the 66th term of the arithmetic sequence - 10, 7, 24, ...

The slope of the linear equation is 0, so this is a horizontal line.

A linear equation is of the form:

y = a*x + b

Where a is the slope and b is the y-intercept.

Particularly, if a a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have the points  (7, -4) and (11,−4), then the slope is:

a = (-4 + 4)/(11 - 7) = 0

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Answer:

the answer will be a negative answer

Step-by-step explanation:

The smallest drawing will be the one that has the smallest drawing unit with respect to the the actual unit.

We have:

A. 1 in to 1 ft

B. 1 in to 1 m

C. 1 in to 1 yd

If we put them all in meters, we have:

A. 1 in to 0.3048 m

B. 1 in to 1 m

C. 1 in to 1/1.1 = 0.90... meters

Then, the small drawing will be B, as 1 meter is the largest actual unit.

Second, will be B, that has 1 in by approximately 0.9 meters.

Third and last, option A, which drawing has an scale of 1 in in 0.3048 meters.

We can calculate the scale as a ratio between the drawing units and actual units, expressed in the same units.

For example, for A, we have:

So the scale is 1:12.

NOTE: look that we have cancelled all the units with this operation.

For B, we have:

For C, we have:

You can verify that B has the smallest scale (0.0254)

The condition for the figure to be similar is that; DE = FD

Similar figure are zoomed in or zoomed out (or just no zoom) version of each other. They are scaled version of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.

In the problem, the ratio should be CD/DE = GD/DF

We can also write the ratios of the corresponding sides as:

CD/DE = GD/DF

Therefore, CE and GF are similar

Thus, the condition for the figure to be similar is that;

DE = FD

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The $7,834.54 borrowed at 18.6% annual interest rate with the landscape architect's monthly payment of $500, gives the number of months it will take to repay the debt as approximately 19 months

Monthly payment on a loan, is the amount the person who takes the loan, pays each month in order to settle the loan in a given time period.

The monthly payment formula is presented as follows;

[tex] \displaystyle{M = \frac{P \cdot \left( \frac{r}{12} \right) \cdot \left( 1 + \frac{r}{12} \right)^{n} }{\left( 1 + \frac{r}{12} \right)^{n} - 1} }[/tex]

Where;

M = The amount the landscape architect paid monthly = $500

P = The amount loaned or borrowed = $7,834.54

r = The interest per annum = 18.6%

n = The number of monthly payment made

Therefore;

[tex] \displaystyle{500 = \frac{7834.54 \cdot \left( \frac{0.186}{12} \right) \cdot \left( 1 + \frac{0.186}{12} \right)^{n} }{\left( 1 + \frac{0.186}{12} \right)^{n} - 1} }[/tex]

Evaluating the above equation gives;

[tex] \displaystyle{500 = \frac{121.43537.1 \cdot 1.0155^{n} }{1.0155^{n} - 1} }[/tex]

[tex] \displaystyle{500 \times (1.0155^{n} - 1) = 121.43537.1 \cdot 1.0155^{n} }[/tex]

[tex] \displaystyle{500 \times 1.0155^{n} - 121.43537.1 \cdot 1.0155^{n} ) = 500 }[/tex]

Which by taking natural logarithms of both sides gives;

n•ln(1.0155) = ln(1.32077843609)

n = ln(1.32077843609) ÷ ln(1.0155) ≈ 18.09

Rounding up to the nearest month gives;

The number of months it will take the architect to pay the debt is approximately 19 months

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The radical form of the expression  (5ab)[tex]^\frac{3}{2}[/tex]  is √(125 a³b³).

Simply put, simplifying a radical eliminates the need to find any more square roots, cube roots, fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.

The sign used to represent the square root or nth root. Square-root-containing expressions are known as radical expressions.

Radical equation  = b[tex]\frac{m}{n}[/tex]  

= [tex]\sqrt[n]{b^m}[/tex]

So,

(5ab)[tex]^\frac{3}{2}[/tex] = [tex]\sqrt[2]{5^3}[/tex]

[tex]\sqrt[2]{5^3}[/tex] a³ b³

5³ = 125

√(125 a³b³)

The radical form of the expression  (5ab)[tex]^\frac{3}{2}[/tex]  is √(125 a³b³).

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The value for the volume of the room is 31. 84  cubic centimeters(cm³)

The mass of the air in the room is  41. 39 kg

The formula for calculating the volume of the room is expressed as;

Volume = l × w × h

Where;

From the information given, we have to substitute the values of the measurements of the room into the formula.

