The vertices of a composite figure are given. Find the area of the figure.

G(-5, -1), H(-5, 1), I(2, 4), J(5, -1), K(1, -3)

Answer:

1.46m or 14600cm are left over

Step-by-step explanation:

Assuming you mean that there were 4m of string and 254cm were used/removed.

Answer:

C

Step-by-step explanation:

The red dotted line we see is the asymptote, which is a line that the functions will never cross.

The asymptotes we see currently is:

x = -3

and

x = 2

We can find the vertical asymptotes using the denominator of the function since the x value that makes the denominator 0 is the asymptote. Since -3 and 2 is the asymptote, the denominator of the function will be:

(x-2) (x+3)

If we look at the answer choices, we can see that C is the only option with a denominator of (x-2)(x+3), so that is our answer.

Answer:

C

Step-by-step explanation:

there are 2 vertical asymptotes at x = - 3 and x = 2

then the factors on the denominator will be (x + 3) and (x - 2)

then

f(x) = [tex]\frac{1}{(x-2)(x+3)}[/tex]

Answer:

what is the question show the pic

Based on the information provided, the individuals in this study are: D. the students.

A study can be defined as a strategic process or technique through which a scientist (researcher) observes and measures the effect of a risk factors, diagnostic test, or treatments on a particular population of interest.

In Mathematics, a variable can be defined as the measurable conditions, events, characteristics, individuals, or behaviors that a scientist (researcher) can control or observe when performing a study.

Based on the information provided, the individuals in this study are the students and these include the following subclasses:

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The students are the individuals in this study and is therefore denoted as option D.

This refers to a group of people which are chosen or taken from a large population for measurement or surveys.

In this scenario, the study was conducted in a school with different types of students according to their grades such as freshman, sophomore etc. This therefore makes the individuals in the study to be students and is the most appropriate choice.

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Answer:

10 m/s

Step-by-step explanation:

Let x = speed of fish and y = speed of current. When swimming with current, the fish's speed is x + y. When swimming against it, the speed is x - y. Therefore, we can set up a system of linear equations to solve for x, the speed of fish.

x + y = 14

x - y = 6

2y = 8

y = 4

x - 4 = 6

x = 10

The speed of fish in still water is 10 m/s, and the speed of current is 4 m/s.

Answer:

Speed of fish in still water = 10 m/s

Speed of current = 4 m/s

Step-by-step explanation:

Let the speed of the fish in still water = x m\s

Let the speed of the current  = y m/s

Speed of the fish with the current = x + y

 x +y = 14 m/s ------------------(I)

Speed of the fish against current = x -y

 x - y = 6 m/s ----(II) &

Add the equations (I) & (II) and 'y' will be eliminated and we can find the value of 'x'.

     x + y = 14

     x - y =  6      {Now, add)

     2x    = 20

           x = 20/2

          x = 10

[tex]\sf \boxed{\text{\bf Speed of fish in still water = 10 \ m / s}}[/tex]

Plugin x = 10 in equation (I)

    10 + y = 14

            y = 14 - 10

           y = 4

[tex]\sf \boxed{\text{\bf Speed of the current = 4 \ m/s}}[/tex]

The surface area of the given two rectangular prism is given as follows:

498 cm².

The surface area of a rectangular prism of length l, width w and height h is given as follows:

S = 2(lw + wh + hl).

For this problem, there are two prisms, with dimensions given as follows:

Hence the surface area of the figure is the combined surface area of each figure, hence:

S = 2(7 x 7 + 12 x 7 + 12 x 7) + 2(2 x 7 + 2 x 2 + 7 x 2) = 498 cm².

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Answer:

$270

Step-by-step explanation:

Find her gross income....then subtract taxes:

       30 hr/week * $10/hr        - $ 30     = $270

Answer:

x = 8 ± [tex]\sqrt{10}[/tex]

Step-by-step explanation:

x² - 16x + 54 = 0 ( subtract 54 from both sides )

x² - 16x = - 54

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 8)x + 64 = - 54 + 64

(x - 8)² = 10 ( take the square root of both sides )

x - 8 = ± [tex]\sqrt{10}[/tex] ( add 8 to both sides )

x = 8 ± [tex]\sqrt{10}[/tex]

then

x = 8 - [tex]\sqrt{10}[/tex] , x = 8 + [tex]\sqrt{10}[/tex]

Answer:

The increase is $18.

