cake in whole. you get,

length (l)= 16 in

breadth (d)= 6 in

and height (h)= 4 in

now, as it is a rectangle shaped cake,

volume of a whole cake (v)= l×b×h

or, v= 16 in × 6 in × 4 in.

Therefore, the volume of whole cake is 384 cubic inch.

now,

let's find the volume of eaten part,

As per the picture, the 1/4th part of cake is eaten so,

length = 8 in

breadth = 3in

and height = 4in.

so, volume of eaten part = l × b × h

v= 8in × 3in × 4in

Therefore , v= 96 cubic inch.

now, lastly finding the volume of remaining part,

v. of remaining part = v.of whole cake - v. of eaten part.

or, v. of remaining part = 384 in^3 - 96 in^3

Therefore, the volume of remaining part is 288in^3.

Hope it helps....

Answer:

[tex]\Large \boxed{- \frac{1}{5}}[/tex]

Step-by-step explanation:

[tex]\displaystyle \sqrt[3]{-\frac{1}{125} }[/tex]

Distribute the cube root to the numerator and denominator.

[tex]\displaystyle -\frac{\sqrt[3]{1} }{\sqrt[3]{125} }[/tex]

Solve for the cube root.

[tex]\displaystyle - \frac{1}{5}[/tex]

Answer:

Step-by-step explanation:

400 km  =       x    

  6 min         9 min  

cross multiply:

6x = 400 ( 9)

x = 3600 / 6

x = 600 km

Answer: Angle Addition Postulate

Step-by-step explanation:

In the given picture, we have ∠MRO and ∠MRS on line SRO.

So, ∠SRO = ∠MRO +∠MRS  [By angle addition postulate]

So the postulate that justify the statement " ∠SRO = ∠MRO +∠MRS" is Angle Addition Postulate.

Answer:

5 ml of 50% syrup solution will be used to create the final solution

Step by step Explanation:

Let the amount of 50% solution that was used = b

Which means ( 30 - b ) is the amount of 1/200 solution used then we can derive an equation as follows,

set up will then be,

0.5b +0.05(30 -b) = 1/8 (30)

We can simplifiy this as

0.5b+ 1.5 -0.05b = 3.75

Then make b the subject of the formula we have

0.45b = 2.25

b= 2.25/0.45

b = 5 ml

Therefore, 5ml of 50% syrup solution will be used to create the final solution

Answer:

(10, -2)

Step-by-step explanation:

The inequalities are:

y < x - 7               (1)

y < (1/5)x - 2        (2)

To solve this problem, we have to solve both equations simultaneously and then find the value of x and y that makes the inequality true.

To solve the inequality, subtract inequality (2) from inequality (1) which gives:

0 < (4/5) x - 5

-(4/5)x < -5

Dividing both sides of the equation by -4/5 gives:

-(4/5)x / (-4/5) < -5/ (-4/5)

x > 6.25

Put x > 6.2 in inequality 1

y < 6.25 - 7

y < -0.75

The solution of the inequality is x > 6.25 and y < -0.75

From the list of option, the correct answer is (10, -2) since 10 > 6.25 and -2 < -0.75

Answer:

1

Step-by-step explanation:

Let's ignore the absolute value signs for a moment.

We have the expression [tex]10-11[/tex]. We know that if we subtract 10 from 10 we get 0, so if we subtract 11 from 10 we must get -1.

However, there is an absolute value sign. This means that whatever number is inside it has to be converted to a positive number.

-1 as a positive number is +1, or just 1.

Hope this helped!

Answer:

PQ = 17

Step-by-step explanation:

Tangents drawn to a circle from an external point are congruent, thus

TS = TU = 6

VU = VO = 20

PO = PQ = 37 - VO = 37 - 20 = 17

That is PQ = 17

Greetings from Brasil...

According to the statement, one figure is scaled in relation to another, so we can apply similarity to polygons.....

So

BIG/small = BIG/small

or

small/BIG = small/BIG

12.5/10 = X/16

OR

10/12.5 = 16/X

12.5/10 = X/16

10X = 12.5 · 16

X = 200/10

ANSWER:

               It is C

NO EXPLANATION

Answer:

The distance between the two train stations is 1728 km

Step-by-step explanation:

The speed of the bus = 54 km/h

The speed of the truck = 48 km/h

When the bus and truck meet again, the distance covered by the bus = 216 km more than he distance traveled by the truck

Let the distance between the two train stations = x

Let the location where they first meet be y from station A we have;

The location where they meet again = y - 216 km

Therefore, we have;

Location where they

The time for the truck and the bus to meet again = t

Therefore, 54 × t - 48 × t = 216 km

6·t = 216 km

t = 36 hours

Therefore, the time for the bus to travel x + 216 km = 36 hours

54 × 36 = 1944 = x + 216

x = 1944 - 216 = 1728 km

The distance between the two train stations = 1728 km.

Answer:

Step-by-step explanation:

2x + 2y = 18

-2x -2y = -18

0 = 0

infinite solution of equations

Answer:

a or b

Step-by-step explanation:

it just looks like b or a

H(t) = -4.9t^2 + 25t + 2

Height is a function of time

plug in 0, 1,2,3,4, and 5 to find the height at 0, 1,2,3,4, and 5 seconds.

at t = 0

H(0) = -4.9(0)^2+25(0) + 2 = 2 meters

Repeat for T=1,2,3,4 and 5

Notice the ball peaks around t = 3 seconds and starts to descend.  

