What is the approximate total length of iron edging needed to create the square frame and the two diagonals? 43. 5 inches 50. 9 inches 54. 0 inches 61. 5 inches.

There were 7 students who signed up but did not attend the field trip. There were 36 students who initially signed up to go on the field trip. However, on the day of the trip, only 29 students showed up.

On the day of the field trip, only 29 students were present out of the 36 students who initially signed up.

There were 36 students who initially signed up to go on the field trip. However, on the day of the trip, only 29 students showed up. This means that 7 students who had originally signed up did not attend the trip.

The difference between the initial number of sign-ups (36) and the number of students present (29) gives us the number of students who did not show up:

36 - 29 = 7.

Therefore, there were 7 students who signed up but did not attend the field trip.

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An hour before show time, only people are seated for a. According to ticket sales, % of the people have yet to arrive. How many tickets were sold for the ​?

Solution:Since only 200 people are seated for a show an hour before the showtime, the remaining number of people who have yet to arrive can be found by subtracting the number of people who are seated from the total number of tickets sold.Let the total number of tickets sold be t.Then the number of people who have yet to arrive is `t - 200`.The percent of people who have yet to arrive is given to be More than 250 percent. Since percentages cannot be greater than 100%, this is impossible and the problem is incorrectly stated. Therefore, the number of tickets sold cannot be determined from the given information.

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The profit from selling the DVDs for the ski trip is £850.

To calculate the profit, we need to determine the total revenue and the total cost.

The total revenue is calculated by adding the revenue from selling 300 DVDs at £2 each (£600), the revenue from selling 250 DVDs at £2 each (£500), and the revenue from selling the remaining DVDs at £6 each (£300). This gives us a total revenue of £1,400.

The total cost is calculated by adding the cost of purchasing 300 DVDs (£300) and the cost of purchasing 250 DVDs (£250), which gives us a total cost of £550.

To find the profit, we subtract the total cost (£550) from the total revenue (£1,400), resulting in a profit of £850.

Therefore, the profit from selling the DVDs for the ski trip is £850.

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To determine the age of the counsellor, we can set up a system of equations based on the given information. By solving the equations simultaneously, we find that the counsellor is currently 28 years old.

Let's denote the counsellor's present age as x and the campers' age as y. Based on the given information, we can set up the following equations:

Equation 1: x + 4 = 2y

Equation 2: x - 5 = (3/4)(y + 8)

To solve this system of equations, we can substitute the value of x from Equation 1 into Equation 2:

(2y - 4) - 5 = (3/4)(y + 8)

2y - 9 = (3/4)(y + 8)

Multiplying both sides by 4 to eliminate the fraction:

8y - 36 = 3y + 24

5y = 60

y = 12

Substituting the value of y back into Equation 1:

x + 4 = 2(12)

x + 4 = 24

x = 20

Therefore, the counsellor is currently 28 years old.

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To factor the expression, we should first apply difference of squares method. This method is suitable because expression can be written as the difference of two perfect squares, namely (7x^3)^2 - (5y)^2.

The expression 49x^7 - 25y^2 can be rewritten as (7x^3)^2 - (5y)^2, which represents the difference of two perfect squares. The difference of squares method states that for any two perfect squares, say a^2 - b^2, it can be factored as (a + b)(a - b).

In this case, a = 7x^3 and b = 5y. Applying the difference of squares formula, we can factor the expression as follows:

49x^7 - 25y^2 = (7x^3 + 5y)(7x^3 - 5y).

Thus, the first method of factoring to be used for the given expression is the difference of squares method.

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The degree of the polynomial is 3.True. The degree of the polynomial is determined by the highest power of x, which is 3 in this case.The coefficient of the x^3 term is 2.True. The coefficient of the x^3 term is indeed 2.

The y-intercept is (0, 3).True. The y-intercept is found by setting x = 0, which results in f(0) = 2(0)^3 + 3 = 3.The graph of the function is always increasing.False. The graph of the function may not always be increasing. It depends on the sign of the coefficient of the x^3 term and the values of x. The function is an even function. False. The function is not an even function because it does not exhibit symmetry around the y-axis (i.e., f(-x) ≠ f(x)). The given function is f(x) = 2x^3 + 3. By analyzing the properties of the function and its equation, we can determine the truth or falsehood of each statement. The degree and coefficient of the x^3 term can be identified directly from the equation. The y-intercept is obtained by substituting x = 0. To determine whether the graph is increasing, we would need to examine the derivative or analyze the function's behavior at different intervals. The evenness or oddness of a function can be determined by evaluating f(-x) and comparing it to f(x).