(In case you are asked about the percent increase,

percent increase = 20%)

Step-by-step explanation:

To find an increase, subtract.

$108 - $90 = $18

The increase is $18.

Answer: The increase is $18.

If you are asked about the percent increase, then use this formula:

percent change = (new number - old number)/(old number) × 100%

Here, the new number is $108. The old number is $90.

percent change = ($108 - $90)/($90) × 100%

percent change = $18/$90 × 100%

percent change = 0.2 × 100%

percent change = 20%

Since the percent change is a positive number, it is a percent increase.

Answer: percent increase = 20%

Answer:

9

Step-by-step explanation:

6 ÷ 2/3   =    6 /  (2/3 )   =  (6/1) / (2/3)  = 6/1  x  3/2 = 18/2 = 9

Answer:

7.88 x 10^5 is 788,000 is scientific notation

The number that will be the sum of 994 and a 2 digit number is 1004 (option 3). Details about digits of numbers can be found below.

A digit is the whole numbers from 0 to 9 and the arabic numerals representing them, which are combined to represent base-ten numbers.

A 2-digit number is any number between 10 and 99.

According to this question, 994 is said to be added to a 2 digit number to result into either 1001, 1002 or 1004.

Therefore, the number that will be the sum of 994 and a 2 digit number is 1004.

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Answer:

[tex]12.3 - 33.9 = 21.6 \div 10 = 2.16[/tex]

Answer:

b = 2a

Step-by-step explanation:

a = [tex]\frac{1}{2}[/tex] b ( multiply both sides by 2 to clear the fraction )

2a = b

Answer: b = 2a

Step-by-step explanation:

Original equation

a = (1/2) b

Multiply 2 on both sides

a * 2 = (1/2) b * 2

[tex]\Large\boxed{b=2a}[/tex]

Hope this helps!! :)

Please let me know if you have any quesitons

Answer:

the answer is 100,008.

Step-by-step explanation:

To convert temperatures in degrees Fahrenheit to Celsius, subtract 32 and multiply by 5556

Answer: 50° F = 10° C

Step-by-step explanation:

Given information

Convert 50° Fahrenheit to Celcius

Given formula

[tex]C~=~\frac{5}{9}~ (F-32)[/tex]

Substitute values into the formula

[tex]C~=~\frac{5}{9}~ (F-32)[/tex]

[tex]C~=~\frac{5}{9}~ ((50)-32)[/tex]

Simplify values in the parenthesis

[tex]C~=~\frac{5}{9}~ (18)[/tex]

Simplify the multiplication

[tex]\Large\boxed{C=10^\circ C}[/tex]

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Answer:

  D.  x = -7/3

Step-by-step explanation:

A graphical solution is often easier when the problem is written in the form f(x) = 0. That way, the x-intercept(s) of the function f(x) will be the solution.

The desired form can be found by subtracting 16 from both sides of the equation:

  [tex]\left(\dfrac{1}{64}\right)^{-x-3}=16\qquad\text{given}\\\\\left(\dfrac{1}{64}\right)^{-x-3}-16=0\quad\Longrightarrow\quad f(x)=\left(\dfrac{1}{64}\right)^{-x-3}-16[/tex]

A graph is attached, showing x=-7/3 is the solution.

Using powers of 4, the equation can be rewritten ...

  [tex]\left(\dfrac{1}{4^3}\right)^{-x-3}=4^2\qquad\text{given}\\\\4^{3(x+3)}=4^2\\\\3(x+3)=2\qquad\text{equating exponents, or taking base-4 logs}\\\\x=\dfrac{2}{3}-3=\boxed{-\dfrac{7}{3}}\qquad\text{divide by 3, subtract 3}[/tex]

Based on the number of years that Peter and Blair have till retirement, the total amount that they need to save to completely fund their income shortfall is $65,545.72.

