Let z = 3(cos(15°) + i sin(15°)) and w = 5(cos(90°) + i sin(90°)). What best describes the geometric construction of the quotient z/w on the complex plane?

z is scaled by a factor of One-fifth and rotated 90 degrees clockwise.
z is scaled by a factor of 1 and rotated 90 degrees clockwise.
z is scaled by a factor of 1 and rotated 90 degrees counterclockwise.
z is scaled by a factor of One-fifth and rotated 90 degrees counterclockwise.

The additional information which would be sufficient to conclude that LMNO is a parallelogram is; ML ∥ NO, LO ≅ MN, and ML ≅ LO.

The condition for a quadrilateral to be a parallelogram is that; the opposite pairs must be parallel and consequently opposite pairs are congruent as they have equal length measures.

On this note, it can be concluded that the additional information which would be sufficient are; ML ∥ NO, LO ≅ MN, and ML ≅ LO.

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(A.) ML ∥ NO,

(C.) LO ≅ MN.

Have a great day and hydrate!! <3

Answer:

A varicocele measures more than 2 mm in diameter.

Step-by-step explanation:

pampiniform plexus veins measuring more than. 2 mm in diameter at rest and which increased in diameter by 1 mm, and subjective color Doppler.

Answer:

5x - y = 9

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

y = 5x - 9 ( subtract 5x from both sides )

- 5x + y = - 9 ( multiply through by - 1 )

5x - y = 9 ← in standard form

Fencer X attacks. Fencer Y makes a parry, and scores a riposte to the valid target of Fencer X. During the parry, Fencer Y strikes Fencer Xs mask with the bell guard. annual the touch fencer Y recieves  a RED CARD.

what are the fencing rules ?

Penalty cards or flags are also used in modern fencing. Each card has a unique meaning. A fencer who receives a yellow card is warned, but no further action is taken. A fencer who receives a red card is warned, and their opponent receives a touch. A fencer who receives a black card is disqualified from the competition and may be disqualified from the tournament, expelled from the venue, or suspended from future tournaments if the offence is serious. However, black cards are rarely given to fencers. It should be noted that spectators can (and occasionally are) carded or expelled.

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Answer:

A) Equation of the line of best fit: y = -5x + 62

B) y = -3

Explanation:

Given points: {(5, 38), (6, 34), (7, 27), (8, 21), (9, 17), (10, 14)}

Plot these points on the graph and draw a straight line between them.

A)

The points (7, 27), (9, 17)

Find slope:

[tex]\sf slope: \dfrac{17-27}{9-7} = -5[/tex]

Equation:

[tex]y - y_1 = m(x - x_1)[/tex]

[tex]\sf y - 27= -5(x - 7)[/tex]

[tex]\sf y = -5x + 35 + 27[/tex]

[tex]\sf y = -5x + 62[/tex]

B) If x = 13, then approximate value of y is

insert x = 13 in equation

y = -5x + 62

y = -5(13) + 62

y = -3

The answers are :

A) y = -5x + 64

B) -1

Part (A) :

Finding the slope : Take the points (6, 34) and (10, 14)

m = Δy/Δx

m = 14 - 34 / 10 - 6

m = -20/4

* m = -5 *

Using point slope formula to find equation :

y - y₁ = m (x - x₁)

y - 34 = -5 (x - 6)

y - 34 = -5x + 30

y = -5x + 64

Part (B) :

Substitute x = 13 in the line of best fit equation

y = -5(13) + 64

y = -65 + 64

y = -1

The surface area of the composite figure is 444m²

Given a composite figure which is shown in the question.

The  area of ​​a shape (in square units) is the number of unit squares required to cover the entire area without gaps or overlaps. If a hologram has planes, those faces are called faces. Area is the sum of the areas of the faces.

Firstly, we will find the area of front and end triangles by using the formula

Area=(1/2)×b×h and we will multiply this area by 2 because we are finding the area of two same triangles.

Here, h=6 and b=16 and substitute these values in the formula, we get

A₁=2×(1/2)×16×6

A₁=2×8×6

A₁=96m²

Now, we will find the area of the left and right side rectangles which joined both the triangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=10 and b=5 and substitute these values in the formula, we get

A₂=2×10×5

A₂=100m²

Further, we will find the area of the front and end side rectangles that joined both by the base of the triangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=16 and b=4 and substitute these values in the formula, we get

A₃=2×16×4

A₃=128m²

Furthermore,  we will find the area of the left and right side rectangles which joined by the front and end rectangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=4 and b=5 and substitute these values in the formula, we get

A₄=2×4×5

A₄=40m²

Now, we will find the area of the base of the composite figure which is rectangle.

We will find the area by using the formula Area=l×b.

here, l=16 and b=5 and substitute these values in the formula, we get

A₅=16×5

A₅=80m²

So, the surface area of the given composite figure will be

Surface area=A₁+A₂+A₃+A₄+A₅

Surface area=96m²+100m²+128m²+40m²+80m²

Surface area=444m²

Hence, the surface area of the given composite figure is 444m².

