Write a proof
given: angle 1 and angle 3 are supplementary
prove: m is parallel to n

The graph of the model is (c) and the equation of the model is (d) y = 1.030 * 3.709^x

From the table of values, we can see that:

As the time increases, the distance increases

However, the increment in the distance is not a linear increment.

This means that:

The graph (b) represents an exponential model.

When the points on the table are entered in a graphing calculator, we have the regression equation to be

y = 1.030 * 3.709^x

Hence, the graph of the model is (c) and the equation of the model is (d) y = 1.030 * 3.709^x

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The work required to pump the water out of the spout is 5000ft⋅lb

Given

The volume V=12(4ft)(5ft)(6ft)=60ft3,

Then the weight is w = γV = (62.5lb /ft³) (60ft³) = 3750lb.

Since work is force × distance, you need a distance here, and the appropriate one is the distance you must raise the center of mass to get the H2O out of the spout.

Since the center of mass of a uniform triangular area is 13 of the way from any side, the distance is (4ft)/3 so the work is (3750lb) (4ft)/3=5000 ft-lb.

In calculus, the area of a horizontal section yft from the lowest point is (5ft) × (6ft) × y / (4ft) = 7.5y ft2.

We have to lift that slice 4ft−y, so work is

w = [tex]\int\limits^4_0[/tex] (62.5)(4 − y) (7.5y)

dy = (62.5)[15y2−2.5y3]40  = 5000ft⋅lb

The work required to pump the water out of the spout is  5000ft-lb

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Answer:

62 and 150

Step-by-step explanation:

let the 2 numbers be x and y , x > y , then

x + y = 212 → (1)

x - y = 88 → (2)

add the 2 equations term by term to eliminate y

2x + 0 = 300

2x = 300 ( divide both sides by 2 )

x = 150

substitute x = 150 into (1)

150 + y = 212 ( subtract 150 from both sides )

y = 62

the 2 numbers are 62 and 150

Answer:

a. 6x^5- 3x^3+ 21

b. (6x^5+ 4x^4+21) -  (4x^5+ 3x^4+11)=  2x^5+ x^4+10 

Step-by-step explanation:

The degree of the polynomial is the highest power of the terms of the polynomial .e.g

x³+ 2ax+ b² is a polynomial of 3rd degree because the highest power of the terms given is 3.

As we need a polynomial of 5th degree the highest power will be

5.6x^5+ 4x^4+ 3x^3+ 5x^2+ x+21

But this polynomial has 5 terms. We need a 5th degree polynomial with three terms so it can be any one of the following

6x^5- 3x^3+ 21

6x^5+ 4x^4+21

6x^5+  5x^2+21

6x^5 + x+21

All of the above polynomials are in the standard form because the powers of the terms are given in decreasing order. The first term has the highest power and so on.

Part B:

Suppose we have 2 polynomials 

6x^5+ 4x^4+21 and 4x^5+ 3x^4+11

When the closure property of subtraction is applied 

(6x^5+ 4x^4+21) -  (4x^5+ 3x^4+11)

= 6x^5+ 4x^4+21 -  4x^5- 3x^4-11  → coefficients are changed b/e of subtraction

= 2x^5+ x^4+10 

the coefficients are changed because of subtraction.

In Polynomials the sign is changed due to subtraction and  same degree terms ( like terms) are subtracted to get the answer.

The formula speed = distance ÷ time can be rearranged, just like any other equation. The formula can be rearranged in three ways: speed = distance ÷ time , distance = speed × time.

Speed tells us how slow or fast an object moves.  Distance refers to extent of space between two events. Time refers to an interval separating two events.

ASSUME a ferry travels 1/7th of the distance between two ports in 3/5 hours , then it will be able to cover 5/6th part of the distance between two ports  in 3.5 hours.

Distance that the ferry would be able to trave in 1 hour can be found out by :

unit rate=distance / time

=1/7÷3/5

Reciprocal:

=1/7×5/3

=5/21th of distance per hour

The distance that the ferry would be able to travel in 3.5 hours:

= (5/21 ) ×3.5

=(5/21)×(7/2)

Further solving:

=(5/3)×(1/2)

5/6th of the distance between two ports.

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Disclaimer:

Your question was incomplete. Please check below the full content.

Complete question could be a ferry travels 1/7th of the distance between two ports in 3/5 hours , then it will be able to cover 5/6th part of the distance between two ports  in 3.5 hours.

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Answer:

Step-by-step explanation:

Answer:

9% only a guess.May not be correct..

[<Answer>] (3):

Hello! I'm Avery. And I would love to help you :)

---------------------------------------------------------------------------------------------------------

[<The Explanation>}:

Step one: Distribute

[tex]144 = -12(x + 5)[/tex]
[tex]144 = -12x - 60[/tex]

Step two: Add 60 to both sides

[tex]144 = -12x - 60\\144 + 60 = -12 - 60 + 60[/tex]

Step three: Simplify

Adding..Adding..(Done!): [tex]204 = -12x[/tex]


Step four: Divide both sides by the same factor

[tex]204 = -12x\\\frac{204}{-12} = \frac{-12x}{-12}[/tex]

Last and not least..Step five:

Divide then, Cancel the terms, Move the Variable to the left...