First, find the income shortfall:

= 75,017 - 54,000

= $21,017

The amount they need to save to cover this shortfall is the future value of this amount at retirement. The rate will be the real rate which is:

= 6% - 2% inflation

= 4%

The future value is:

= Income shortfall x future value interest factor, 4%, 29 years

= 21,017 x 3.1187

= $65,545.72

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Answer: [tex]\Large\boxed{2a^3+4ab^2-3a^2b-6b^3}[/tex]

Step-by-step explanation:

Given expression

(2a - 3b) (a² + 2b²)

Apply the FOIL method (First Outer Inner Last)

Please refer to the attachment below for a graphical understanding

= 2a · a² + 2a · 2b² - 3b · a² - 3b · 2b²

Simplify by multiplication

=2 (a · a²) + 4 (a · b²) - 3 (b · a²) - 6 (b · b²)

[tex]\Large\boxed{=2a^3+4ab^2-3a^2b-6b^3}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Your answer is 2a³ + 4ab² - 3a²b - 6b³.

Step-by-step explanation:

(2a - 3b) (a² + 2b²)

=2a (a² + 2b²) -3b (a² + 2b²)

=2a.a² + 2a.2b² - 3b.a² - 3b.2b²

=2a³ + 4ab² - 3a²b - 6b³        ans.

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The true statements are:

The median number of pages of the sixth graders is 76.

One-fourth of the students have read less than 72 pages.

One-half of the students have read between 72 and 86 pages.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers.

The end of the first line represents the minimum number and the end of the second line represents the maximum number. The difference between the minimum number and the maximum number is the range.

Range = 92 - 61 = 31

On the box, the first line to the left represents the lower (first) quartile. 1/4 of the score represents the lower quartile. The next line on the box represents the median. 1/2 of the score represents the median. The third line on the box represents the upper (third) quartile. 3/4 of the scores represents the upper quartile.

First quartile = 72

Third quartile = 86

Median = 76

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Answer: 15/2 or 7.5

Step-by-step explanation:

2/3x = 5

5 divided by 2/3 or 5 x 3/2

= 15/2 or 7.5

Answer: 15/2

Step-by-step explanation:

[tex]\frac{2}{3} x-1=4\\\\\frac{2}{3}x=5\\ \\x=5(\frac{3}{2})\\\\x=\frac{15}{2}[/tex]

Using a calculator, the critical value for the t-distribution, with a confidence level of 99%, a sample size n = 20 and a two-tailed test is of Tc = 2.8609.

It is found using a calculator, with three inputs, which are given by:

In this problem, the inputs are given as follows:

Hence, using a calculator, the critical value is of is of Tc = 2.8609.

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The coordinates of C - (2n, 0) and the coordinates of D - (n, -p). The diagonals of a rhombus are perpendicular and bisect each other.

The properties of a rhombus are:

The given rhombus BCDE has B(n, p) and E(0, 0).

Since the diagonals of a rhombus are perpendicular bisectors,

EO = OC or BO = OD

Where O is the midpoint of EC and BD.

In the given diagram, points B and D are opposite each other. They are reflecting each other over the x-axis.

So, if B has coordinates (n, p) then its reflection over the x-axis is (x, -y) i.e., (n, -p).

Thus, we have B(n, p), D(n, -p), and E(0, 0)

Consider the coordinates of C as (x, y).

The midpoint of BD = ([tex]\frac{n+n}{2}[/tex], [tex]\frac{p-p}{2}[/tex])

⇒ coordinates of O = (n, 0)

So,

The midpoint of EC = ([tex]\frac{0+x}{2}[/tex], [tex]\frac{0+y}{2}[/tex])

⇒ coordinates of O = (x/2, y/2)

⇒ (n, 0) = (x/2, y/2)

∴ x = 2n and y = 0

Then, the coordinates of C are (2n, o)

Therefore, the required coordinates of the given rhombus are C(2n, 0) and D(n, -p).