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The solution to the given inequality is y < 5

Inequality are equations  not separated by an equal sign. Given the following parameters

15 > y + 10

Subtract 10 from both sides

15 - 10 > y + 10 - 10

5 > y

Swap

y < 5

Hence the solution to the given inequality is y < 5

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Answer:

See below

Step-by-step explanation:

The larger is  

7-6 = 1 unit bigger than the smaller....and this unit = 24 gallons

   each unit is 24 gallons

larger barrel holds   24 * 7 = 168 gal

smaller barrel holds  24 * 6 = 144 gal

Answer:

Small barrel=144 large barrel=168

Step-by-step explanation:

The ratio is 6 to 7 so lets assign x as a factor.

6x=Small barrel (S)

7x=Large barrel (L)

7x-6x=x

x is the difference so x is 24

x=24

6*24=144=S

7*24=168=L

Answer:

Option B: 3

Step-by-step explanation:

#1: Substitute in 6 for [tex]y[/tex] and 3 for [tex]x[/tex]: [tex]13=(3)(6)-5[/tex]

#2: Multiply 3 and 6: [tex]13=18-5[/tex]

#3: Evaluate the equation: [tex]13=18-5[/tex] → [tex]13=13[/tex]

#4: Check if the solution is equal: [tex]13=13[/tex] ✓

[tex]x[/tex] is equal to 3 (Option B).

Answer:

[tex] y = \pm \sqrt{\dfrac{x - 7}{6}} [/tex]

Step-by-step explanation:

f(x) = 6x² - 7

y = 6x² - 7

x = 6y² - 7

6y² = x - 7

[tex] y^2 = \dfrac{x - 7}{6} [/tex]

[tex] y = \pm \sqrt{\dfrac{x - 7}{6}} [/tex]

For the following pair of functions, the vertex of g(x) 2 units to the right of f(x),

f(x) = x² and g(x) = (x - 2)²

What are functions?

Defining a relationship between an independent variable and a dependent variable using mathematical expressions, rules, or laws is known as a function. Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.

Determining the Correct Pair of Functions

For a given function f(x), its horizontal translation would be f(x + a). Here, a is the distance translated, owing to which f(x + a) is generated.

If a > 0, then it indicates a right translation of a units.

If a < 0, then it indicates a left translation of a units.

The required functions are to be such that the vertex of g(x) is 2 units to the right of the vertex of f(x).

Thus, if f(x) = x², then g(x) = (x - 2)²

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Option D. What we can conclude is that  If the end result from the second column is not 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.

An operation is done on a first column of numbers. When this operation is repeated on the second column, we would have option D.

If the sum of the numbers that are in the third can be seen to be greater than three, then the sums are not going to be seen as equal

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One column of numbers consists of 28, 42, and 14. When the digits of the numbers are added together, the result is 2 + 8 + 4 + 2 + 1 + 4 = 21, and when the digits of 21 are then added together, the end result is 2 + 1 = 3. If the same process is performed on the numbers in a second column, what can be concluded?

A. If the end result from the second column is also 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.

B. If the end result from the second column is not 3, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.

C. If the end result from the second column is also 3, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.

D. If the end result from the second column is not 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.

Answer:

118

Step-by-step explanation:

The total area is the area of the large rectangle in the middle plus the areas of the two triangles.

The length of the entire rectangle is 5 cm + 5 cm + 4 cm = 14 cm.

The width of the rectangle is 7 cm.

Each triangle has a base of 4 cm and a height of 5 cm.

A = LW + 2 × (1/2)bh

A = (14 cm)(7 cm) + (4 cm)(5 cm)

A = 98 cm² + 20 cm²

A = 118 cm²

The logarithmic form of 13^2=169 is [tex]\log_{13}(169) = 2[/tex]

The equation is given as

13^2=169

Take the logarithm of both sides

log(13^2) = log(169)

This gives

2log(13) = log(169)

Divide both sides by log(13)

[tex]\log_{13}(169) = 2[/tex]

Hence, the logarithmic form of 13^2=169 is [tex]\log_{13}(169) = 2[/tex]

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Answer:

$13.20

Step-by-step explanation:

A dozen consists of 12 items. If you have 3 you must multiply the current amount by 4 to get 12. Therefore you must also multiply the price by 4.

3.30*4=13.20

The angle between their paths to the nearest degree is 68⁰.

first displacement, a = 15 km/h  x (45/60)

first displacement, a = 11.25 km

second displacement, b = 18 km/h  x (45/60)

                                     b = 13.5 km

c² = a² + b² - 2ab(cosθ)

2ab(cosθ) = a² + b² - c²

cosθ =  (a² + b² - c²)/(2ab)

cosθ = (11.25² + 13.5² - 14²) / (2 x 11.25 x 13.5)

cosθ = 0.371

θ = arc cos(0.371)

θ = 68.22 ⁰

Thus, the angle between their paths to the nearest degree is 68⁰.