And.. x = -17 is the answer :D

----------------------------------------------------------------------------------------------------------

[<Ending>] <3

Hope this helps and if it's wrong, you can't sue me! >:D

Bye! Hope this works for you :)

Have a nice day! - Avery <3

The permutation illustrates that when the teacher decides to only use 6 posters, the number of arrangements that can be made will be 665280 ways.

When the teacher decides to only use 6 posters, the number of arrangements will be:

= 12P6

= 12!/(12 - 6)!

= 12!/6!

= 665280 ways.

The fundamental principle will be:

= 12 × 11 × 10 × 9 × 8 × 7

= 665280 ways

When the teacher uses all 12 posters, but wants to have a black & white poster at each end, the number of arrangements will be 203212800 ways.

When the teacher uses all 12 posters, but wants all the colored posters to be side-by-side, the number of arrangements will be:

= 4!8!

= 4 × 3 × 2 × 1 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 967680 ways.

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The true options include the following:

This is defined as a pictorial representation of data or variables in an organized manner.

Function f(x) = (x + 4)(x – 6)

Graph intersects the x-axis at points (-4,0) and (6,0).

x-coordinate of vertex = -4+6/2 = 1

y-coordinate of vertex = (1+4) (1-6) = 5(-5) = -25

The vertex is at the point (1,-25).

The graph is positive for all x< -4 or x>6.

The graph is negative for –4 < x < 6.

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sin(Q) = -(12/13)

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.  It is a branch of mathematics that deals with the relation between the angles and sides of a right-angled triangle.

cot(Q) = 5/12

sin(Q) = 1/cosec(Q)

[tex]sin(Q) = \frac{1}{\sqrt{1+{cot}^2(Q)}}\\sin(Q) = \frac{1}{\sqrt{1+\frac{25}{144}}}\\sin(Q) = \frac{1}{\sqrt{\frac{169}{144}}}\\[/tex]

sin(Q) = ±12/13

Because, π < Q < (3/2)π

Therefore, sin(Q) = -12/13

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Answer:

A- -12/13

Step-by-step explanation:

Answer:

Julia and Liz worked 10 hours to finish the project.

Step-by-step explanation:

I don't know if I am 100% right, but I believe this is the answer.

If you take the 24 hours it will take Julia to finish the project on her own and subtract the time it would take Liz you would have 12 hours left then take the 2 hours Liz has already been working on the project you would have 10 hours for both of them to finish the project together.

24 -12 = 12

12 - 2 = 10

Answer:

1 4/5

Step-by-step explanation:

On the number line, for every whole integer, the line is divided into fifths. The dot is one fifth away from the number two. Therefore, it is 4/5 in from 1 and the answer is 1 [tex]\frac{4}{5}[/tex].

Based on the vertices of quadrilateral PQRS, we can infer that quadrilateral PQRS is NOT a parallelogram.

Quadrilateral PQRS would be a parallelogram if the sides have the same slope as this would prove that they are parallel.

The slope of PQ is:

= (6 - 5) / (6 - 4)

= 1/2

The slope of RS is:

= (2 - 4) / (7 - 9)

= -2 / -2

= 1

The slopes are not the same so quadrilateral PQRS is NOT a parallelogram.

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Answer: The quadrilateral is not a parallelogram.

Step-by-step explanation:

I am given that the vertices of quadrilateral  PQRS are P(4,5), Q(6,6), R(9,4) and S(7,2). The slope formula applied to each pair of adjacent vertices gives the slopes of the sides:

slope of PQ= 1/2

slope of QR= -2/3

slope of RS= 1

slope of SP= -1

Since each side has a different slope, none of the sides are parallel. So quadrilateral  PQRS is not a parallelogram.

The perimeter of the inside of the track is 444.44m

Based on the information given, the length will be 150m and the width is 46m.

The circumference will be:

=2πr

= (2 × 3.14 × 46/2)

= 144.44

The length will be:

= 2 × 150

= 300

The perimeter of the oval will be:

= 300 + 144.44

= 444.44m

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By applying basic proportionality theorem (BPT), the length of side PC and BR are 25 cm and 9 cm respectively.

In order to determine the length of side PC and BR, we would apply basic proportionality theorem (BPT) as follows:

PC/CQ = AR/AQ

PC/15 = 20/12

Cross-multiplying, we have:

12PC = 20 × 15

PC = 300/12

PC = 25 cm.

For the length of side BR, we have:

PC/CQ = PB/BR

PC/15 = 15/BR

25/15 = 15/BR

25BR = 225

BR = 225/25

BR = 9 cm.

