the measures of two acute angles of a right triangle differ by 22 degrees. find the measure of each angle.

Answer:

Mira's monthly income: Rs. 55,000

Allowance: Rs. 3,000

Total monthly income before festival expenses: Rs. 58,000

Festival expenses (equivalent to monthly basic salary): Rs. 55,000

Total monthly income including festival expenses: Rs. 113,000

Amount deducted for provident fund (10% of monthly income excluding allowance and festival expenses):

10% of (Rs. 55,000) = Rs. 5,500

Total monthly deduction for provident fund: Rs. 5,500

Taxable income:

Total monthly income including festival expenses - Total monthly deduction for provident fund = Rs. 107,500

To calculate the annual tax to be paid by Mira, we need to know the income tax rates and tax slabs applicable for the current financial year. Without this information, we cannot provide an accurate answer

The missing value in the arithmetic sequence is 11.

What is Arithmetic Sequence?

An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

To find the missing value in the arithmetic sequence, we need to first determine the common difference between consecutive terms.

To do this, we can subtract any two consecutive terms, such as the second and first terms:

3.8 - 2 = 1.8

This tells us that the common difference is 1.8.

Now, we can use this common difference to find the missing value, which is the sixth term in the sequence. We can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1)d

where a_n is the nth term, a_1 is the first term, n is the position of the term we want to find, and d is the common difference.

Using this formula with a_1 = 2, d = 1.8, and n = 6, we get:

a_6 = 2 + (6 - 1)1.8

a_6 = 2 + 5(1.8)

a_6 = 2 + 9

a_6 = 11

Therefore, the missing value in the arithmetic sequence is 11.

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The number of groups of five courses the student can select for the next semester is 126.

In order to answer this question, we must first determine how many courses the student has already taken. If the student has already taken 11 courses, then the total number of courses she needs to take is 9.

We can use the formula for combinations, nCr, to calculate the number of groups of five courses that she can select for the next semester. The formula is nCr=n!/(r!(n-r)!). In this case, n is the total number of courses (9) and r is the number of courses in each group (5).

Therefore, the number of groups of five courses the student can select for the next semester is 9C5, or 9!/[5!(9-5)!], which equals 126. This means the student can select 126 different groups of five courses for the next semester.

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Using L'Hopital's rule, verified that Lim_x→0 (4^(2 x) - 1)/(7 x) = (2 log(4))/7

To solve the limit, we can use L'Hopital's rule. First, let's rewrite the limit as

lim_x→0 [(4^(2x) - 1)/x]/(7/2)

Now, we can apply L'Hopital's rule to the numerator

lim_x→0 [(4^(2x) - 1)/x] = lim_x→0 [8x*4^(2x-1)] = 0

So we get:

lim_x→0 [(4^(2x) - 1)/x]/(7/2) = (0)/(7/2) = 0

Therefore, the limit is 0.

Now let's verify the given answer using logarithmic properties

(4^(2x) - 1)/(7x) = (2 log(4))/7

Multiplying both sides by 7x

4^(2x) - 1 = 2x log(4)

Using the identity a^2 - b^2 = (a+b)(a-b), we can rewrite the left-hand side as:

(4^x + 1)(4^x - 1) = 2x log(4)

Dividing both sides by (4^x - 1)

4^x + 1 = (2x log(4))/(4^x - 1)

Now, taking the limit as x approaches 0, we get:

lim_x→0 [(2x log(4))/(4^x - 1)] = lim_x→0 [(2 log(4))/(ln(4) × 4^x)] = (2 log(4))/7

Therefore, the given answer is verified.

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The percentage of area under the density curve where x is less than 2 is 20%

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",

The area of the whole density curve is ;

A = 1/2 (a+b)h

This is because the curve takes the shape of a trapezium.

A = 1/2 ( 4+6) 0.2

A = 1/2 × 10 × 0.2

A = 5 × 0.2

A = 1

The area of the curve in region less than 2

= 1/2 bh

= 1/2 × 2 × 0.2

= 0.2

The percentage of the area less than 2 in the curve is

x/100 × 1 = 0.2

x = 0.2 × 100

x = 20%

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Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.

To find 7/8 of 3.5, we can simply multiply 7/8 and 3.5 together.

7/8 x 3.5 = (7/8) x (7/2) = 49/16

So, the answer is 49/16. However, we need to write the answer as a mixed number in the simplest form.

To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator. In this case, 49 divided by 16 is 3 with a remainder of 1.

So, the mixed number is 3 1/16.

To simplify the mixed number, we need to check if we can reduce the fraction part (1/16) further. 1 is not divisible by any number other than 1 itself, so it is already in its simplest form.

Therefore, the final answer is 3 1/16.

In summary, to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.

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Answer:  it is a

Step-by-step explanation:

A system loses 640 J of potential energy. In the process, it does 660 J of work on the environment and the thermal energy increases by 120 J .  Change in kinetic energy is -1420 J.

Solution:

To find the change in kinetic energy, we can use the conservation of energy principle. In this case, the loss of potential energy is converted into work done on the environment and an increase in thermal energy, as well as the change in kinetic energy.

The equation for this would be:

Loss of Potential Energy = Work Done + Increase in Thermal Energy + Change in Kinetic Energy

Let's plug in the values:
-640 J (loss of potential energy) = 660 J (work done) + 120 J (increase in thermal energy) + Change in Kinetic Energy

Now, solve for the change in kinetic energy:
-640 J = 660 J + 120 J + Change in Kinetic Energy
-640 J = 780 J + Change in Kinetic Energy

Change in Kinetic Energy = -640 J - 780 J
Change in Kinetic Energy = -1420 J

So, the change in kinetic energy is -1420 J.

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Answer:

Answer B

Step-by-step explanation:

you want the answer or not i dont need to explain myself

Alden probably used the observational method to collect data for his box plot.

What is a case study?

A case study is an in-depth study on a particular topic collecting information in various ways in a real-world context. Using a range of data sources, a case study permits the analysis of a genuine topic within a specified framework.  Here Alden is conducting his own case study on Calories in Sodas.

In a case study, data is collected through various methods including the observational method, survey method, interview, etc. The observational method is observing the event or stimulus in real time and recording of its data. Therefore, Alden could have employed the observational method by visiting a nearby store and reading and recording the various labels of sods for their data.

And so, Alden collected the data for his box plot using the observational method.

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Answer:

0.0593, or 5.93%

Step-by-step explanation:

There are a total of 8 x 8 = 64 one-foot tiles in the foyer. Since two of them are cracked, there are 62 tiles that are not cracked.

To find the probability that the two cracked tiles share a common edge, we need to first determine the total number of pairs of adjacent tiles in the 62 remaining tiles. Each tile has four adjacent tiles (unless it is a tile on the edge of the foyer), so the total number of pairs of adjacent tiles is:

4 x (62 - 14) + 3 x 8 = 220

We subtracted 14 from 62 because there are 14 tiles on the edges of the foyer that only have three adjacent tiles, and we added 3 x 8 to account for the eight corner tiles that only have two adjacent tiles.

Next, we need to determine the number of ways that the two cracked tiles can be placed such that they share a common edge. There are 60 possible locations for the first cracked tile, and once it is placed, there are only 3 possible locations for the second cracked tile (it can only be placed in one of the three tiles adjacent to the first cracked tile). Therefore, the total number of ways that the two cracked tiles can be placed next to each other is:

60 x 3 = 180

Finally, we can calculate the probability by dividing the number of favorable outcomes (i.e., the number of ways that the cracked tiles can be placed next to each other) by the total number of possible outcomes (i.e., the total number of ways that the two cracked tiles can be placed):

P = 180/ (62 choose 2) = 180/ (62 x 61/2) = 0.0593 (approximately)

Therefore, the probability that the two cracked tiles share a common edge is approximately 0.0593, or 5.93%.

8 Cans of mandarin oranges are needed to serve a part of 200 people if each person is to receive a 3-ounce serving and each can weights 5 pounds 10 oz (9 ounces of that as liquid which you will discard).

Given that each can of mandarin oranges weighs 5 pounds 10 oz (9 ounces of that as liquid which you will discard).We are to find out how many cans of mandarin oranges are needed to serve a part of 200 people if each person is to receive a 3-ounce serving.

Convert 3 ounces into pounds and ounces

3 ounces = 3/16 pound (1 pound = 16 ounces)

Amount of mandarin oranges required by one person = 3/16 pound

Amount of mandarin oranges required by 200 people = 200 * (3/16) pound

Amount of mandarin oranges required by 200 people = 37.5 pound

Convert the amount of mandarin oranges required into cans

Weight of one can of mandarin oranges = 5 pounds 10 oz = (5*16 + 10) ounce = 90 ounce

Weight of mandarin oranges only in one can = 90 ounce - 9 ounce = 81 ounce (9 ounce is liquid which you will discard)

Number of cans required = (total weight required) / (weight of one can)Number of cans required = (37.5 * 16) / 81 Number of cans required = 7.4 cans

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From the given information provided, the 12th term of the geometric sequence 7, -35, 175 is -341,796,875.

To find the 12th term of the geometric sequence 7, -35, 175, we can use the formula for the nth term of a geometric sequence:

an = a₁ × r⁽ⁿ⁻¹⁾

where aₙ is the nth term, a₁ is the first term, r is the common ratio, and n is the term number we want to find.

First, we need to find the common ratio (r) between any two consecutive terms. We can do this by dividing any term by its preceding term:

r = (-35) / 7 = -5

Now, we can use the formula to find the 12th term:

a₁₂ = 7 × (-5)⁽¹²⁻¹⁾

a₁₂ = 7 × (-5)¹¹

a₁₂ = 7 × (-48828125)

a₁₂ = -341,796,875

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Answer:

Step-by-step explanation:

150.7083

The function represents exponential decay with a rate of 4.98% per time unit.

An exponential function is a mathematical function of the form f(x) = a^x, where a is a positive constant (called the base) and x is a variable that can take on any real value. The exponent x determines how quickly the function grows or decays.

If a is greater than 1, the function represents exponential growth, since each increment of x leads to a proportionally greater increase in the function value. If a is between 0 and 1, the function represents exponential decay, since each increment of x leads to a proportionally smaller decrease in the function value.

For example, the function f(x) = 2^x represents exponential growth, since each time x increases by 1, the value of the function doubles. On the other hand, the function g(x) = (1/2)^x represents exponential decay, since each time x increases by 1, the value of the function is halved.

The given function is y = 990(0.95)ˣ.

We can determine whether the change represents growth or decay by looking at the base of the exponential term, which is 0.95. Since this value is between 0 and 1, we know that the function represents decay.

To determine the percentage rate of decrease, we can compare the value of the function at x=0 (the initial value) with the value of the function at x=1 (one time unit later).

When x=0, we have:

y = 990(0.95)⁰ = 990

When x=1, we have:

y = 990(0.95)¹ = 940.5

Therefore, the percentage rate of decrease is:

[(990-940.5)/990] x 100% = 4.98%

So the function represents exponential decay with a rate of 4.98% per time unit.

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The mole is currently considered a base unit in the SI system, but it was not always the case. Until 2019, it was defined as a derived unit, which was dependent on the kilogram, which is one of the seven SI base units. However, the mole was redefined in 2019 as an independent base unit, with a fixed value based on the Avogadro constant, which is a fundamental constant of nature.

The mole is a crucial unit in chemistry, as it provides a means to measure the amount of a substance on a molecular scale. It is a unit of measurement for the number of particles (such as atoms, molecules, or ions) in a given sample. Thus, the mole is not a unit of measure in the way that meters, seconds, and kilograms are. Instead, it is a measure of the number of particles present in a sample, and it is used to calculate other properties such as molar mass, molarity, and stoichiometry.

While calculations performed with the number of moles of a substance could also be performed with the number of particles of a substance, the mole is still considered a base unit in the SI system because it is a fundamental unit that provides a bridge between the macroscopic and microscopic worlds. It is an essential unit for chemists and physicists, and its inclusion as a base unit in the SI system reflects its importance in these fields.

In summary, while the mole is not a unit of measure in the same way as meters, seconds, and kilograms, it is still considered a base unit in the SI system because of its importance in chemistry and physics. Its inclusion as a base unit reflects its fundamental role in these fields, and its recent redefinition as an independent base unit highlights its significance as a measure of the number of particles in a sample.

The ratio of the surface area to the volume of the cylinder is 2/r + 1/9.

Mathematically, the surface area (SA) of a cylinder can be calculated by using this formula:

SA = 2πrh + 2πr²

Where:

By substituting the given parameters into the formula for the surface area of a cylinder, we have;

Surface area (SA) of cylinder = (2 × π × r × 18) + 2πr²

Surface area (SA) of cylinder = 36πr + 2πr²

For the volume, we have:

Volume of cylinder = πr²h

Volume of cylinder = πr²(18)

Volume of cylinder = 18πr²

Now, we can determine the ratio;

Ratio = (36πr + 2πr²)/18πr²

Ratio = 2/r + 1/9

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To check if the line drawn is diameter it should be intersected at centre and it must be equidistant from the centre of the circle.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

To determine if the line Neil drew is an actual diameter of the circle and not just a smaller chord, he can use the following method -

Extend the line on both sides to create two lines that intersect at a point outside the circle.

Use a compass to draw a circle with the same center as the original circle, and with a radius that is greater than half the length of the line Neil drew.

Check if the two lines intersect the circle at two points that are equidistant from the center of the circle.

If they do, then the line Neil drew is an actual diameter of the circle.

If they do not, then the line Neil drew is just a chord.

This method works because a diameter of a circle is the longest chord that passes through the center of the circle.

By extending the line Neil drew and creating two lines that intersect outside the circle, we can compare the distance from the center of the circle to each of the two intersection points with the radius of the circle we drew.

If the distances are equal, then the line Neil drew must be a diameter of the circle.

Therefore, the method to find the actual diameter is explained.

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Answer:

y=-3x+5

Step-by-step explanation:

A line that is parallel to y=-3x-5 will have the same slope, which is -3.

Using the point-slope form, we can write the equation of the line as:

y - 8 = -3(x + 1)

Simplifying:

y - 8 = -3x - 3

Adding 8 to both sides:

y = -3x + 5

Therefore, the equation of the line in slope-intercept form that is parallel to y=-3x-5 and goes through the point (-1,8) is y = -3x + 5.

Answer:

Trina is 56 years old

Explanation:

If Duane is 6 years older than his brother, who just turned 14, we are adding 14+6, which is 20.

If trina is 4 years less than TRIPLE Duanes' age, then we first find triple of Duanes' age 20 x 3, which is 60. Then we find 4 less than 60, which is 56.

Answer: 85%

Step-by-step explanation:

percentage increase/decrease formula: new-old/old x 100

122914-66440/66440x100=85

To find a nonzero solution to a system of homogeneous equations, the corresponding matrix must be singular, meaning it has no inverse and its determinant is zero, allowing for the existence of eigenvectors corresponding to the eigenvalue λ = 0.

When we have a system of homogeneous equations, it means that all the equations in the system have a right-hand side of zero. Such a system can be written as Ax = 0, where A is the coefficient matrix and x is the column vector of variables.

To find a nonzero solution, we need to find a value of x such that Ax = 0, but x ≠ 0.

If A is a singular matrix, it means that it has no inverse, and its determinant is zero. This implies that the rows of A are linearly dependent, which in turn means that the columns of A are also linearly dependent. In other words, some of the columns of A can be expressed as linear combinations of the others.

When we multiply a singular matrix A by any nonzero vector x, we get a linear combination of its columns that equals zero, since the columns of A are linearly dependent.

Therefore, we can always find a nonzero vector x that satisfies Ax = 0. This nonzero vector x is called an eigenvector corresponding to the eigenvalue λ = 0, which is the only eigenvalue of a singular matrix.

Hence, finding a nonzero solution to a system of homogeneous equations requires that the matrix corresponding to this system is singular because only singular matrices have eigenvectors corresponding to the eigenvalue λ = 0, which are the solutions to the homogeneous equation Ax = 0.

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The expression given as 11 + 8p²q² - 9pq - 8 - 20p²q² + 22pq when simplified is 3 +13pq - 12p²q²

Given that

11 + 8p²q² - 9pq - 8 - 20p²q² + 22pq

The given expression 11 + 8p²q² - 9pq - 8 - 20p²q² + 22pq contains several terms with different variables and exponents.

To simplify the expression, we need to combine the like terms.

So, we have

11 + 8p²q² - 9pq - 8 - 20p²q² + 22pq = 11 - 9pq - 8 - 12p²q² + 22pq

Similarly, we can combine the other terms

So, we have

11 + 8p²q² - 9pq - 8 - 20p²q² + 22pq = 3 +13pq - 12p²q²

So, the solution is 3 +13pq - 12p²q²

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The average total lung capacity (TLC) of an average man is around 6 liters. However, the average total lung capacity of a man like Tom Sietas cannot be determined precisely as it depends on factors like height, weight, age, and physical condition.

What is lung capacity? Lung capacity refers to the total amount of air that your lungs can hold. Lung capacity is measured by a spirometer, a machine that measures the amount of air that you can breathe in and out. The total lung capacity (TLC) is the sum of four different volumes that include the tidal volume, inspiratory reserve volume, expiratory reserve volume, and residual volume.What is Tom Sietas’ total lung capacity?Tom Sietas is a German freediver who set a world record for holding his breath for 22 minutes and 22 seconds underwater in 2012. He is known for his exceptional lung capacity and has been reported to have a total lung capacity of 14 liters, which is more than double the average TLC of an average man. However, this figure may vary depending on several factors like height, weight, age, and physical condition.

