Triangle D has been dilated to create triangle D’. Use the image to answer the question.
Determine the scale factor used.

A. Scale factor of 1/3
B. Scale factor of 3
C. Scale factor of 1/2
D. Scale factor of 2

The points 2, -1+i√3, and -1-i√3 form an equilateral triangle on the Argand plane.

To prove that the points 2, -1+i√3, and -1-i√3 form an equilateral triangle on the Argand plane, we need to show that the distances between these points are equal.

Let's calculate the distances between the points using the distance formula:

Distance between 2 and -1+i√3:

d₁ = |2 - (-1+i√3)|

= |3 - i√3|

= √(3² + (√3)²)

= √(9 + 3)

= √12

= 2√3

Distance between -1+i√3 and -1-i√3:

d₂ = |-1+i√3 - (-1-i√3)|

= |-1+i√3 + 1+i√3|

= |2i√3|

= 2√3

Distance between -1-i√3 and 2:

d₃ = |-1-i√3 - 2|

= |-3 - i√3|

= √((-3)² + (√3)²)

= √(9 + 3)

= √12

= 2√3

We have shown that the distances between the three pairs of points are all equal to 2√3.

Therefore, the points 2, -1+i√3, and -1-i√3 form an equilateral triangle on the Argand plane.

To find the length of a side of this equilateral triangle, we can take any of the distances calculated above. In this case, each side of the triangle has a length of 2√3.

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Answer:

Step-by-step explanation:

sin (B) = [tex]\frac{2}{5}[/tex]

The graph of the function f(x) = (2)ˣ is added as an attachment

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

f(x) = (2)ˣ

The above function is an exponential function that has been transformed as follows

Initial value = 1

Growth factor = 2

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

M = a + 24, where a is James' age and M is his mother's

Step-by-step explanation:

a = James' age

His sister is 4 years younger than him:

a - 4 represents his sister's age.

His mother is 28 years older than his sister:

(a - 4) + 28

or a + 24 represents his mother's age

Let M = his mother's age

M = a + 24

Answer:

16

Step-by-step explanation:

find volume of pool

(multiply everything together)

since each otter needs 30 m^3 of space, divide the volume by 30

answer comes to 16.8. however since we can't put 0.8 of an otter in the pool, you round down to 16

The percentage of scores below 260 is 15.87%.

A. For the function f(x) = -2x³ - x² + 5x - 1:

- Degree: The degree of a polynomial is the highest power of the variable. In this case, the degree is 3 since the highest power of x is ³ (cubed).

- Leading coefficient: The leading coefficient is the coefficient of the term with the highest power. In this case, the leading coefficient is -2.

- Constant: The constant term is the term without a variable. In this case, the constant term is -1.

B. For the function g(x) = 3(x + 2)(x - 4):

- Degree: The degree of a polynomial is determined by the highest power of the variable. In this case, the degree is 2 since the highest power of x is ² (squared).

- Leading coefficient: The leading coefficient is the coefficient of the term with the highest power. In this case, the leading coefficient is 3.

C. For the function f(x) = -x² + 5x + 3:

- Degree: The degree of a polynomial is determined by the highest power of the variable. In this case, the degree is 2 since the highest power of x is ² (squared).

- Leading coefficient: The leading coefficient is the coefficient of the term with the highest power. In this case, the leading coefficient is -1.

- Constant: The constant term is the term without a variable. In this case, the constant term is 3.

D. For the function f(x) = 3x⁵ - x¹⁰:

- Degree: The degree of a polynomial is determined by the highest power of the variable. In this case, the degree is 10 since the highest power of x is ¹⁰ (tenth power).

- Leading coefficient: The leading coefficient is the coefficient of the term with the highest power. In this case, the leading coefficient is 3.

- Constant: The constant term is the term without a variable. In this case, there is no constant term (it is 0).

