find the smallest number by which 29160 should be divided so that the quotient becomes a perfect cube

The best description of the geometric construction of the quotient z/w on the complex plane is; Option A; z is scaled by a factor of One-fifth and rotated 90 degrees clockwise

We are given;

z = 3(cos(15°) + i sin(15°))

w = 5(cos(90°) + i sin(90°))

Now, if we want to find the quotient z/w, it is clear that in geometric construction, the procedure will be to scale z by a factor of 1/5 and thereafter we will rotate by 90° clockwise.

Thus, option A is the correct answer.

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Answer:

Below in bold.

Step-by-step explanation:

(a) Using the Pythagoras theorem:

30^2 = 21^2 + p^2

p^2 = 30^2 - 21^2 = 459

p = √459

  = 21.4 cm to nearest tenth.

(b) cos P = 21/30 = 0.70

   m < P = 45.57 degrees to nearest hundredth.

Answer:

a)  p = 21.4 cm (nearest tenth)

B)  P = 45.6° (nearest tenth)

Step-by-step explanation:

As triangle PQR is a right triangle, we can use Pythagoras Theorem to find the length of p.

Pythagoras Theorem

[tex]a^2+b^2=c^2[/tex]

where:

From inspection of the triangle:

Substitute the given values into the formula and solve for p:

[tex]\implies 21^2+p^2=30^2[/tex]

[tex]\implies 441+p^2=900[/tex]

[tex]\implies 441+p^2-441=900-441[/tex]

[tex]\implies p^2=459[/tex]

[tex]\implies \sqrt{p^2}=\sqrt{459}[/tex]

[tex]\implies p=\pm 3\sqrt{51}[/tex]

As p is the length, p can be positive only.

Therefore, p = 21.4 cm (nearest tenth)

To find the angle P, use the cosine trigonometric ratio.

Cosine trigonometric ratio

[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]

where:

From inspection of the triangle:

Substitute the given values into the formula and solve for P:

[tex]\implies \sf \cos P=\dfrac{21}{30}[/tex]

[tex]\implies \sf P=\cos^{-1}\left(\dfrac{21}{30}\right)[/tex]

[tex]\implies \sf P=45.572996^{\circ}[/tex]

Therefore, the measure of angle P is 45.6° (nearest tenth).

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The standard form of the given equation is: y = -3(x-6)²+35.

In mathematics, the most typical way to represent a specific element is called standard form.

A standard form is a way to express a particular mathematical idea, such as an equation, number, or expression, in prose that adheres to a set of criteria.

Given equation is: y = − 3x² + 36x - 73

In order to convert to the standard form,

y+73 = −3x² +36x

Subtract 108 from both the sides,

y+73-108 = −3x² +36x-108

y-35 = -3(x² -12x+36)

y-35 = -3(x-6)²

y = -3(x-6)²+35

This is the required standard form, corresponding to the given equation.

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Answer:

no hdjsjfjabjsjfbsbajdisjsb

The triangle can be a right triangle

The side lengths are given as:

3, 3 and 3√2

If the triangle is a right triangle, then the following must be true

a^2 = b^2 + c^2

Where a is the longest side.

So, we have:

[tex](3\sqrt 2)^2 = 3^2 + 3^2[/tex]

Evaluate the expressions

18 = 18

Both sides of the equation are equal

Hence, the triangle can be a right triangle

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Answer:

Simplified = 5

Classification = Monomial

Step-by-step explanation:

Given expression:

 3x² + 6x + 5 - 3x (2 + x)

Expand parenthesis by distributive property:

= 3x² + 6x + 5 - 3x (2) - 3x (x)

= 3x² +6x + 5 - 6x - 3x²

Put like terms together:

= 3x² - 3x² + 6x - 6x + 5

= 0 + 0 + 5

= [tex]\boxed{5}[/tex]

Concept:

Polynomial is classified by the number of terms a polynomial has.

Classify the given expression:

Original = 3x² + 6x + 5 - 3x (2 + x)

Simplified = 5

5 is a constant and it has only one term

Therefore, it is a monomial.

Hope this helps!! :)

Please let me know if you have any questions

The answer is 5, which is a monomial.

Let's simplify using the distributive property.

If the resulting expression has only one term, it is classified as a monomial.