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The value of x in the trapezoid is 11.

Therefore, the angle 9x and 7x + 4 are supplementary.

Hence,

9x + 7x + 4 = 180

16x + 4 = 180

16x  = 180  - 4

16x = 176

x = 176 / 16

x = 11

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Answer:11

Step-by-step explanation:Easy

in standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to 5. 04 × 10 ^3

Standard form is simply a value with an exponential powerl

Given the values;

It is important to note that any number to the power of O is equivalent to 1

So, we have

10^ 0 = 1

4( 10^-3) = 37

5(10^3) = 5000

Now, let's substitute the values

(10°) + 4 (10-3) + 5 (10³)

It is equivalent to

⇒1 + 4 × 10^-3 + 5 × 10^3

⇒1 + 37 + 5000

Add the values

= 5038

Let's convert it to standard form, we have

= 5. 04 × 10 ^3

Thus, in standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to 5. 04 × 10 ^3

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The relative frequency of students who have three siblings is 25% given that there are 60 students in a class in which 5 have no siblings, 26 have one sibling, 14 have two siblings and 15 have three siblings. This can be obtained by using the formula for relative frequency.

Given that,

total number of students in the class = 60

number of students who have no sibling = 5

number of students who have 1 sibling = 26

number of students who have 2 sibling = 14

number of students who have 3 sibling = 15

Formula for relative frequency = f/n, where f is the number of times the data occurred, n is the total number of frequencies.

Therefore,

relative frequency of students who have three siblings = 15/60 = 0.25

In percentage ⇒ 0.25 × 100 = 25%

Hence the relative frequency of students who have three siblings is 25% given that there are 60 students in a class in which 5 have no siblings, 26 have one sibling, 14 have two siblings and 15 have three siblings.

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The value of f⁻¹(f(58)) is 58 and the value of the function f(f(5)) is 11

As a general rule, we have:

f⁻¹(f(x)) = x

Substitute 58 for x

So, we have:

f⁻¹(f(58)) = 58

Hence, the value of f⁻¹(f(58)) is 58

Also, we have:

f(f(5))

From the table, we have:

f(5) = 9

So, we have:

f(f(5)) = f(9)

From the table, we have:

f(9) = 11

So, we have:

f(f(5)) = 11

Hence, the value of the function f(f(5)) is 11

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Answer: A

Step-by-step explanation:

[tex]P(x) Q(x)=R(x)\\\\(x+1)Q(x)=2x^3 + 2x^2 - 3x-3\\\\Q(x)=\frac{2x^3 + 2x^2 - 3x-3}{x+1}\\\\Q(x)=\frac{2x^2 (x+1)-3(x+1)}{x+1}\\\\Q(x)=2x^2 - 3[/tex]

The quotient of 3 by 1/ 6 and that of 3/4 by 1/ 8 is 1/2 and 4 respectively

From the given equation, we have to find

= 3/4 ÷ 1/8

First , we take the denominator of the second fraction to be the numerator, we have

=

[tex] \frac{3}{4} \times \frac{8}{1} [/tex]

Multiply through

=

[tex] \frac{24}{4} [/tex]

=

[tex]6[/tex]

To find the quotient of 3 by 1/6

=

[tex]3 \times \frac{1}{6} [/tex]

=

[tex] \frac{3}{6} [/tex]

=

[tex] \frac{1}{2} [/tex]

Thus, the quotient of 3 by 1/ 6 and that of 3/4 by 1/ 8 is 1/2 and 4 respectively

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Answer:

screenshot attached of graph

Step-by-step explanation:

Answer:

A. y= cos x - 1

Step-by-step explanation:

short answer: this is basically the parent graph cos(x), just vertically shifted down 1 unit.

longer answer:

standard form is y = a cos(bx-c) +d

a = amplitude

b = 2pi/period

c = horizontal shift

d = vertical shift (also equal to midline)

for this graph

a=1

period is 2pi, so b=1

there is no horizontal shift so c=0

d= -1 because it is shifted down one unit from axis (midline is at -1)

Answer: plot points (0,-2) (1.-5) (2.-8) (-1.1) (-2.1) makes a upside down V

-3|0+2|+4=-2

-3|1 +2|+4= -5

-3|2+2|+4= -8

-3|-1+2|+4=1

+3|-2+2|+4=1

Step-by-step explanation:

The relationship of the data can be classified as a fairly strong positive correlation.

Correlation is a statistical measure used to measure the relationship that exists between two variables.

Positive correlation is when two variables move in the same direction. If one variable increases, the other variable also increases. When there is a positive correlation, the graph of the variables is upward sloping

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Answer:

5 hours 20 minutes.

Step-by-step explanation:

8 * 2/3

= 16/3

= 5 1/3

= 5 hours 20 minutes.

Answer:

? = 4

Step-by-step explanation:

4/5 = 4/1 x 1/5

4/5 = 4/5