The function values are:

f(-1) = -9

f(1) = -5

We have,

From the graph,

We have the coordinates as:

(-1, -9) (2, 0), (-4, 0), and (1, -5)

Now,

The coordinates mean (x, y).

x is the x-axis and y is the function value.

f(x) = y

So,

We can have,

When x = -1, y = -9 or f(-1) = -9

And,

When x = 1, y = -5 or f(1) = -5

Thus,

The function values are:

f(-1) = -9

f(1) = -5

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Based on the Triangle Inequality Theorem, the sets of side measurements that could form a triangle are:

13, 19, 7

25, 12, 13

18, 2, 24

The set of side measurements 3, 1, 5 could not form a triangle.

To determine which set of side measurements could form a triangle, we need to check if the sum of the lengths of the two shorter sides is greater than the length of the longest side. This is known as the Triangle Inequality Theorem.

Let's check each set of side measurements:

13, 19, 7:

The sum of the two shorter sides is 7 + 13 = 20, which is greater than the longest side (19). Therefore, this set of side measurements could form a triangle.

25, 12, 13:

The sum of the two shorter sides is 12 + 13 = 25, which is equal to the longest side (25). Therefore, this set of side measurements could form a triangle.

18, 2, 24:

The sum of the two shorter sides is 2 + 18 = 20, which is greater than the longest side (24). Therefore, this set of side measurements could form a triangle.

3, 1, 5:

The sum of the two shorter sides is 1 + 3 = 4, which is less than the longest side (5). Therefore, this set of side measurements could not form a triangle.

Based on the Triangle Inequality Theorem, the sets of side measurements that could form a triangle are:

13, 19, 7

25, 12, 13

18, 2, 24

The set of side measurements 3, 1, 5 could not form a triangle.

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The probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.

Option B is the correct answer.

We have,

To find the probability that the mean of the sample will be between 94.7 inches and 95.3 inches, we can use the Central Limit Theorem.

According to the Central Limit Theorem, the distribution of sample means approaches a normal distribution as the sample size increases.

In this case, the mean of the population (μ) is 95 inches and the standard deviation of the population (σ) is 0.52 inches.

Since the sample size is sufficiently large (n = 30), we can assume that the distribution of sample means will be approximately normal.

To calculate the probability, we need to standardize the sample mean using the z-score formula:

z = (x - μ) / (σ / √n)

where:

x = sample mean

μ = population mean

σ = population standard deviation

n = sample size

Let's calculate the z-scores for the lower and upper limits:

z1 = (94.7 - 95) / (0.52 / √30)

z2 = (95.3 - 95) / (0.52 / √30)

Now, we can use a standard normal distribution table or a calculator to find the probability associated with these z-scores.

Using a standard normal distribution table or a calculator, we find:

P(z1 < Z < z2) ≈ 0.436

Therefore,

The probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.

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Based on the information we can infer that the pool cover costs: $1568.25

To find the price of the pool cover we must take into account the pool area. In this case, being an irregular polygon, we must divide it into regular polygons to find its area.

According to the above, the pool area is 697 square meters. So the value of the cover would be:

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The correct answer is "A. control group."

In an experiment, the control group refers to the group of subjects that does not receive any treatment or intervention.

They are used as a comparison or baseline to evaluate the effects of the treatment being tested.

In this case, the control group consists of dogs aged 10 and older with high blood pressure who are not given any medication.

By comparing the blood pressure measurements of this control group to the group of dogs receiving the new blood pressure medication, the scientist can determine the effectiveness of the medication.

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Since a kite is a quadrilateral, it has the value of 360 total degrees.

The force on the longer side of the aquarium is 515200 N.

Given,Aquarium's width = 2 ft, length = 4 ft, and height = 2 ft.To find:The force on the longer side of the aquarium.Solution:The longer side of the aquarium is 4 ft long.

The force on the longer side of the aquarium can be calculated using the formula:

F = ρghA

Where,F = force on the surface ρ = density of the fluid h = depth of the fluidA = area of the Surface We know that the density of water is ρ = 1000 kg/m³.