H(1) = (-4.9)(1^2) + 25(1) + 2 = 22.1 meters

H(2) = (-4.9)(2^2)+25(2)+2=32.4 meters

H(3) = 32.9 meters

H(4) = 23.6 meters

H(5) = 4.5 meters

Answer:

30.9 mb

Step-by-step explanation:

Answer:

same side interior angles

Step-by-step explanation:

<4 and <6 are same side interior angles

Same  side interior angles are on the same side of the transversal and inbetween the two lines

Answer:

[tex]2 \frac{4}{9} [/tex]

[tex] = \frac{ - 5}{6} + 1 \frac{2}{9} [/tex]

[tex] = \frac{ - 5}{6} + \frac{11}{9} [/tex]

[tex] = \frac{ - 5 \times 2 + 11 \times 1}{9} [/tex]

[tex] = \frac{ - 10 + 9}{9} [/tex]

[tex] = \frac{-1}{9} [/tex]

Answer:

B, C , and E

Step-by-step explanation:

for 9 ml of hot sauce (x) +6 ounces of BBQ sauce(y)= flaming BBQ(c)

9x+6y=c

B: 3x+2y will give the same taste ( the quantity reduced to one third)

C: 45x+30y will give the same taste ( the quantity multiply by 5)

E:12 x+8y will give the same taste ( the quantity multiplied by 0.75)

The Variable d in the equation represents the time per minute Lilianna spends walking to the park

The equation:

d(3/4 + 1) = 12 1/4

d(3+4/4) = 12 1/4

d(7/4) = 49/4

d = 49/4 ÷ 7/4

= 49/4 × 4/7

= 49/7

d = 7

Complete question:

Lilianna uses 3/4 calories per minute just by sitting. She uses 1 more calorie per minute by walking. Liliana uses a total of 12 1/4 calories walking to the park. Lilianna uses the equation, d(3/4+1)=12 1/4 to represent the situation. What does the variable d represent in the equation?

Learn more about variable:

https://brainly.com/question/11885867

#SPJ1

Answer:

7). 1

8). 3

9). 1

Step-by-step explanation:

7). [tex][3\div (2\times 1)]\frac{2}{3}[/tex]

  [tex]=[3\div 2]\frac{2}{3}[/tex]

  [tex]=\frac{3}{2}\times \frac{2}{3}[/tex]

  [tex]=1[/tex]

8). [tex]2(3\times 2-5)+3\times \frac{1}{3}[/tex]

  [tex]=2(6-5)+\frac{3}{3}[/tex]

  [tex]=2(6-5)+1[/tex]

  [tex]=2+1[/tex]

  = 3

9). [tex]6\times \frac{1}{6}+5(12\div 4-3)[/tex]

  [tex]=6\times \frac{1}{6}+5(\frac{12}{4}-3 )[/tex]

  [tex]=1+5(3-3)[/tex]

  = 1

Answer:

Answer:

-0.65

Step-by-step explanation:

Step 1: Write out fraction

-13/20

Step 2: Evaluate fraction

-13/20 = -0.65

distance of a point [tex](x,y)[/tex] from origin is $\sqrt{x^2+y^2}$

so distance is $\sqrt{(-15)^2+(8)^2}=\sqrt{225+64}=\sqrt{289}=17$

Answer:

Distance=17 units

Step-by-step explanation:

Coordinates of the origin: (0, 0)

Coordinates of the point in question: (-15, 8)

Distance formula for any two points [tex](x_1,y_1), (x_2,y_2)[/tex] on the plane:

[tex]distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance=\sqrt{(-15-0)^2+(8-0)^2}\\distance=\sqrt{(15)^2+(8)^2}\\distance=\sqrt{225+64} \\distance=\sqrt{289} \\distance=17[/tex]

Answer:

I HOPE IT WILL WORK

Step-by-step explanation:

let age of Maggie =x years

as given that Maggie brother is 3 year less than twice of her age

hence

brother = (2x-3) years

also given that sum of ages =24

hence

x+(2x-3)=24

3 x-3=24

3 x=27

x=9 years Maggie

so his brother=9-3=6 years

pls hit the star and brainlist it if you found it helpfull thanks

Answer:

3(-8 + 1) = 3(-8) + 3(1)

Step-by-step explanation:

The distributive property is quite literally when you distribute numbers. This is the only instance of that happening here

The first two are the communitive property of addition, and the last one is the communitive property of multiplication.

Cheers.

Answer:

c

Step-by-step explanation:

Answer:

x = 28

Step-by-step explanation:

12/x = 3/7

Using cross products

3x = 12*7

3x = 84

Divide by 3

x = 28

Answer:

Recorrera 495 km con 11 galones de gasolina

Y necesitara 14.44 galones para recorrer 650 km

Step-by-step explanation:

k          g                                                                  k             g

90         2                                                                 90           2

x            11                                                                650         x

=(11 x 90)/2                                                              =(650x2)/90

=990/2                                                                    =1300/90

=495 km                                                                 =14.44

Answer:

N(t)=N∗.5t/h where n(t) is amount of substance left, N = initial amount, t = current time, and h = half-life time.h = 24 hours t= 45 hours, N = 130mg

therefore, N(t)=130∗.545/24=35.44mg

Step-by-step explanation:

N(t)=N∗.5t/h where n(t) is amount of substance left, N = initial amount, t = current time, and h = half-life time.h = 24 hours t= 45 hours, N = 130mg

therefore, N(t)=130∗.545/24=35.44mg

Answer:

≈ 130 mg

Step-by-step explanation:

This is about the half-life of the substance.

There is a formula for this kind of calculations:

N(t)= N₀*(0.5)^(t/T), where

In our case, we have:

And the calculation:

Answer: about 130 mg of substance remains after 20 hours