What is the area of this polygon?

The coordinates of vertex B' are (76, -86).

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 9 centered at the point D (-5, 5) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate B, we have;

Coordinate B = (4, -4)  →  (9(4 - (-5)) + (-5), 9(-4 - 5) + (-5))

Coordinate B = (4, -4)  →  (9(9) - 5, 9(-9) - 5)

Coordinate B = (4, -4)  →  (81 - 5, -81 - 5)

Coordinate B' = (76, -86).

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Complete Question:

ΔABC with vertices at A (-1, -1). B (4,-4), and C (2, -6) is dilated by a scale factor of 9 to create ΔA'B'C'. The center of dilation is the point (5, -6).

What are the coordinates of vertex B'?

Answer:

2(1/2)(11)(13) + 2(1/2)(10)(13.2) + 10(11)

= 143 + 132 + 110 = 385 square feet

B is the correct answer.

Answer:

It is a function

Step-by-step explanation:

It's a function because it does not over lapp

Answer:

4:5 or 4/5 or .8 or 80%

Step-by-step explanation:

divide both by 3. then convert to percent or decimal

0.034141137 o sobre 17/500

Answer:

x = 3

Step-by-step explanation:

4x + 2x - 3 = 15 ← collect like terms on left side

6x - 3 = 15 ( add 3 to both sides )

6x = 18 ( divide both sides by 6 )

x = 3

Answer:

x=3

Step-by-step explanation:

You can start of by adding 4x and 2x because they both share the same variable "x". Now you have 6x-3=15. Using the addition property of equality, you can add 3 on both sides of the equation to cancel it out. You are left with 6x=18. Divide both sides by 6 and that leaves you with x=3

Answer: 17/24 for both jobs

Step-by-step explanation:

The monthly payments and total cost of interest depend on the interest rate and the length of the loan. Generally, a lower interest rate or a shorter loan term results in lower total interest costs.

To calculate the monthly payments, we can use the formula for the present value of an annuity:

[tex]PV = P * (1 - (1 + r)^{-n}) / r[/tex]

where PV is the present value of the loan, P is the principal (the amount borrowed), r is the monthly interest rate, and n is the number of monthly payments.

(a) 30 years, 5%:

PV = 0.9 * $90,000 = $81,000 (since she puts 10% down)

r = 0.05 / 12 = 0.0125(monthly interest rate)

n = 30 * 12 = 360 (number of monthly payments)

Using the formula, we get:

PV = $81,000

Monthly payment = $436.82

Total cost of interest = $57,255.85

(b) 30 years, 5.12%:

r = 0.0512 / 12 = 0.00427 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $439.88

Total cost of interest = $59,956.19

(c) 30 years, 6%:

r = 0.06 / 12 = 0.005 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $485.24

Total cost of interest = $95,687.34

(d) 15 years, 3.78%:

n = 15 * 12 = 180 (number of monthly payments)

r = 0.0378 / 12 = 0.00315 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $591.93

Total cost of interest = $34,147.07

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The value of the radius is 13.04

Pythagoras theorem states that: The sum of square of the two legs of a right triangle is equal to the square of the other side.

Therefore c² = a² + b²

Since MN is perpendicular to JK , this means MK = JM = JK/2

= 14/2 = 7

HI = JK, therefore LI is also 7

and MN = LN = 11

Therefore,

NI =√ LN)² + LI)²

NI = √ 11² + 7²

NI = √121+49

NI = √ 170

NI = 13.04( nearest hundredth)

therefore the radius of the circle is 13.04

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a) The exponential growth function for a city's population that was 6.53 million in 2012 with an exponential growth rate of 2.79% per year is y = 6.53(1.0279)^t.

b) Based on the exponential growth function y = 6.53(1.0279)^t the population of the city in 2018 is 7.7 million.

c) The population of the city will be 10 million in 2028.

d) The doubling time for the population is 25 years.

An exponential growth function is one of the two exponential functions, including an exponential decay function.

An exponential growth function shows the relationship between two variables with an exponent and exhibits a constant rate of growth per period.

Population of the city in 2012 = 6.53million

Exponential growth rate = 2.79% per year

Let the number of growth years = t

a) y = 6.53(1.0279)^t

b) From 2012 to 2018, the number of years = 6 years

Population in 2018, y = 6.53(1.0279)^6

= 7.7 million

c) When the population will be 10 million = 15.5 years

10 = 6.53(1.0279)t

t = 15.5 years

= 16 years

= 2028

d) 13.06 = 6.53(1.0279)t

t = 25.189 years

= 25 years

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The rate at which the temperature of the compound rose was 5¹/₄ degrees per hour.

To find the rate at which the temperature of the compound rose, we need to divide the change in temperature by the time interval during which the change occurred.

The temperature rose 3¹/₂ degrees every 2/3 of an hour. To write this as a fraction, we can first convert 3¹/₂ to an improper fraction:

3¹/₂= 7/2

Now, we can write the rate of change as a fraction:

Rate of change = (7/2) / (2/3)

To divide by a fraction, we can multiply by its reciprocal:

Rate of change = (7/2) x (3/2)

Simplifying, we get:

Rate of change = 21/4

Therefore, the rate at which the temperature of the compound rose was 5¹/₄ degrees per hour.