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The correct option is C) The speed is decreasing because the distance traveled during each time increment is increasing.

The answer to the question is option C) The speed is decreasing because the distance traveled during each time increment is increasing.

Explanation:A group of students collected distance versus time data for a model car. There could be many types of data that can be collected with respect to distance and time.

For instance, distance could be in miles or kilometers, whereas time could be in seconds, minutes, or hours.In this case, the relation between the distance and time of a model car is given, and we have to describe how the speed of the car is changing over time. If the distance traveled during each time increment is increasing, then the speed is decreasing.

Thus, the correct option is C) The speed is decreasing because the distance traveled during each time increment is increasing.

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The actual distance between the two cities is 10.5 miles

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

Scale: 2 inches = 7 miles

Given that

Map distance = 3 inches

using the above as a guide, we have the following:

1.5 * 2 inches = 7 miles * 1.5

Evaluate the products

3 inches = 10.5 miles

Hence, the actual distance between the two cities is 10.5 miles

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Some energy workers are considered to work in the agriculture industry because their work relates to providing power and energy solutions specifically tailored for agricultural processes.

These employees are engaged in the creation and execution of environmentally-friendly energy systems specifically designed for agricultural operations and farming facilities.

One possible rephrased sentence could be: In order to produce renewable energy for farming activities such as irrigation and utilizing machinery, farmers could prioritize the implementation of solar panels, wind turbines, or biomass systems.

Moreover, professionals who work with energy in the agricultural sector can focus on enhancing energy effectiveness, incorporating intelligent farming techniques, or incorporating mechanisms for storing energy.

Their primary objective is to advocate for sustainable farming methods by decreasing dependence on conventional energy sources and advancing ecologically sound alternatives.

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The width of the rectangle is 10 inches, as it is calculated by finding the square root of the ratio of the area to the length.

Let's denote the width of the rectangle as "w" inches. According to the given information, the length of the rectangle is 4 times its width, so the length can be expressed as "4w" inches.

The formula for the area of a rectangle is length multiplied by width. In this case, the area is 400 square inches, so we have the equation:

Area = Length × Width

400 = (4w) × w

400 = 4w^2

To find the width, we can rearrange the equation and solve for "w":

4w^2 = 400

w^2 = 100

w = √100

w = 10

Therefore, the width of the rectangle is 10 inches. This means that the length of the rectangle is 4 times the width, which is 40 inches.

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i) I was proven innocent by virtue of the law.

ii) Don’t leave without your coat.

In sentence (i), the prepositional phrase "by virtue of" introduces the reason or cause for being proven innocent. It indicates that the law is the basis or foundation for the proof.

In sentence (ii), the prepositional phrase "without your coat" indicates the absence or lack of something. It specifies that the action of leaving should not occur unless the person has their coat with them.

Prepositional phrases consist of a preposition (such as "by," "of," or "without") followed by a noun or pronoun object. They provide additional information about location, time, manner, or other relationships in a sentence. Recognizing and understanding prepositional phrases helps in comprehending the structure and meaning of sentences.

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Under the given conditions and assuming an ambient temperature of 20°C, the stagnation temperature on the nose of the X-15 airplane would be approximately 2337.8 Kelvin.

We have,

Let's proceed by assuming a general value for the ambient temperature. We'll use 20°C as an approximation.

Given:

V = 7274.69 km/h

T = 20°C = 20 + 273.15 K = 293.15 K (conversion to Kelvin)

c_p = 1005 J/kg°C

Now we can substitute these values into the total temperature equation:

T(0) = T + (V² / (2 x c(p)))

T(0) = 293.15 K + ((7274.69 km/h)² / (2 x 1005 J/kg°C))

First, we need to convert the velocity from km/h to m/s:

V = 7274.69 km/h x (1000 m/km) / (3600 s/h) ≈ 2026.86 m/s

Now we can calculate the stagnation temperature:

T(0) = 293.15 K + ((2026.86 m/s)² / (2 x 1005 J/kg°C))

T(0) = 293.15 K + (4111017.56 m²/s² / 2010 J/kg°C)

T(0) ≈ 293.15 K + 2044.65 K

T(0) ≈ 2337.8 K

Therefore,

Under the given conditions and assuming an ambient temperature of 20°C, the stagnation temperature on the nose of the X-15 airplane would be approximately 2337.8 Kelvin.