We have;

Volume, v = 4. 02 × 3. 37 × 2. 35

Volume, v = 31. 84 cubic centimeters(cm³)

To determine the mass of the air in the room, we use the formula for mass which is expressed as;

Mass = Density × volume

Given that;

Substitute the values

Mass = 1. 3 × 31. 84

Mass = 41. 39 kg

Hence, the volume is 31. 84  cubic centimeters(cm³)

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Answer:

Paint them white as it looks better

Step-by-step explanation:

Yellow is a very bad choice to paint a room

Answer:

1100

Step-by-step explanation:

783 rounded to the nearest hundred is 800

329 rounded to the nearest hundred is 300

800+300=1100

The estimation of 783 + 329 = 1100.

Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.

Given:

783 + 329

Now rounding off nearest hundred

783 rounded off to 800

and, 329 rounded off to 300.

So, 800+ 300 = 1100

Hence, the estimation is 1100.

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Answer: Number 5. is B-7CM

Number 8. is y=2/x

Step-by-step explanation:math

The length of the other parallel side = 7.5 cm

what is trapezium?

Trapezium is the quadrilateral whose only one pair of side is parallel.

as we know ;

       AREA OF TRAPEZIUM=1/2*(sum of parallel side)*(height)

       given:- one parallel side = 10 cm

                    height = 16 cm

                    Area= 140 cm

         Assume:-

                    other parallel side =x cm

   so,

           140=1/2*(10+x)*16

           140*2/16=10+x

           280/16=10+x

           35/2=10+x

           17.5-10=x

           x= 7.5cm

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The equation of the line that passes through the graph is y + 2 = -3/2(x - 2)

The graph represents the given parameter

From the graph, the points are given as

(0, 1) and (2, -2)

Calculate the slope of the points using

Slope = (y₂ - y₁)/(x₂ - x₁)

Rewrite as

m = (y₂ - y₁)/(x₂ - x₁)

This means that

Slope = m

So, we have the following representation

m = (-2 - 1)/(2 - 0)

Evaluate

m = -3/2

The equation of the line is then calculated as

y = m(x - x₁) + y₁

Where

(x₁, y₁) = (2, -2)

m = -3/2

So, we have

y = -3/2(x - 2) - 2

Add 2 to both sides

y + 2 = -3/2(x - 2)

Hence, the equation of the line is y + 2 = -3/2(x - 2)

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Answer:

Describe how anthropology challenges more commonly held notions of progress

Step-by-step explanation:

Answer:

y = x in the slope intercept form

y - 2 = 1(x -2) in the point-slope form of a line

Step-by-step explanation:

Perpendicular slopes are opposite reciprocals of each other.  So the perpendicular slope would be 1.

We could write this in the point slope form of a line and the answer would be:

y - 2 = 1(x -2)  This would be the point slope form of a line.

If you want your answer in the slope intercept form

y -2 = 1(x-2)

y - 2 = x - 2  Add two to both sides

y = x

WHAT DO WE KNOW ABOUT PERPENDICULAR LINES ?

IS THAT WHEN THEIR GRADIENTS ARE MULTIPLIED THEY GIVE A PRODUCT OF -1.

TO FIND THE GRADIENT OF THE LINE PERPENDICULAR TO THE LINE WITH SLOPE/GRADIENT -1 WE CAN SAY

[tex]m1 \times m2 = - 1 \\ - 1 \times m2 = - 1 \\ m2 = 1[/tex]

THIS MEANS THAT THE GRADIENT OF THE NEW LINE IS 1

the general equation of the straight line is y=mx+c

[tex] - 2 = 1(2) + c \\ - 2 = 2 + c \\ c = - 2 - 2 \\ c = - 4[/tex]

This means that

[tex]y = 1x - 4 \\ simply \\ y = x - 4[/tex]

The first skater has a 40 meter d and is traveling at a rate of 12 meters second, second skater is traveling rate of 14 meters per second. it will take 20 seconds for second skater to pass the first skater.

Time is continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in conscious experience. Time is often referred to as fourth dimension, along with three spatial dimensions.

Time has long been an important subject of study in religion, philosophy, and science, but defining it in manner applicable to all fields without circularity has consistently eluded scholars. Nevertheless, diverse fields such as business, industry, sports, the sciences, and performing arts all incorporate some notion of time into their respective measuring systems.

12x+40=14x

40=2x

x=20

it will take 20 seconds for second skater to pass the first skater.

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Answer:

If area of sector = area of circle

1/3π(r+4)^2= πr^2

r^2-4r-8 =0

A sector is a cut out section of a circle. It is of two radii and an arc .