Answer:

100

Step-by-step explanation:

If the base is 20, then 2 of the sides must have a length of 20. This means that the TOTAL length of the remaining sides is 10. (20*2) + (10) = 50. If we divide that in half, we get 5. That is the side length of the remaining 2 sides. This means that 20 * 5 will give us the area (b*h).

Given,

base, b = 20mm &

perimeter, p = 50mm.

the area of the rectangle : (50 – 20 × 2) ÷ 2 = 5. 5 × 20 = 100 [tex]mm^{2}[/tex].

Perimeter and area are two important and basic mathematical subjects. They help quantify the physical space and also provide a more advanced foundation of mathematics in algebra, trigonometry, and calculus. Perimeter is a measure of the distance around a shape, and area indicates how much area the shape covers.

The perimeter of a 2D shape is the distance around the shape. You can imagine wrapping a string around a triangle. The length of this cord is around the triangle. Or, if you're traveling outside the park, take a route that goes around the edge of the park.

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The number of songs that Deante' would have downloaded during month 9 is 58 songs.

A regression line is a statistical line that best describes the behavior of a data set and such, it is a line that best fits a set of data.

By using Microsoft excel to plot the data on a scatter plot, we can logically deduce that line of best fit for the songs downloaded is given by:

y = 2.03x + 39.7

Thus, the number of songs that Deante' would have downloaded during month 9 is:

y = 2.03(9) + 39.7

y = 18.27 + 39.7

y = 57.97 ≈ 58 songs.

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Answer:

A) ŷ = 2.03X + 39.73

B) 58

Step-by-step explanation:

A line of best fit is a line drawn on a scatter plot that shows the trend and the best estimation of the relationship between x and y.

After graphing it, it's easy to find the point at which x and why intersect along the line where x is nine.

Using the equation, just replace x with nine and solve.

Using the binomial distribution, the probabilities are given as follows:

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters for this problem are:

n = 10, p = 0.4.

The probability that more than 4 weigh more than 20 pounds is:

[tex]P(X > 4) = 1 - P(X \leq 4)[/tex]

In which:

[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.4)^{0}.(0.6)^{10} = 0.0061[/tex]

[tex]P(X = 1) = C_{10,1}.(0.4)^{1}.(0.6)^{9} = 0.0403[/tex]

[tex]P(X = 2) = C_{10,2}.(0.4)^{2}.(0.6)^{8} = 0.1209[/tex]

[tex]P(X = 3) = C_{10,3}.(0.4)^{3}.(0.6)^{7} = 0.2150[/tex]

[tex]P(X = 4) = C_{10,4}.(0.4)^{4}.(0.6)^{6} = 0.2502[/tex]

Hence:

[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0061 + 0.0403 + 0.1209 + 0.2150 + 0.2502 = 0.6325[/tex]

[tex]P(X > 4) = 1 - P(X \leq 4) = 1 - 0.6325 = 0.3675[/tex]

0.3675 = 36.75% probability that more than 4 weigh more than 20 pounds.

The probability that fewer than 3 weigh more than 20 pounds is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0061 + 0.0403 + 0.1209 = 0.1673

0.1673 = 16.73% probability that fewer than 3 weigh more than 20 pounds.

For more than 7, the probability is:

[tex]P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 8) = C_{10,8}.(0.4)^{8}.(0.6)^{2} = 0.0106[/tex]

[tex]P(X = 9) = C_{10,9}.(0.4)^{9}.(0.6)^{1} = 0.0016[/tex]

[tex]P(X = 10) = C_{10,10}.(0.4)^{10}.(0.6)^{0} = 0.0001[/tex]

Since P(X > 7) < 0.05, it would be unusual if more than 7 of them weigh more than 20 pounds.

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The total earnings in commission is $93.50

The given parameters are:

Commission = $5.50

Items = 17

The total commission is:

Total = $5.5 0 * 17

Evaluate

Total = $93.50

Hence, the total earnings in commission is $93.50

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Answer:

33600 m²

Step-by-step explanation:

The top and bottom horizontal sides are parallel, so this is a trapezoid with bases DC and AB. The height is BC.

area of trapezoid = (a + b)h/2

where a and b are the lengths of the bases, and h is the height.

We need to find the height, BC.

Drop a perpendicular from point A to segment DC. Call the point of intersection E. E is a point on segment DC.

DE + EC = DC

EC = AB = 360 m

DC = 600 m

DE + 360 m = 600 m

DE = 240 m

Use right triangle ADE to find AE. Then BC = AE.