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The distinct orders of light bulbs are there if two light bulbs of the same color are considered identical = 4,620

Here, the total number of bulbs = 11

The number of red light bulbs = 3

The number of yellow light bulbs = 2

and the number of  pink light bulbs = 6

We know that the formula for the permutation with repetition is:

n! / (n1! × n2! x ... × nk!)

We use this formula to find the required number of light bulbs.

Here, two light bulbs of the same color are considered identical

We divide by 3! in order to adjust for overcounting, because we have 3 red light bulbs.

simmilarly for the 2 yellow light bulbs, we divide with 2!.

and for the 6 pink light bulbs, we divide by 6!

Thus, the total number of distinct orders of bulbs will be:

11! / (3! × 2! × 6!) = 4,620

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The distance from the point A to point B is s√3

From the question, we have the following parameters that can be used in our computation:

Perfect cube with sides of length s.

The distance from point A to point B is calculated as

Distance^2 = s^2 + s^2 + s^2

When evaluated, we have

Distance^2 = 3s^2

Take the square roots of both sides

Distance = s√3

Hence, the distance = s√3

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Answer:

x = 3; z = 60°

Step-by-step explanation:

x:

The angles measuring 120° and (8x + 96)° are vertical angles, which means they're congruent and equal.

Thus, we can solve for x by setting the two angles equal to each other and isolate x:

[tex]120=8x+96\\24=8x\\3=x[/tex]

We can check our answer by plugging in 3 for x and ensure that we get 120:

[tex]120=8(3)+96\\120=24+96\\120=120[/tex]

z:

We see that a horizontal straight line separates the angle measuring 120° and z°.  Straight lines create straight angles, which equal 180°.

Thus, we can find the measure of z by adding the 120° angle and the z° and set them equal to 180.  Then, we must isolate z:

[tex]120+z=180\\z=60[/tex]

In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,

∠A = ∠L, ∠D =∠M , ∠C = ∠N , and

AB = LB , CD = NM ,  DA = ML.

Quadrilateral ABCD rotates 180 degrees around point B,

New quadrilateral formed named LBMN

The corresponding angle after rotation of 180 degrees around B is equals to,

B remain at same position.

A rotates and point L take the position of A.

D rotates and point M take the position of D.

C rotates and point N take the position of C.

Corresponding angle to A is angle L.

Corresponding angle to D is angle M.

Corresponding angle to C is angle N.

Similarly corresponding segments are of ABCD and LBNM are

Line segment AB corresponds to line segment LB.

Line segment CD corresponds to line segment NM

Line segment DA corresponds to line segment ML.

Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.

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To draw the graph of y = g(-x), we need to replace x with -x in the original function.

If y = g(x) is given by the following graph:

(see attachment labeled "Attachment1")

Then y = g(-x) can be obtained by reflecting the graph of y = g(x) about the y-axis:

(see attachment labeled "Attachment 2")

Therefore, the graph of y = g(-x) is the reflection of the graph of y = g(x) about the y-axis.

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It will take 5 seconds for the object to hit the ground

From the question, we have the following equation that can be used in our computation:

-16r^2 + 400 = 0

So, we have

- 16r^2 = -400

Divide by -16

This gives

r^2 = 25

Take the square root of both sides

r = 5

Hence, the number of seconds is 5

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Based on the information, the correct information regarding the graph is that C. Quantity demanded decreases as price increase.

The graph shows that for every increase of 100 units of the goods demanded, price reduces by 1 unit.

When 500 units was demanded, the price was at 1. Therefore, if 550 units are demanded, the price will reduce by half, which means the price would drop to 0.5.

The price would drop to 0.5. In this case, the the correct information regarding the graph is that Quantity demanded decreases as price increase.

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Monthly you should deposit approximately $43 to accumulate ​$76,000 in 4 ​years.

Given that,

f = $76,000

r = 4% = 0.04/12 = 0.0033

n = 4×12 = 48

We know that, a = (f×r)/((1+r)ⁿ⁻¹)

a is the annuity.

f is the future amount.

r is the interest rate per time period.

n is the number of time periods.

Here,

a = (76,000 ×0.0033)/((1.0033)⁴⁸⁻¹)

a = 76,000 ×0.0033×0.17132

a = 42.96

a ≈ $43

Therefore, monthly you should deposit approximately $43 to accumulate ​$76,000 in 4 ​years.

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The match of the given words as per the definition of the terms related to data set is as follow.

1 → g

2 →c

3 → b

4 → d

5 → f

6 → a

7 → e

The description of the each word as per the definition is ,

Mean represents the average of the data.

1→g

Spread represents the similarity or variability of  the set of observed values of the data.

2→c

Center represents the middle value of the data set.

3→ b

Shape represents the values of the data set when plotted on the graph.

4 → d.