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The number that should be placed in the empty box is 13.

In the given division problem, we start by dividing 4498 by 346. The quotient obtained is written above the solid line as 13. Then, we subtract 13 times 346 (which is 4498) from 4498 itself and write the result, -3900, below the line. Next, we bring down the 598 and subtract 598 from -3900, resulting in -3498.

We continue the process, bringing down the minus sign and subtracting 78 from -3498, which gives us -3576. Finally, we bring down the 0 and subtract 0 from -3576, resulting in 0. Since there is no remainder, the division is complete. Therefore, the number that should be placed in the empty box is 13.

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Katie completed 15 math problems. That is 5 times as many math problems as Katie completed.

Let's suppose the number of math problems that Katie solved is x.Therefore, 5 times the number of math problems that Katie solved is 5x. Eric completed 75 math problems.So, the expression representing the number of math problems that Eric solved is 75. Hence, the following equation can be written to determine the number of math problems that Katie solved:5x = 75Divide both sides by 5:x = 15Therefore, the number of math problems that Katie solved is 15.

Eric completed 75 math problems. That is 5 times as many math problems as Katie completed. How many math problems did Katie complete?Let's suppose the number of math problems that Katie solved is x.Therefore, 5 times the number of math problems that Katie solved is 5x. Eric completed 75 math problems.So, the expression representing the number of math problems that Eric solved is 75. Hence, the following equation can be written to determine the number of math problems that Katie solved:5x = 75Divide both sides by 5:x = 15Therefore, the number of math problems that Katie solved is 15.

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Total cost after 4 years = (2 * X) + (2 * Y) + (2 * Z) + (2 * W).

To determine Shelly's total cost after 4 years of attending community college and transferring to the university, we need to consider the costs associated with each institution separately.

Community College:

Let's assume the cost of tuition per year at the community college is $X.

Shelly will attend the community college for 2 years, so the total cost for tuition at the community college would be 2 * X.

In addition to tuition, there may be other expenses such as textbooks, supplies, and fees. Let's assume these additional expenses for each year at the community college amount to $Y per year. So, the total additional expenses for 2 years would be 2 * Y.

Therefore, the total cost for Shelly's education at the community college for 2 years would be:

Total cost at community college = (2 * X) + (2 * Y)

University:

Let's assume the cost of tuition per year at the university is $Z.

Shelly will transfer to the university for 2 years, so the total cost for tuition at the university would be 2 * Z.

Similarly, there will be additional expenses for each year at the university, which we'll assume amount to $W per year. Thus, the total additional expenses for 2 years at the university would be 2 * W.

Therefore, the total cost for Shelly's education at the university for 2 years would be:

Total cost at university = (2 * Z) + (2 * W)

To calculate the total cost for Shelly's education after 4 years, we sum up the costs at the community college and the university:

Total cost after 4 years = Total cost at community college + Total cost at university

Total cost after 4 years = (2 * X) + (2 * Y) + (2 * Z) + (2 * W)

Please note that the values of X, Y, Z, and W represent the respective costs per year at the community college and the university, and these values are not provided in the question.

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The most likely next step is 2x = -25.To find the most likely next step, let's analyze the given equations:

Step 1: 6x + 10 - 4x = -4 - 11

Step 2: 6x + 10 - 4x = -15

Step 3: 2x + 10 = -15

In Step 2, the equation simplifies by combining like terms on both sides of the equation, resulting in -15 on the right side.

To proceed, we need to isolate the variable x. In this case, we can continue by subtracting 10 from both sides of the equation:

Step 4: 2x = -15 - 10

Simplifying further:

Step 4: 2x = -25

Therefore, the most likely next step is 2x = -25.