The area of a sector is angle substended/ 360 x area of a circle

area of a circle is πr^2

if area of circle is equal to the area of sector

120/360×π(r+4)^2=πr^2

divide both side by π

1/3(r+4)^2=r^2

multiply both sides by 3

(r+4)^2=3r^2

opening the bracket

(r+4)(r+4)=3r^2

r^2+ 8r +16=3r^2

3r^2-r^2- 8r -16=0

2r^2- 8r -16=0

divide all by 2

r^2- 4r -8=0

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Answer:  8x + 3, where x is the number of hours

Answer:

40

Step-by-step explanation:

[tex]m \angle 2=20^{\circ}[/tex] (angle sum of triangle)

[tex]m\angle 1=40^{\circ}[/tex] (angle sum of triangle)

Answer:

y = [tex]\frac{1}{4}[/tex] x - 6

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 m = [tex]\frac{1}{4}[/tex] , then

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

to find c substitute (- 8, - 8 ) into the partial equation

- 8 = - 2 + c ⇒ c = - 8 + 2 = - 6

y = [tex]\frac{1}{4}[/tex] x - 6 ← equation of line

The recursive formula of the arithmetic sequence is:

xₙ = n*4 + 13

With that we can see that x₁₁ = 57

Here we know that the first elements of the sequence are:

17, 21, 25, 29, ...

To find the common difference, d, we take the difference between any two consecutive elements, so we have:

c = 21 - 17 = 4

Then the recursive formula for the n-th term is:

xₙ = n*4 + d

The first element x₁ is 17, so we will have:

17 = 1*4 + d

17 - 4 = d = 13

The recursive formula is:

xₙ = n*4 + 13

b) the eleventh term of the sequence is given by replacing n in the above formula by 11.

x₁₁ = 4*11 + 13 = 44 + 13 = 57

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The equation for the line that is parallel to the given line and goes through the point (-8 2), is y = 3x + 26. See the explanation below.

Recall that the equation for the line is always given as:

y = mx + b

Where m is the slope.

Assuming that you have a line  y = 3x + 2

The line parallel to this line but intersecting the point (-8,2) is found by using y = mx + b and solving for b

m = 3; x = -8; and y = 2

b = y - mx

b = (2) - (3) (-8)

b = 26

Hence the equation for the line that is parallel to the given line going through point (-8, 2) is
y = 3x + 26

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Full Question:

Find the equation in slope-intercept form of the line y= 3x + 2 that passes through the point (-8,2) and is parallel to the line.

Answer:

Step-by-step explanation:

The option that is most suitable for tabular data will be provided by-

Jasim's last week's total pay was £286.2.

Tabular data is data presented in the form of rows and columns.

Here,

Total time for which Jasim works last week = 30 hours

Time for which Jasim works at the weekend = 12 hours

Time for which Jasim works at the weekdays = (30 - 12) hours

                                                                           = 18 hours

Jasim's pay during weekdays = £8.70

Jasim's pay during weekends = £10.80 per hour

Jasim's pay during weekdays last week = £8.70 [tex]\times[/tex] 18

                                                                   = £156.6

Jasim's pay during weekends = £10.80

Jasim's pay during weekends = £10.80 per hour

Jasim's pay during weekdays last week = £10.80 [tex]\times[/tex] 12

                                                                   = £129.6

Total pay of Jasim for last week = £(156.6 + 129.6)

                                                     = £286.2

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The ordered pairs in the solution set of the system of linear inequalities y ≥ -1/3x +2 and y < 2x + 3 are (2, 2), (3, 1), and (4, 2).

Given linear inequalities represented in the graph are:

y ≥ -1/3x +2

y < 2x + 3

In the graph, the shaded region above the solid line denotes the inequality,

y ≥ -1/3x +2

The shaded area on the right side of the dotted line denotes the inequality's solution set,

y < 2x + 3

And the common area of these inequalities will denote the solution set of the system of linear inequalities.

Ordered pairs are (2, 2), (3, 1), and (4, 2) and will therefore be located in the shared shaded area.

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The maximum amount Cedar should pay for monthly rent is 13,500.

We need to know the maximum amount of monthly rent cost to solve this problem. In this country, the department of housing and urban development has ruled that the maximum monthly rent cost is 30% of gross profit.

Max cost = 30% Gross

From the question above, the given parameter is

Gross profit = 45,000

By substituting the given parameter, the maximum monthly rent cost is

Max cost = 30% Gross

Max cost = 30% x 45,000

Max cost = 13,500

Hence, the monthly rent cost should have a maximum amount of 13,500.

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Answer: yes it is rational

Step-by-step explanation:

Answer: 89.396668... is a rational number

Step-by-step explanation:

Answer:

168 and 170

Step-by-step explanation:

Answer:

mperpendicular = −2/5

Step-by-step explanation: