The “box” part of a box-and-whisker plot represents __________.
A.
the lower half of the data set
B.
the middle half of the data set
C.
the upper half of the data set
D.
the entire data set

Step-by-step explanation:

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The expressions which are equivalent to the complex number 45 + 2i is E. (9 + 4i) + (36 - 2i)

D. (2 + 8i) + (30 - 6i)

To determine which expressions are equivalent to the complex number 45 + 2i, we can simplify each expression and check if it matches the given number.

Let's evaluate each option:

A. (2 + 8i) + 2(9 + 6i)(1 - i) = 2 + 8i + 2(9 + 6i - 9i - 6i^2) = 2 + 8i + 2(9 + 6i - 9i + 6) = 2 + 8i + 2(15 - 3i) = 2 + 8i + 30 - 6i = 32 + 2i

B. (9 + 4i) + 2(4 + 7i)(1 - 2i) = 9 + 4i + 2(4 + 7i - 8i - 14i^2) = 9 + 4i + 2(4 + 7i - 8i + 14) = 9 + 4i + 2(23 - i) = 9 + 4i + 46 - 2i = 55 + 2i

C. (13 + 4i) + 2(7 + 2i)(2 - i) = 13 + 4i + 2(7 + 2i - 14i - 4i^2) = 13 + 4i + 2(7 + 2i - 14i + 4) = 13 + 4i + 2(24 - 12i) = 13 + 4i + 48 - 24i = 61 - 20i

D. (2 + 8i) + (30 - 6i) = 2 + 8i + 30 - 6i = 32 + 2i

E. (9 + 4i) + (36 - 2i) = 9 + 4i + 36 - 2i = 45 + 2i

F. (13 + 4i) + (32 - 6i) = 13 + 4i + 32 - 6i = 45 - 2i

From the evaluations above, we can see that options E and D are equivalent to the given complex number 45 + 2i.

The correct options are:

E. (9 + 4i) + (36 - 2i)

D. (2 + 8i) + (30 - 6i)

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The  expressions that are equivalent to the given complex number 45 + 2i are: (9 + 4i) + (36 - 2i) and (2 + 8i) + (30 - 6i).

Thus, option (D) and (E) are correct.

Given complex number 45 + 2i.

A. (2 + 8i) + 2(9 + 6i)(1 - i)

Simplifying: (2 + 8i) + 2(9 + 6i - 9i - 6)

= (2 + 8i) + 2(3 + 3i)

= 2 + 8i + 6 + 6i

= 8 + 14i

B. (9 + 4i) + 2(4 + 7i)(1 - 2i)

Simplifying: (9 + 4i) + 2(4 + 7i - 8i - 14)

= (9 + 4i) + 2(-10 - i)

= 9 + 4i - 20 - 2i

= -11 + 2i

C. (13 + 4i) + 2(7 + 2i)(2 - i)

Simplifying: (13 + 4i) + 2(14 + 4i - 7i - 2)

= (13 + 4i) + 2(12 - 3i)

= 13 + 4i + 24 - 6i

= 37 - 2i

D. (2 + 8i) + (30 - 6i)

Simplifying: 2 + 8i + 30 - 6i

= 32 + 2i

E. (9 + 4i) + (36 - 2i)

Simplifying: 9 + 4i + 36 - 2i

= 45 + 2i

F. (13 + 4i) + (32 - 6i)

Simplifying: 13 + 4i + 32 - 6i

= 45 - 2i

Thus, option (D) and (E) are correct.

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Answer:

The equation of line perpendicular to given line passing through (3,4) is:

[tex]y = -\frac{3}{2}x+\frac{17}{2}[/tex]

Step-by-step explanation:

Given equation of line is:

[tex]4x - 6y + 7 = 0[/tex]

Given equation is in standard form. It has to be converted into slope-intercept form to extract slope from the equation.

So,

[tex]4x+7 = 6y\\6y=4x+7\\\frac{6y}{6} = \frac{4x+7}{6}\\y = \frac{4}{6}x+\frac{7}{6}\\y=\frac{2}{3}x+\frac{7}{6}[/tex]

The standard form of slope-intercept form of equation is:

[tex]y=mx+b[/tex]

Here, the co-efficient of x is the slope of the line.