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Step-by-step explanation:

we have a rectangle, that is then cut in half diagonally into 2 right-angled triangles.

in our problem it does not matter which side is the larger and which is the shorter one, because the distance calculation for both cases involve one short and one long side. the sequence does not matter.

Mary walks one short and one large side to get to the opposite corner (from D to F) :

264 + 900 = 1,164 ft

Kate walks diagonally. and that diagonal is the Hypotenuse of the right-angled triangle with a short and a long side of the rectangle.

so, Pythagoras applies :

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), and a and b are the legs.

in our case that means

diagonal² = 264² + 900² = 69,696 + 810,000 =

= 879,696

diagonal = sqrt(879,696) = 937.9211054... ft ≈ 938 ft

so, Kate walked

1,164 - 938 = 226 ft

less than Mary.

The difference between the total number of wholesalers and those that supply on 30-day credit, gives the number that require cash on delivery as 2

The number of wholesalers Sue has sourced = 4

Terms of two suppliers = 30 days credit

Amount of stock Sue has = $15000

Amount of stock on credit = $10000

Operating cash reserve of the business = $20000

Required:

The number of wholesalers that require terms of cash on delivery

Solution:

Given that the number of wholesalers = 4

The number number of suppliers (wholesalers) that supply on 30-day credit = 2

Therefore;

The number of wholesalers that require terms of cash on delivery = 4 - 2 = 2

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The area of the tarp is 54.125 square feet

From the figure in the question, we have the following angle measure:

DCE= 120

This means that:

<C = DCE - 90

Substitute the known values in the above equation

<C = 120 - 90

Evaluate the difference

<C = 30

The measure of D is then calculated as

<D = 90 - <C

This gives

<C = 90 - 30

Evaluate the difference

<C = 60

Represent the height with h.

This is then calculated as:

sin(D) = h/5

This gives

sin(60) = h/5

Multiply both sides by h

h = 5 * sin(60)

Evaluate

h = 4.33

This is calculated as:

A = 0.5 * (10 + 15) * 4.33

Evaluate

A = 54.125

Hence, the area of the tarp is 54.125 square feet

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Answer:

In the image

Hope this helps!

Step-by-step explanation:

To find the height, first find that ∠D is 60°. This means the height of the trapezoid is approximately 4.3 feet. So, the area of the tarp is approximately 53.7 square feet.

The expression that represents the number of reams of paper produced in the second year is 4.704 x [tex]10^{10}[/tex] (option d)

The quantity of paper produced in the first year is written in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers.  

In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

For example, The number 5 x 10³ is equivalent to 500

Paper produced in the second year = paper produced in the first year x 5.6

(8.4 x [tex]10^{9}[/tex] ) x 5.6 = 47.04 x [tex]10^{9}[/tex]

4.704 x [tex]10^{9 + 1}[/tex]

= 4.704 x [tex]10^{10}[/tex]

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Given the following:

The economic order quantity is 24.

Eoq = √2 * demand * ordering cost / holding cost)

= √(2 * 1050 * 15 / 55)

EOQ = 24

The  Average inventory = EOQ / 2

= 24 / 2

= 12

Expected number of orders = demand / EOQ

= 1050 / 24

= 44

Annual holding cost (AHC) = (EOQ / 2) * Holding cost

= (24 / 2) * 55

= 660

Annual ordering cost (AOC) = (demand / EOQ) * ordering cost

= (1050 / 24) * 15

= 656

Thus,

Total cost of managing = AHC + AOC

= 660 + 656

TCM = 1,316

5. For holding cost of 60

EOQ= √(2 * demand * ordering cost / holding cost)

= √(2 * 1050 * 15 / 60)

= 23

Annual holding cost = (EOQ / 2) * holding cost

this gives us

= (23 / 2) * 60

= 690

Annual ordering cost = (demand / EOQ) * ordering cost

= (1050 / 23) * 15

= 685

Total cost of managing = AHC+ AOC

= 690 + 685

= 1375

Change in total annual cost = new - old

= 1375 - 1316

= 59

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Answer:-2,0 & 1,0

Step-by-step explanation:

Substitute them in with zero product property