The area of the surface is A = l × h = 4 × 2 = 8 sq ft (as the aquarium is rectangular)

The depth of the fluid (water) on the longer side is h = 2 ft.

The force on the longer side can be calculated as follows:

F = ρghA= 1000 × 32.2 × 2 × 8= 515200 N

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The set of all functions from X to Y, mathematicians can explore the relationships and Transformations between different sets.

"The set of all functions from X to Y" refers to the collection or group of all possible functions that can be defined from the set X to the set Y. In mathematics, a function is a relation between two sets, where each element in the first set (X) is associated with a unique element in the second set (Y).

When we talk about the set of all functions from X to Y, we are considering all the different ways in which elements from X can be mapped or related to elements in Y. Each function within this set represents a distinct mapping or correspondence between the elements of X and Y.

The set of all functions from X to Y can be denoted as F(X, Y) or sometimes written as Y^X, emphasizing that it represents the power set or the collection of all possible functions from X to Y.

The elements of this set are individual functions, where each function takes an input from X and produces an output in Y. These functions can have various properties, such as being continuous, differentiable, or having specific algebraic expressions.

By considering the set of all functions from X to Y, mathematicians can explore the relationships and transformations between different sets. This concept plays a fundamental role in various branches of mathematics, including analysis, algebra, topology, and more. It provides a framework for studying functions and their properties, enabling deeper insights into mathematical structures and their interconnections.

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Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.

Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).

Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.

Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.

The area of the trapezium is 99.225 inches².

A trapezium is the a quadrilateral. Therefore, the area of the quadrilateral can be calculated as follows:

area of the trapezium = 1 / 2 (a + b)h

where

Therefore,

area of the trapezium = 1 / 2 (6.3 + 12.6)10.5

area of the trapezium =  1 / 2 (18.9)10.5

area of the trapezium = 198.45 / 2

area of the trapezium = 99.225 inches²

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Answer:
Final Price: $318.50
You save: $136.50

Step-by-step explanation:

To find the discount for a $455 designer purse that is on sale for 30% off, we can follow these steps:

Step 1: Calculate the discount amount

Discount Amount = Original Price * Discount Percentage

= $455 * 30% = $455 * 0.3 = $136.50

Step 2: Calculate the final price after the discount

Final Price = Original Price - Discount Amount

= $455 - $136.50 = $318.50

The discount for the $455 designer purse that is on sale for 30% off is $136.50. The final price after the discount is $318.50.

Answer:

Step-by-step explanation:

Discount: subtract the percentage from the sale price:

$455.00 x 30% = $136.50

then you subtract the amount $136.50 from the original price of $455.00 = $318.50  The customer will pay $318.50 because a discount was for 30% off from the original price.

The value of the expression [tex]2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.[/tex]

Let's simplify the expression step by step:

Recall the values of trigonometric functions for common angles:

cos(60°) = 1/2

sin(30°) = 1/2

tan(60°) = √(3)

cot(45°) = 1

sec(30°) = 2

Substitute the values into the expression:

[tex]2(cos^4 60 + sin^4 30) - (tan^2 60 + cot^2 45) + 3sec^2 30[/tex]

= [tex]2((1/2)^4 + (1/2)^4) - (\sqrt{(3)^2 + 1^2} ) + 3(2^2)[/tex]

= 2(1/16 + 1/16) - (3 + 1) + 3*4

= 2(1/8) - 4 + 12

= 1/4 - 4 + 12

= -15/4 + 12

= -15/4 + 48/4

= 33/4

Therefore, the value of the expression [tex]2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.[/tex]

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Answer:

1, 215

Step-by-step explanation:

To calculate the cost of the cover, we need to know the area of the pool. Assuming that the pool is rectangular and has the dimensions given by the four numbers provided (30, 18, 18, 6), we can calculate the area as follows:

Area = length * width

Area = 30 * 18

Area = 540 square feet

Therefore, the cover for this pool would cost:

Cost = Area * Price per square foot

Cost = 540 * $2.25

Cost = $1,215

So the cover would cost $1,215.

