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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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Answer: yes it is rational

Step-by-step explanation:

Answer: 89.396668... is a rational number

Step-by-step explanation:

A) W is a sub space of V

given that V =R^4 and W= [(x1, x2, x3, 0)|x1 ,x2, x3 E..R]

W is a subspace of V because of the following.

let  (x1, x2, x3, 0), (y1, y2, y3, 0)  ∈  W and a, b  ∈ V

now  

a(x1, x2, x3, 0)+b (y1, y2, y3, 0)= (a x1, a x2, a x3, 0)+(b y1, b y2,b y3, 0)

= (a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ,0+0)=  

(a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ,0+0)

LHS =RHS

∈W

since  (a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ) are all elements of R

W is closed under vector addition and scalar multiplication.

Hence W is a sub space of V.

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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.

by using the unitary method, 11 inches of wire can be bought for 44 cents.

We are given that:

14 inches of wire costs 56 cents.

14 inches = 56 cents

Now, by using the unitary method, we get that:

1 cent = 14 / 56 inches.

1 cent = 1 / 4 inches.

Now, for 44 cents, by using the multiplication, we get that:

44 cents = 1 / 4 inches × 44

44 cents = 11 inches.

Therefore, we get that, by using the unitary method, 11 inches of wire can be bought for 44 cents.

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The counterexample of the statement "the difference of two numbers is greater than the greater number if the smaller number is greater than twice the additive inverse of the greater number"

"The difference of two numbers less than the greater number," is how the claim is expressed.

Give us x and y, where x is greater than y.

Thus, the statement can be interpreted as follows:

x - y < x

To both sides, add x.

-y < 2x

Replace with: y > -2x

This indicates that only when the smaller number is higher than twice the additive inverse of the larger number is the assertion true.

The smaller number must be bigger than twice the additive inverse of the larger number in order for the statement "the difference of two numbers is greater than the greater number" to be false.

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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:

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]

Answer: 6391000 or 6.391 x 10^6

Step-by-step explanation:

**First, convert 7.7 x 10^2 to a number**

770

**Then multiply 8300 and 770**

6391000

**Convert to scientific notation**

6.391 x 10^6

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The area hexagon using Lin's and Andre's method is:

By Lin's method = 93.48inch^2

By Andre's method = 93.53 inch^2

What is Mensuration ?

The field of mathematics known as mensuration explores how to measure geometric objects and their attributes, such as length, volume, shape, surface area, lateral surface area, etc.

By Lin's method

He parted the hexagon into six equilateral triangle

So, area of equilateral triangle = √3/4 × (side)^2

Since the given side = 6inch

Therefore,

                area of equilateral triangle = √3/4 × (6)^2

                                                              =√3/4 × 36

                                                              = √3 x 9

                                                              = 1.732 x 9

                                                              = 15.58inch^2

The area of hexagon will be = 15.58 x 6

                                               = 93.48inch^2

Now, By Andre's method

he parted two triangle and one rectangle

The triangle has two equal side that means its an isosceles triangle

Area of isosceles triangle using only sides = ½[√(a^2 - b^2/4) × b]

given,

base = 10.4 inch

side = 6 inch

Area of isosceles triangle using only sides = ½[√(a^2 - b^2/4) × b]  

                                                                       = ½[√(6^2 - 10.4^2/4) × 10.4]

                                                                       = ½[√(36 - 108.16 /4) ×10.4]

                                                                       = ½[√(36 - 27.04) × 10.4]      

                                                                       = ½[√(8.96) × 10.4]

                                                                       = ½[2.99 × 10.4]  

                                                                       = 15.56inch^2

for two triangles the area will be =    15.56 x 2

                                                      = 31.13 inch^2

Now, area of rectangle = length x width

where,

Length = 10.4 inch

Width = 6 inch

So,

     area of rectangle = 10.4 x 6

                                   = 62.4 inch^2

Then, The area of hexagon will be = area of rectangle + area of two triangle

                                                          = 62.4 inch^2 + 31.13 inch^2

                                                          = 93.53 inch^2

Hence, by both methods the area from Lin's method = 93.49 inch^2

and by Andre's method = 93.53 inch^2

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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 function is decreasing because it is going down.

The domain is the set of x-values, which is [tex]x \leq 4[/tex] or [tex](-\infty, 4][/tex].

The range is the set of y-values, which is [tex]-6 \leq y < -1[/tex] or [tex][-6, -1)[/tex].

Answer:

Paint them white as it looks better

Step-by-step explanation:

Yellow is a very bad choice to paint a room

⇒[tex]=(y+3)(y+7)\\=y(y+7)+3(y+7)\\=y^{2} +7y+3y+21\\=y^{2} +10y+21[/tex]

Attached is the solution in detail

Answer:

168 and 170

Step-by-step explanation:

Answer:

Describe how anthropology challenges more commonly held notions of progress

Step-by-step explanation:

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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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 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 inequality that shows the least amount of money she needs to deposit to avoid a fee is 585.43 - 302.05 + x ≥ 300

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let x represent the least amount of money Keisha needs to deposit to avoid a fee. Keisha has $585.43 in her checking account and must maintain a balance of $300 to avoid a fee. She wrote a check for $302.05 today, Hence:

585.43 - 302.05 + x ≥ 300

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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:

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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When Walt mixes fruit punch for a party, the total liquid measure of the punch is 53 pints.

As given in the question,

Conversion factor as follows:

1 gallon = 8 pints.

1 quart = 2 pints.

Walt is mixing fruit punch for a party

Convert all the units to pints we get,

Walt combines 1 gallon 2 quarts 3 pints of orange juice, which is equivalent to 15 pints

He also combines 1 gallon 3 quarts 7 pints of pineapple juice, which is equivalent to 21 pints

He then combines 1 gallon 3 quarts 3 pints of ginger ale, which is equivalent to 17 pints.

Total measure of the punch = 15 + 21 + 17 = 53 pints.

Therefore, when Walt mixes fruit punch for a party, the total liquid measure of the punch is 53 pints.

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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 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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