So the slope of given line is: 2/3

m = 2/3

The product of slopes of two perpendicular lines is -1

Let m1 be the slope of line perpendicular to given line

Then

[tex]m.m_1 = -1\\\frac{2}{3} . m_1 = -1\\m_1 = -1*\frac{3}{2}\\m_1 = -\frac{3}{2}[/tex]

The equation of perpendicular will be:

[tex]y = m_1x+b[/tex]

Putting the value of slope

[tex]y = -\frac{3}{2}x+b[/tex]

To find the value of b, putting (3,4) in the equation

[tex]4 = -\frac{3}{2}(3)+b\\4 = -\frac{9}{2}+b\\b = 4+\frac{9}{2}\\b= \frac{8+9}{2}\\b=\frac{17}{2}[/tex]

So the equation of line perpendicular to given line passing through (3,4) is:

[tex]y = -\frac{3}{2}x+\frac{17}{2}[/tex]

Answer:

bbhwhehwyayyquqysyegegegsgsgsgsusus

Step-by-step explanation:

vgsgahah z z zb

Answer:

Y=-3/5x

Step-by-step explanation:

Answer:

y = 3/2x -14

Step-by-step explanation:

y = -2/3 x

has a slope of -2/3

We want a line perpendicular

Take the negative reciprocal to find the slope

- (1 / -2/3)

3/2

The slope of a line perpendicular is 3/2

Using the slope intercept form of a line

y = mx+b where m is the slope and b is the y intercept

y = 3/2x +b

Substitute a point into the equation

-8 = 3/2(4) +b

-8= 6+b

Subtract 6 from each side

-8-6 = b

y = 3/2x -14

Answer:

k = 3/2

Step-by-step explanation:

assuming k is your slope

rise/run = y/x

k = 1/3 therefore, (3,1) is your (x,y) points

k=3/2 therefore, (2,3) is your (x,y) points

as you can see, you move 2 more units up on the y-axis with k =3/2. Therefore, it is steeper.

Answer:

a

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

Answer:

6/25

Step-by-step explanation:

Answer:

The answer is B 6/25

Step-by-step explanation:

ITs B because you would first get 12/50 and then just simplify it by even numbers.

hope I helped. :)

Answer:

b. (-5, 4)

Step-by-step explanation:

edge2020

Answer:

$22.50

Step-by-step explanation:

As it is 30% off, $15.75 is 70% of the full price. You can then divide 15.75 by 70 [= 0.225] to get 1% of the full price. Multiply 0.225 by 100 to get the full price. 0.225 x 100 = 22.5

We can check that this answer is correct by multiplying 22.50 by 0.7. If you get 15.75 you know the answer is correct as 15.75 is 70% of the full price.

Answer:

x is 50

y is 55

Step-by-step explanation:

Let us start working with the second patio

At any point in time, the total measure of the angles of a triangle is 180

Thus in the second patio;

x + 20 + 50 + 60 = 180

x + 130 = 180

x = 180-130

x = 50

In the first patio;

x + 10 + y + 15 + 70 = 180

substitute 50 for x

50 + 10 + y + 65 = 180

60 + 65 + y = 180

y = 180-60-65

y = 55

Answer:

the other answer above is wrong,

x=50

y=35

Answer: 2π x radius

Step-by-step explanation:

The circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line then the length of that line will be the circle's circumference.

Answer: 69.2

Step-by-step explanation:

Answer:

where are the options

Step-by-step explanation:

Answer:

Step-by-step explanation:

10 is your answer

Answer:

6 check how I did to understand it

Step-by-step explanation:

42:7=6

Answer: A

Step-by-step explanation: 22.00, 19.00 and 11.00 are all less than 25. $32.00 is the only logical explanation.

Answer:

A. -$32.00

Step-by-step explanation:

This is because it is a greater debt than 25 and all the other choices are greater than $25.

Answer:

y+1 = -(x-4)

Step-by-step explanation:

find slope: (-1-2)/(4-1) = -1

y+1 = -(x-4)

Answer:

you didnt put anything like the full question but it equals 20

Step-by-step explanation:

so yea 2000

Answer:

A.-5

Step-by-step explanation:

I have used an online calculator to check my answer against so this answer is 100% correct. I used "Slope Calculator" by Omni.

PLEASAE MARK BRAINLIEST

Answer:

f(x)=56

Step-by-step explanation:

2(24)+8=56

Answer:

Step-by-step explanation:

the first one

Answer:

Its the first one W'Z||X'Y'

Step-by-step explanation:

The translation is just upwards meaning the points dont move other then the Y changing, the original has WZ parallel to XY so having it translated up will still have it be parallel

Answer:

0

Step-by-step explanation:

Answer:

Slope is 2; y-intercept is (0,-6)

Step-by-step explanation:

Slope intercept form looks like 3y = 2x - 6

In the equation y=mx+b, M is always the slope, and B is always the y-intercept. Therefore if you look back at the problem the slope number should be in front of the x which makes it 2. Since the y-intercept is always b, y = -6.

Slope or m = 2; y-intercept is (0,-6)

Answer:

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

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Given

- 2x + 3y = - 6 ( add 2x to both sides )

3y = 2x - 6 ( divide all terms by 3 )

y = [tex]\frac{2}{3}[/tex] x - 2 ← in slope- intercept form

with slope m = [tex]\frac{2}{3}[/tex] and y- intercept c = - 2