Answer:

k = 6 and k = -4

Step-by-step explanation:

To determine two integral values of k (integer values of k) for which the roots of the quadratic equation kx² - 5x - 1 = 0 will be rational, we can use the Rational Root Theorem.

The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -1) and q must be a factor of the leading coefficient (in this case, k).

Possible p-values:

Possible q-values:

Therefore, all the possible values of p/q are:

[tex]\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 1}{\pm k}=\pm 1, \pm \dfrac{1}{k}[/tex]

To find the integral values of k, we need to check the possible combinations of factors. Substitute each possible rational root into the function:

[tex]\begin{aligned} x=1 \implies k(1)^2-5(1)-1 &= 0 \\k-6 &= 0 \\k&=6\end{aligned}[/tex]

[tex]\begin{aligned} x=-1 \implies k(-1)^2-5(-1)-1 &= 0 \\k+4 &= 0 \\k&=-4\end{aligned}[/tex]

[tex]\begin{aligned} x=\dfrac{1}{k} \implies k\left(\dfrac{1}{k} \right)^2-5\left(\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}-\dfrac{5}{k}-1 &= 0 \\-\dfrac{4}{k}&=1\\k&=-4\end{aligned}[/tex]

[tex]\begin{aligned} x=-\dfrac{1}{k} \implies k\left(-\dfrac{1}{k} \right)^2-5\left(-\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}+\dfrac{5}{k}-1 &= 0 \\\dfrac{6}{k}&=1\\k&=6\end{aligned}[/tex]

Therefore, the two integral values of k for which the roots of the equation kx² - 5x - 1 = 0 will be rational are k = 6 and k = -4.

Note:

If k = 6, the roots are 1 and -1/6.

If k = -4, the roots are -1 and -1/4.

Answer:

P'(-2,3)

Step-by-step explanation:

We see that P(-2,1) is 1 point down y = 2, so reflection across the line y = 2 will be 1 point up y = 2, so the answer is (-2,3)

The new coordinates of the vertex D are given as follows:

D'(0, -2.5).

A dilation is defined as a non-rigid transformation that multiplies the distances between every point in a polygon or even a function graph, called the center of dilation, by a constant factor called the scale factor.

The coordinates of the vertex D are given as follows:

D = (0, -5).

The scale factor is given as follows:

k = 1/2.

Hence the dilated coordinates are given as follows:

D'(0, -2.5).

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To set up the amortization table, we can use the mortgage and interest formulas as follows:

Mortgage formula:

M = P [ i(1 + i)^n / (1 + i)^n - 1]

where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (APR divided by 12), and n is the total number of payments (20 years multiplied by 12 months per year).

Interest formula:

I = P * i

where I is the monthly interest payment, P is the remaining principal balance, and i is the monthly interest rate.

Using these formulas, we can set up the following amortization table for the first two months:

Month Payment Principal Interest Balance

1    $400,000

2    

To fill in the table, we need to calculate the monthly payment (M) and the monthly interest payment (I) for the first month, and then use these values to calculate the principal payment for the first month. We can then subtract the principal payment from the initial balance to get the balance for the second month, and repeat the process to fill in the remaining columns.

To calculate the monthly payment (M), we can use the mortgage formula:

M = P [ i(1 + i)^n / (1 + i)^n - 1]

where P is the principal amount, i is the monthly interest rate, and n is the total number of payments.

Plugging in the given values, we get:

M = 400,000 [ 0.00279 (1 + 0.00279)^240 / (1 + 0.00279)^240 - 1]

M = $2,304.14

Therefore, the monthly payment is $2,304.14.

To calculate the interest payment for the first month, we can use the interest formula:

I = P * i

where P is the remaining principal balance and i is the monthly interest rate.