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The given function, g(x), is defined piecewise: g(x)=  x+4, & -5 leq x leq -1
2-x, & -1 < x leq 5

To find the value of the function g at different values of x in its domain, we simply need to plug in the value of x into the function. This means that if we know the value of x, we can use the appropriate formula in the piecewise definition to find g(x).

g(-4) when x = -4,  we use the first formula since -5 ≤ -4 ≤ -1:

g(-4) = -4 + 4

g(-4) = 0

Therefore, g(-4) = 0.g(-2)

when x = -2, we use the first formula since -5 ≤ -2 ≤ -1:
g(-2) = -2 + 4

g(-2) = 2
Therefore, g(-2) = 2.g(0)

when x = 0, we use the second formula since -1 < 0 ≤ 5:
g(0) = 2 - 0

g(0) = 2
Therefore, g(0) = 2.g(3)

when x = 3, we use the second formula since -1 < 3 ≤ 5:
g(3) = 2 - 3

g(3) = -1
Therefore, g(3) = -1.g(4)

when x = 4, we use the second formula since -1 < 4 ≤ 5:
g(4) = 2 - 4

g(4) = -2

Therefore, g(4) = -2

The final answers are: g(-4) = 0g(-2) = 2g(0) = 2g(3) = -1g(4) = -2. Therefore, the answer is in 120 words.

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The median 0-10 10-20 20-30 30-40 40-50 50-60 frequency 5, 8, 20, 12, 7, 5 is 39.58.

To find the median 0-10 10-20 20-30 30-40 40-50 50-60 frequency 5, 8, 20, 12, 7, 5, follow the steps below:

Step 1: Write the frequency of each class in a column.Frequency05,820,312,75,Step 2: Find the total frequency.

N = 5 + 8 + 20 + 12 + 7 + 5N = 57Step 3: Find the median class.

The median class is the class where the cumulative frequency is equal to N/2 or the total frequency divided by 2. Thus, N/2 = 57/2 = 28.5The cumulative frequency starting from the first class is 5, which is less than 28.5. Therefore, the median class falls within the 20-30 class.

Step 4: Find the lower limit and upper limit of the median class.

The lower limit of the median class is 20 and the upper limit is 30.Step 5: Find the class width. Class width = Upper limit – Lower limit Class width = 30 – 20Class width = 10Step 6: Find the median. Median = L + [(N/2 – CF) / f] × w Where, L = lower limit of the median class N = total frequency CF = cumulative frequency of the class preceding the median class f = frequency of the median class w = class width   Substitute the values: Median = 20 + [(28.5 – 5) / 12] × 10Median = 20 + (23.5 / 12) × 10Median = 20 + 19.58Median = 39.58

Therefore, the median 0-10 10-20 20-30 30-40 40-50 50-60 frequency 5, 8, 20, 12, 7, 5 is 39.58.

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So, option (d) is the correct answer. A triangle with coordinates F(−2, 3), G(−4, 1), and H(−2, −2) is translated and its image has coordinates F’(0, 0), G’(−2, −2), and H’(0, −5). The correct rule for the translation is (x, y) → (x - 2, y - 3).

Let's find the distance and direction that the triangle is translated. The coordinates of the image are (0,0), (-2,-2) and (0,-5). We are going to get these coordinates from the original coordinates by applying a translation. Consider the vertex F first.The translation takes F to F'. In other words, we go from (-2,3) to (0,0).What did we do to get from F to F'?We subtracted 2 from the x-coordinate and 3 from the y-coordinate. In other words, we applied the rule(x, y) → (x - 2, y - 3)Thus the rule for the translation is (x, y) → (x - 2, y - 3). Therefore, option (d) (x, y) → (x - 2, y - 3) is the correct answer.

First of all, we will plot the coordinates of the initial and final triangle on the coordinate axis and name the initial triangle as FGH and the final triangle as F'G'H'As per the question, the coordinates of initial triangle are F(-2,3), G(-4,1) and H(-2,-2)The coordinates of final triangle are F'(0,0), G'(-2,-2) and H'(0,-5)Now let's find out the horizontal and vertical translation of the initial triangle to get the final triangle. To get F', we have to move 2 units in the right direction and 3 units in the upward direction. Let's see how this can be calculated:F to F' will move 2 units in the right direction and 3 units in the upward direction.-2 → 0 (2 units to the right)-3 → 0 (3 units upward)Therefore, we can say that the rule of translation is (x,y) → (x-2,y-3). So, option (d) is the correct answer.

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The given number is 271403. 271403 rounded off to the nearest hundred thousand is 300000. Answer: 300000

Rounding off is a way to make a number easier to work with.