DE² + AE² = AD²

DE² + 240² = 250²

DE² = 62500 - 57600

DE² = 4900

DE = √4900

DE = 70

BC = 70 = h

area = (a + b)h/2

area = (600 m + 360 m)(70 m)/2

area = 33600 m²

Answer:

33,600 m^2.

Step-by-step explanation:

This is a trapezium, so

Area = (h/2)(a + b)

=  (h/2) ( 360 + 600)

= 960h / 2

= 480h,

We find the value of h using Pythagoras:

250^2 = h^2  + (600-360)^2

h^2 =  250^2 - 240^2 = 4900

h = 70.

So the Area = 70 * 480

= 33,600 m^2

The equation that describes how the parent function, y = x³, is vertically stretched by a factor of 4 is y = 4x³.

When an equation is vertically stretched, it means that the parent equation has been multiplied by a number that is more than one.

This means that the equation is multiplied by some factor.

It is given that we should describe how the parent function is vertically stretched by a factor of 4.

The parent function is given as y = x³.

Since the equation is said to be vertically stretched by a factor of 4, we must multiply the parent equation by 4 to stretch it.

Therefore, we have found the equation that describes how the parent function, y = x³, is vertically stretched by a factor of 4 to be y = 4x³.

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Answer: C

Step-by-step explanation:

Just C

Answer:

10. Area: ((6+4) * 8)/2 = 40 ft^2

Perimeter: 6 + 4 + 8 + 12.8 = 30.8 ft

8. 22 + 22 + 22 + 38 + 27.2 = 131.2 ft

A system equations that can be used to determine after how many months the boys will owe the same amount is

60 x = $ 1000

20 y = $ 600

In mathematics, a system of equations, also known as a system of simultaneous or systems of equations, is a finite system of equations for which we have sought common solutions. A system of equations can be classified in a similar way to simple equations. A system of equations finds application in our everyday life in modeling problems where unknown values can be represented in the form of variables.

In algebra, a system of equations contains two or more equations and looks for common solutions to the equations. "A system of linear equations is a set of equations that are satisfied by the same set of variables."

We need to find a system equations that can be used to determine after how many months the boys will owe the same amount

Let lan take x months to pay $ 1000 to his parents

In 1 month Ian pays $60

In x months Ian pays =

60 x= $ 1000

Let Ken take y months to pay $ 600 to his parents

In 1 month Ian pays $20

In y months Ian pays =

20 y= $ 600

Hence 60 x= $ 1000 and 20 y= $ 600 are the system of equations

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Answer:

The Answer Is 382...

Step-by-step explanation:

The Mean will decrease while the Median and the Mode will remain with the same amount.

For Central Measures, we have Median, Mode and  Mean. They try to describe the whole distribution by one value, in the center of it.

For this question, let's pick some examples from the Old Faithful, WY Station to the National Oceanic and Atmospheric Administration from 2015, January

1st Case Scenario:

For 7 days of precipitation, (Snow, ice pellets, etc. rain) in inches:

19 19 19 24 23 23 23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Mean = 5

Median=0 (the sum of the 15th+16th position over 2)

Mode=0 (Most common observations)

2nd Case Scenario

For 3 days of precipitation, (Snow, ice pellets, etc. rain) in inches:

0 0 0 24 0 0 23 0 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Mean = 2.2

Median =0

Mode=0

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Answer:

[tex]log_{2}[/tex] 20

Step-by-step explanation:

using the rule of logarithms

loga + logb = logab

then

[tex]log_{2}[/tex]4 + [tex]log_{2}[/tex]5

= [tex]log_{2}[/tex] (4 × 5)

= [tex]log_{2}[/tex]20

Step-by-step explanation:

3x° + 2x° = 180° ( supplementary angle )

5x° = 180°

x = 180° / 5

x = 36°

[tex]...[/tex]

The inverse function of [tex]A(b) = 12 \cdot \frac{b + 9}2[/tex] is b(a) = a/6 - 9

The function is given as:

[tex]A(b) = 12 \cdot \frac{b + 9}2[/tex]

Divide 12 by 2

[tex]A(b) = 6 \cdot (b + 9)[/tex]

Rewrite the function as

[tex]a = 6 \cdot (b + 9)[/tex]