Plugging in the values for the first month, we get:

I = 400,000 * 0.00279

I = $1,116.00

Therefore, the interest payment for the first month is $1,116.00.

To calculate the principal payment for the first month, we can subtract the interest payment from the monthly payment:

Principal payment = Monthly payment - Interest payment

Principal payment = $2,304.14 - $1,116.00

Principal payment = $1,188.14

Therefore, the principal payment for the first month is $1,188.14.

To calculate the balance for the second month, we can subtract the principal payment from the initial balance:

Balance = Initial balance - Principal payment

Balance = $400,000 -$1,188.14

Balance = $398,811.86

Therefore, the balance for the second month is $398,811.86.

Using these values, we can complete the first two rows of the amortization table as follows:

Month Payment Principal Interest Balance

1 $2,304.14 $1,188.14 $1,116.00 $398,811.86

2    

To fill in the remaining columns for the second month, we can repeat the process using the new balance of $398,811.86 as the principal amount for the second month. We can calculate the interest payment using the same method as before, and then subtract the interest payment from the monthly payment to get the principal payment. We can then subtract the principal payment from the balance to get the new balance for the third month, and repeat the process for the remaining months of the amortization period.

Algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).

Let's denote the amount of money the insurance company will pay as P. In this scenario, if the value of the stolen items is greater than the deductible, the insurance company will cover the loss, and Ron will receive compensation for the stolen items.

The total value of the stolen items can be calculated by adding the value of the bicycles (2b) and the value of the tools (t). So, the total value of the stolen items is 2b + t.

If the total value of the stolen items is greater than the deductible (d), then the insurance company will pay the difference between the total value and the deductible. Mathematically, this can be represented as:

P = (2b + t) - d

Therefore, algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).

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Answer:

Step-by-step explanation:

To determine which man had the more extreme height, we can calculate the z-scores for both individuals and compare their values. The z-score indicates how many standard deviations a particular value is from the mean.

For the tallest man with a height of 247 cm, we can calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value (247 cm), μ is the mean (175.97 cm), and σ is the standard deviation (7.46 cm).

z = (247 - 175.97) / 7.46 ≈ 9.50

For the shortest man with a height of 122.8 cm, we can calculate the z-score using the same formula:

z = (x - μ) / σz = (122.8 - 175.97) / 7.46 ≈ -7.14

The z-score for the tallest man is approximately 9.50, and the z-score for the shortest man is approximately -7.14.

Since the z-score measures how many standard deviations a value is from the mean, the man with the z-score of 9.50 (the tallest man) has the more extreme height. A higher z-score indicates a more extreme deviation from the mean.

Answer:

B. 14,525

Step-by-step explanation:

If a tablet costs $35 and the school is purchasing tablets for every student, then the total cost to buy tablets for the whole school would be:

$35 x 415 = $14,525

Therefore, the answer is B. $14,525.

Using an exponential growth function or equation, the population of Okrika in 2023 with a population of 5,000 in 2006 is projected to be 8,264.

An exponential growth function is a mathematical equation that shows a constant rate of growth in the value or number over a period.

Exponential growth functions or equations are depicted as y = a(1 + r)ⁿ, where y is the final value, a is the initial value, (1 + r) is the growth factor, r is the growth rate, and n is the time or number of years.

Population of Okrika in 2006 = 5,000

Annual growth rate = 3% = 0.03 (3/100)

Exponential growth factor = 1.03 (1 + 0.03)

The number of years between 2023 and 2006 = 17 years

Let the projected population in 2023 = y

Exponential growth equation or function: y = 5,000 (1.03)¹⁷

y = 8,264.

Thus, based on an exponential growth function, we can conclude that at 3% annual growth rate, the population of Okrika in 2023 will be 8,264.

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Assume a population growth rate of 3% per year for Okrika.

Answer:

Step-by-step explanation:

Triangle BDA right angled at A ⇒ BDA = 90

ABD = BDA - BAD = 90 - 45 = 45