Rounded numbers are an easy way to communicate approximate values.

Rounding a number is done by selecting the closest value to it that is more convenient to work with.

Here, we have to round off 271403 to the nearest hundred thousand.

The digits at the hundred thousand place and beyond will be dropped.

The number 271403 has a digit at hundred thousandth place.

This digit is 2.

Hence, we will look at the digit to its right which is 7.

Since this digit is greater than or equal to 5, we add 1 to 2 which gives us 3.

The hundred thousandth place now has digit 3 and all other digits after that are dropped.

Therefore, 271403 rounded off to the nearest hundred thousand is 300000. Answer: 300000

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271,403 rounded to the nearest hundred thousand is 300,000.

The given number is 271,403.

To round off this number to the nearest hundred thousand, we consider the digits to the left of the hundred thousand digits.

The hundred thousand digit is the fourth digit from the right, which is 1.

We need to round off the number based on the 1 in the hundred thousand's place.

The digit to the right of the hundred thousand digit (i.e., the ten thousand digit) is 4, which is less than 5.

Therefore, we do not add 1 to the hundred thousand digit and we leave it as is.

The digits to the right of the hundred thousand digits are dropped.

Hence, rounding off 271,403 to the nearest hundred thousand is 300,000.

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Two digital communication strategies you can control to protect yourself are:

1. **Strong Passwords**: One of the most effective ways to safeguard your digital communication is by using strong, unique passwords for your online accounts. A strong password should be a combination of upper and lowercase letters, numbers, and special characters. By using strong passwords and regularly updating them, you can prevent unauthorized access to your accounts. This can safeguard you if someone is trying to cause harm by attempting to gain unauthorized access to your personal information or accounts.

2. **Two-Factor Authentication (2FA)**: Enabling two-factor authentication adds an extra layer of security to your digital communication. With 2FA, you need to provide a second form of verification, such as a unique code sent to your mobile device, in addition to your password, to access your accounts. This can protect you if someone manages to obtain your password, as they would still need the second factor to gain access. 2FA makes it significantly harder for malicious individuals to compromise your accounts, providing an added safeguard against potential harm.

By implementing strong passwords and enabling two-factor authentication, you enhance the security of your digital communication and reduce the risk of unauthorized access and potential harm. These strategies provide an additional barrier against malicious activities and help ensure the confidentiality and integrity of your personal information and online accounts.

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The given statement describes a relationship between two angles that are not adjacent, stating that they do not form a linear pair. The different types of logical statementsstatements from this statement are the converse statement, inverse statement, contrapositive statement, and conditional statement.

Converse statement: The converse of a conditional statement switches the hypothesis and the conclusion. In this case, the converse statement would be: If two angles do not form a linear pair, then they are not adjacent.
Inverse statement: The inverse of a conditional statement negates both the hypothesis and the conclusion. The inverse statement would be: If two angles are adjacent, then they form a linear pair.
Contrapositive statement: The contrapositive of a conditional statement switches and negates both the hypothesis and the conclusion. The contrapositive statement would be: If two angles form a linear pair, then they are adjacent.
Conditional statement: The original statement itself is the conditional statement. It follows the form: If two angles are not adjacent, then they do not form a linear pair.
These different logical statements provide alternative ways to express the relationship between angles that are not adjacent and their formation of a linear pair.

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The value of CT is 11.25 units. Given that RT || AC, SR = 25, SA = 15, and ST = 20,

Explanation: we need to find CT.As RT || AC,

we can apply the property, "If a line is parallel to a side of the triangle and it intersects the other two sides of the triangle in two distinct points, then the line divides those sides proportionally.

"Now, using this property, we can say; ST/SA = RT/CT20/15 = RT/CT4/3 = RT/CTCT = 3RT/4

Now, we can apply the Pythagoras theorem in triangle RST,

RS² + ST²

= RT²RT²

= RS² + ST²

= 25² - 20²RT

= √(25² - 20²)

= √225 = 15 units

CT = 3RT/4

= 3 × 15/4

= 45/4 units

= 11.25 units (approx)

Therefore, the value of CT is 11.25 units.

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The simplified equivalent expression for the sum (5x – 2) + (2x + 9) is 7x + 7.