Divide both sides by 6

a/6 = b + 9

Subtract 9 from both sides

b = a/6 - 9

Express as a function

b(a) = a/6 - 9

Hence, the inverse function of [tex]A(b) = 12 \cdot \frac{b + 9}2[/tex] is b(a) = a/6 - 9

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Answer:

13 in

Step-by-step explanation:

let w be width then length is w + 6

the area (A) of a rectangle is calculated as

A = length × width , then

A = w(w + 6) = 91 , that is

w² + 6w = 91 ( subtract 91 from both sides )

w² + 6w - 91 = 0 ← in standard quadratic form

(w + 13)(w - 7) = 0 ← in factored form

equate each factor to zero and solve for w

w + 13 = 0 ⇒ w = - 13

w - 7 = 0 ⇒ w = 7

however, w > 0 then w = 7

and length = w + 6 = 7 + 6 = 13 in

The open circles on 1 and 2 describe the graph of {x | 1 < x < 2}.

According to the statement

we have to describe the graph of {x | 1 < x < 2}.

In this type of graph there will be open circle because there is no equal sign in the statement.

there will be a line segment in between...because basically, u would put an open circle on 1, and open circle on 2 and shading in between.

so, in this statement we have given a some statements which are represent the given graph but only one. and from all of these

The condition having a open circles 1 and 2 represent the graphical representation than others because except this condition all are incapable to represent the graph.

So, The open circles on 1 and 2 describe the graph of {x | 1 < x < 2}.

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AB will be an Identity matrix.

As it is given in the description itself, if the answer to a matrix multiplication problem is an identity matrix, then each of the two matrices is an inverse matrix of the other.

Therefore, AB will be an Identity matrix.

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Answer:

AB= I

ABA=A

BBA=B

BBAA=I

Step-by-step explanation:

just took the test on edge. 2022

Answer:

1/25

Step-by-step explanation:

Answer:

I think it may be 1/1225

Step-by-step explanation:

first chance is 2/50 and second chance is 1/49 as one card decrease at first. So multiplying it we get 1/1225.

Answer:

64 times

Step-by-step explanation:

16 hours to minutes: 16*60 = 960 minutes

vaping every 15 minutes: 960/15 = 64

Answer:

[tex]\sf x = \dfrac{n - 2mp}{2m}[/tex]

Step-by-step explanation:

              [tex]\sf 3m = m + \dfrac{n}{p + x}\\[/tex]

        [tex]\sf 3m - m = \dfrac{n}{p +x}[/tex]

                [tex]\sf 2m = \dfrac{n}{p +x}[/tex]

Now cross multiply,

          2m*(p +x) = n

To open the parenthesis, multiply 2m by p and x.

        2mp + 2mx = n

 Isolate the term with variable 'x'

                    2mx = n - 2mp

Now, isolate 'x', by dividing both sides by 2m

                          [tex]\sf x = \dfrac{n-2mp}{2m}[/tex]                            

Answer:

x = [tex]\frac{N-2MP}{2M}[/tex]

Step-by-step explanation:

3M = M + [tex]\frac{N}{P+x}[/tex] ( subtract M from both sides )

2M = [tex]\frac{N}{P+x}[/tex] ( multiply both sides by P + x to clear the fraction )

2M(P + x) = N ← distribute parenthesis on left side

2MP + 2Mx = N ( subtract 2MP from both sides )

2Mx = N - 2MP ( divide both sides by 2M )

x = [tex]\frac{N-2MP}{2M}[/tex]

Answer:

1954

Step-by-step explanation:

11*7*50

Length of BD is 11 units.

The intersecting chords theorem or just the chord theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.

Let length of AE be x

By intersecting chords theorem,

AE(ED) = BC(DE)

x(x + 12) = (x +2)(x +5)

x² + 12x= x² + 7x + 10

5x = 10

x = 2

BD = BE + DE

= x + x +7

= 2x + 7

= 2(2) + 7

= 11 units

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Answer:

to find domain just take the first values of each ordered pairs.

to find range take the second values of the ordered pairs.

Answer:

B) (6, 17)

Step-by-step explanation:

y = 3x - 1

To find a solution to the equation

Let x = 6

y = 3*6 -1

y = 18-1

y = 17

One possible solution is ( 6,17)

This is choice B

Answer:

Step-by-step explanation:

you are right AC is 16 because A-C are the same length