Median represents the middle value of the data set after arranging in ascending or descending order.

5 →f

Distribution represents measure of all the values of the data set spread.

6→a

variability represents the set of such values which satisfies the statistical question or relation.

7 → e.

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Answer:

i believe the answer would be option D

Step-by-step explanation:

According to the figure,

a. angle LCQ is 45 degrees

b. the major arc are KPR and QRPK

c. congruent minor arcs are LQ and QR

d. the three arcs that form a semicircle are RP,  LQ ,and QR

A major arc designates a segment of an arch with a measurement which surpasses 180 degrees.

Geometrically, the circle, a closed curve, exhibits all its points uniformly spaced from a central focal point named the center of the circle.

The arc is regarded as major when it comprises a superior portion of the circular geometry, extending beyond half of the total circumference.

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A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.

In this question, we have an horizontal line, meaning that it has a constant y-coordinate for each value of the y-input. Hence the graph represents a function.

For the domain and the range, we have that:

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The values of the missing terms are 1) 24 and 2) 1.6.

Given are two similar figures, we need to find the value of x,

According to the definition of similar figures, the ratios of the corresponding sides are equal,

So,

1) GE / EF = RS / TR

5/6 = 20/x

5x = 120

x = 24

2) JH / LK = WX / ZY

3.84 / 2.04 = 3.2 / x

3.84x = 2.04 × 3.2

3.84x = 6.528

x = 1.7

Hence, the values of the missing terms are 1) 24 and 2) 1.6.

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The limit as a definite integral is  given as   lim (n → ∞) Σ(8i²)/n³ = 8/3n³

The area under the curve f(x) from x= a to x  = b is represented by the definite integral of f(x  )

There are 2 kinds of    integrals

To express the limit as a definite integral, we can use the following formul

lim(n → ∞  ) Σf(i)/n = ∫  a^bf(x)dx

where....

a and b are the lower and upper limts of the definite integral

f (x) is the function being integrated

In this case, we have

lim(n → ∞) Σ(8i²)/n³

Let f  (x) = x ²

So, f(i/n) = (i/n) ²

And, the sum can be written as

Σ(8i^2)/n³ = 8/n³ Σi²

= 8/n³ Σ(i/n)²

= 8/n³ Σ[f(i/n)]

= 8/n³ ∫0¹ f(x) dx (using the formula above)

Therefore, the limit can be   expressed as

lim(n → ∞) Σ(8i²)/n³ = 8/n³ ∫0¹ x² dx

Simplifying the integral, we get....

8/n³  ∫0¹ x₂ dx = 8/n^3 [x³/3] from 0 to 1

= 8/3n ³

Se we can say here that  the limit as a definite integral is lim(n → ∞) Σ(8i ₂)/n^3 = 8/3n ₃

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190 percent. you can find this by dividing the numerator by denominater

Answer:

190%

Step-by-step explanation:

19/10 = 19 ÷ 10 = 1.9

1.9 x 100 = 190%

The height of tree is given as follows:

40 ft.

The height of the tree is obtained applying the proportions in the context of this problem.

The proportions are applied as a rule of three can be formed between the heights and the shadows for both the tree and the person, as follows:

h/30 = 6/4.5

Applying cross multiplication, the value of h is obtained as follows:

4.5h = 30 x 6

4.5h = 180

h = 180/4.5

h = 40 ft.

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The area of the shaded region for the normal distribution is approximately 0.6985.

We have,
To find the area of the shaded region under the standard normal distribution curve between z = -0.87 and z = 1.24, we can use a standard normal distribution table or a calculator with a standard normal distribution function.

Using a standard normal distribution table, we look up the area to the left of z = -0.87 and the area to the left of z = 1.24 and then subtract the smaller area from the larger area to find the area between z = -0.87 and z = 1.24.

The table value for z = -0.87 is 0.1949, and the table value for z = 1.24 is 0.8934.

The area between z = -0.87 and z = 1.24 is:

= 0.8934 - 0.1949

= 0.6985

So the area of the shaded region is approximately 0.6985.

Thus,

The area of the shaded region for the normal distribution is approximately 0.6985.

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The ROE (return on equity) for this project if it produces an EBIT (earnings before interest and taxes) of $140,000 is given by A = 15 %

Given data ,

The Return on Equity (ROE) is calculated as the ratio of Net Income to Equity. Net Income is the EBIT (earnings before interest and taxes) minus the taxes, and Equity is the total assets minus the debt.

EBIT = $140,000

Tax rate = 25%

Total assets = $700,000

Debt = 0% (since the project is financed with 100% equity)

Taxes = Tax rate x EBIT

Taxes = 0.25 x $140,000

Taxes = $35,000

And , the net income is

Net Income = EBIT - Taxes

Net Income = $140,000 - $35,000

Net Income = $105,000

Now , the ROE is given by

ROE = (Net Income / Equity) x 100%

ROE = (Net Income / Total assets) x 100%

ROE = ($105,000 / $700,000) x 100%

ROE = 15%

Hence , the ROE is 15 %

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