This can be obtained by combining like terms, which involves adding the coefficients of x and the constant terms separately.

In the given expression, we have (5x – 2) and (2x + 9). To simplify, we can add the coefficients of x together: 5x + 2x = 7x. Similarly, we can add the constant terms: -2 + 9 = 7. Therefore, the simplified expression becomes 7x + 7, where 7x represents the combined coefficient of x and 7 represents the combined constant term.

Overall, by combining like terms, we obtain the simplified equivalent expression of the sum (5x – 2) + (2x + 9) as 7x + 7.


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Here are two independent variables that could affect the cost of school supplies:1. Inflation Rate: The inflation rate is a measure of the overall increase in prices over time.

It can impact the cost of various goods and services, including school supplies. If the inflation rate is high, the prices of school supplies may increase, leading to higher costs for purchasing these items.

2. Demand for School Supplies: The demand for school supplies can also influence their cost. Probability of Higher demand typically leads to increased prices, as suppliers may adjust their prices to match the demand. Factors such as back-to-school seasons, educational policies, and population growth can affect the demand for school supplies.

By considering the inflation rate and the demand for school supplies as independent variables, we can better understand how these factors can impact the cost of school supplies.

However, it's important to note that there could be other variables that can also affect the cost, such as production costs, supply chain disruptions, and changes in government policies related to education or trade.

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The cost c of supplies for school depends on other factors lost at least 2 independent variables that could effect the cost of school supplies?

The greatest common factor (GCF) of the given expressions 24s^3, 12s^4, and 18s is 6s.

To find the GCF, we need to identify the highest power of each variable (s) that appears in all the expressions. In this case, the highest power of s that appears in all the expressions is s^3.Next, we consider the numerical coefficients. The GCF of the numerical coefficients 24, 12, and 18 is 6.

Finally, we combine the GCF of the numerical coefficients (6) with the highest power of the variable (s^3) to obtain the GCF of the entire expressions, which is 6s^3.Therefore, the greatest common factor of 24s^3, 12s^4, and 18s is 6s^3.

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Random questions can be solved in your head. option A

In common usage, randomness is the apparent or actual lack of pattern or predictability in information.

 A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events (or "trials") is predictable

A random question has no particular pattern therefore it can be asked any how.

Therefore, we can conclude that random questions can only be answered in your heard with any research.

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The cost of the lifetime membership in the movie club is $96.  To find the cost of the lifetime membership, we can subtract the cost of the movies from the total amount paid by Andrea.

The average cost per movie is $16, and she has purchased 24 movies. Therefore, the total cost of the movies is $16 * 24 = $384.

Since the membership fee is included in the average cost per movie, we can calculate the cost of the lifetime membership by subtracting the total cost of the movies from the total amount paid. So, the lifetime membership fee is $384 - ($12 * 24) = $96.

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The measure of the angle x is 59 degrees. Option A

The different trigonometric identities are listed as;

From the information given, we have that;

The measure of the adjacent is 880 feet

The opposite side is the ocean's surface = 1450 feet

The angle is x

Using the tangent identity, we have;

tan θ = opposite/adjacent

Now, we have to substitute the values, we get;

tan x = 1450/880

Divide the values, we get;

tan x = 1. 6477

Take the tangent inverse, we get;

x = 59 degrees

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Given that a quadratic equation has a vertical stretch of 4, shift to the left 2 units, and moved up 5 units.In general form the equation for a quadratic function is given by y = ax2 + bx + c

If a is negative, the graph is reflected over the x-axis. And, if a is greater than 1 or less than -1, then the graph will be stretched/compressed in the y-direction and narrow/widen in the x-direction.To obtain the equation for the quadratic function with the given conditions we will use the transformation of quadratic functions. The transformation of a quadratic function

f(x) = ax2 + bx + c

is given by the following formulas:Vertical stretch or compression: g(x) = a · f(x)Horizontal shift:

g(x) = f(x ± h)

Vertical shift: g(x) = f(x) ± k

Therefore, the transformation of

f(x) = ax2 + bx + c to g(x) = a ·

f(x + h) + k is: $$\large

y = a(x-h)^2+k$$Where, a = 4

(vertical stretch), h = 2

(shift to the left) and k = 5

(moved up).Thus, the equation of the quadratic function with the given transformations is:

y = 4(x + 2)² + 5

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