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The plane is approximately 44,197 feet away from the air traffic control tower.

An illustration of an angle of elevation

Between the horizontal line and the line of sight, an angle called the angle of elevation is created. When the line of sight is upward from the horizontal line, an angle of elevation is created.

Trigonometry can be used to resolve this issue. Let's illustrate:

    P (plane)

     /|

    / |

   /  |  h = altitude of plane = 5127 ft

  /   |

 / θ  |

T-----X

 d = ?

In the illustration, T stands for the air traffic control tower, P for the aircraft, for the angle of elevation, X for the location on the ground directly beneath the aircraft, and d for the desired distance.

We can see that the tower, the spot on the ground just beneath the plane, and the actual plane itself make up the right triangle TPX. The triangle's opposite and adjacent sides can be related to the angle by using the tangent function:

tan θ = h / d

where d is the desired distance and h is the plane's altitude.

To find d, we can rearrange this equation as follows:

d = h / tan θ

Inputting the values provided yields:

d = 5127 feet / 7° of tan

Calculating the answer, we obtain:

d ≈ 44,197 ft

Thus, the distance between the aircraft and the air traffic control tower is 44,197 feet.

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There are a few different reasons why certain categorical variables may not be allowed in a linear regression model:

Some software packages require categorical variables to be converted to numerical variables before they can be included in a linear regression model. This is typically done using one-hot encoding, where each category is represented by a binary variable indicating whether or not it is present.

If the number of categories for a given variable is very large, this can create a very large number of new variables, which may exceed the capacity of the software or the memory available on the computer running the analysis.

Some software packages may not allow categorical variables with a very large number of categories, again because of the potential computational demands of encoding these variables as binary variables.

If a categorical variable has a large number of categories relative to the sample size, it may not be possible to estimate the coefficients for each category with enough precision to be useful. Some software packages may not allow categorical variables with missing values, unless those missing values are explicitly coded as a category.

Overall, the decision to include or exclude categorical variables from a linear regression model will depend on a variety of factors, including the number of categories, the software being used, the size of the dataset, and the research question being addressed.

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The nurse will give the patient one tablet of digoxin per day. Each tablet contains 187.5 mcg, so one tablet is the correct dose for the patient.

As per given information,

Patient's daily dose is 187.5 mcg.

Here we have to calculate the number of tablets the nurse will give the patient, use the following formula:

To get the number of tablets,

We have to divide the Patient's daily dose (mcg) by tablet dose (mcg).

Plugging in the numbers from the patient's prescription, we get:

Number of tablets = 187.5 mcg / 187.5 mcg

By simplifying these we get:

Number of tablets = 1

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The probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit 5 test is of:

0%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 48, \sigma = 15, n = 20, s = \frac{15}{\sqrt{20}} = 3.354[/tex]

The probability is one subtracted by the p-value of Z when X = 60, considering the standard error calculated with the Central Limit Theorem, hence:

Z = (60 - 48)/3.354

Z = 3.58

Z = 3.58 has a p-value of 1.

1 - 1 = 0.

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The true statements for the graph of y=(x+2)²2+4 are:, The vertex of the parabola is at the point (-2, 4)., The graph opens upwards, since the coefficient of the squared term is positive., The y-intercept of the graph is at the point (0, 9)., The x-coordinate of the vertex is -2, which is also the axis of symmetry of the parabola., The graph is a parabola, which is a U-shaped curve.

What is graph?

In mathematics, a graph is a visual representation of a set of points, called vertices or nodes, that are connected by lines or curves, called edges. Graphs are used to model relationships between objects or to represent data in a visual way.

In the context of coordinate geometry, a graph is a visual representation of a function or relation, which shows the relationship between the input values (x-axis) and output values (y-axis). The graph is typically a set of points plotted on a Cartesian plane, where each point represents a unique input-output pair.

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Complete Question:

Select the statements that are true for the graph of y = (x+2)²2 + 4.

a) The vertex of the parabola is (-2, 4).

b) The parabola opens upward.

c) The y-intercept of the parabola is 4.

d) The x-intercepts of the parabola are (-4, 0) and (0, 0).

e) The axis of symmetry of the parabola is a vertical line through x = -2.