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The simplest form of 35/6 ÷ 5/4 is 14/3

Given,

35/6 ÷ 5/4

hence it is written as= 35/6 ×4/5

                                = 7×2/3×1

                                = 14/3

The simplest form of fractions are determined by following the given steps:

This number can't be further subdivided. Hence we get the the simplest form of 35/6 ÷ 5/4 as 14/3.

If we get numbers which share common highest common factor then divide the number by both numerator and denominator to bring the simplest form of number.

Therefore we get the simplest form of number as 14/3.

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Answer:

It is B

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

C is most relevant to the question

There are 10 line segments on a line with five different points on it.

Line:

A line is formed with infinite points and it is extended infinitely along a straight path in both directions.

Line segment:

The part of the line that lies between two distinct points on the line. This is also called the shortest distance between two points on the line.

Consider a line with five points on it as A, B, C, D, and E.

So, the possible line segments are

AB, AC, AD, AE, BC, BD, BE, CD, CE, DE

So, there are 10 line segments are formed on line with five different points.

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Option B is right perpendicular bisectors of the sides of the triangle

If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle. We have in a triangle there are some properties inherent.

One is the perpendicular bisectors of all sides are concurrent. These three concur at a point called the circumcentre of the triangle.

When we draw a perpendicular bisector for a side AB, we get that all points on the perpendicular bisector are equidistant from A and B.

When we take the point of intersection of the perpendicular bisector of AB and BC, we have the intersecting point S(say) is equidistant from A and B and also from B and C

In short, this is equidistant from all 3 vertices and hence is the centre of the circumcircle of triangle ABC

Therefore Option B is right perpendicular bisectors of the sides of the triangle.

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Answer:

120

Step-by-step explanation:

For this, all we have to do is multiply 750 by 16%. We know, from percent to decimal conversion, that 16% is 0.16 (divide the percent by 100 to convert to a decimal). From there, if we multiply 750 by 0.16, we get our answer to be 120

Answer:

9x² + 5x

Step-by-step explanation:

4x² + 6x + 5x²-x

Combine like terms:-

4x² + 5x² = 9x²

6x - x = 5x

9x² + 5x

-----------------------------

Answer: 11

Step-by-step explanation:

By the secant-secant theorem,

[tex]5(5+7)=(JK)(15)\\\\60=(JK)(15)\\\\JK=4\\\\\implies IJ=15-4=11[/tex]

The value of tan(Q) = 3/4, given that ΔQRS ~ ΔXYZ. Computed using properties of similar triangles. Hence, the second option is the best choice.

According to the properties of similar triangle, the corresponding sides of similar triangles are in proportion.

In the question, we are given that ΔQRS ~ ΔXYZ.

By properties of similar triangles, we know that:

QR/XY = RS/YZ = SQ/ZX.

From this, we can show that:

RS/SQ = YZ/ZX ...(i).

We are asked to find the value of tan(Q).

By trigonometric ratios, we know that:

tan(Q) = Perpendicular/Base = RS/SQ.

From (i), we know that RS/SQ = YZ/ZX.

From figure, we know that YZ = 9, and ZX = 12.

Thus, YZ/ZX = 9/12 = 3/4.

Thus, tan(Q) = RS/SQ = YZ/ZX = 3/4.

Hence, the value of tan(Q) = 3/4, given that ΔQRS ~ ΔXYZ. Computed using properties of similar triangles. Hence, the second option is the best choice.

The question is incomplete. The complete question can be seen in the figure.

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Answer:

Radius = 8 units

Length of arc AB = 8.37758 units

Step-by-step explanation:

The sector COD is 1/4 the size of the circle.

the vertex angle is 90° and a circle has 360° at the center.

So the area of sector COD/area of Circle = 90/360 = 1/4

This means the area of the circle is 4 * 50.24 = 200.96 square units

Area of circle = πr² where r is the radius
πr² = 200.96

r² = 200.96/ π = 63.9676 ≅ 64
Therefore r = √64 = 8 units

The circumference of the circle is 2πr = 16π units

arc AB has a vertex angle of 30°.

30°/360° = 1/6

So the length of the arc is 1/6th the circumference of the circle =

(1/6) * 16π  = 2.67π  units or 8.37758 units

Answer:

OB

Step-by-step explanation:

it's not a beacuasenhes not doing everyone

and we have no info on whether anyone serveylayed a sport so the only possible option is 2

Step-by-step explanation:

p=2L+2w

factorise

p=2(L+w)

p=2(20+14)

p=2(34)

p=68

This is also a perimeter of a rectangle

Hello!

Here, the 2 mathematical operations involved are : multiplication and addition.

From the order of operations, we know multiplication is followed by addition.

⇒ P = 2(20) + 2(14)

⇒ P = 40 + 28

⇒ P = 68

∴ The answer will be [tex]\fbox {68}[/tex]

Answer:

b = 4.5

Step-by-step explanation:

a = 4

c = 6

c² = a² + b²

6² = 4² + b²

36 = 16 + b²

b² = 36 - 16

b² = 20

[tex]b = \sqrt{20} [/tex]

b = 4.5