I have to find out which quadratic equations are in standard form?

The function f(x) = x⁴ - 10x² + 9 is to be graphed in DESMOS or a graphing calculator.The requested information is to be provided by the student.

Graph of the function:The graph of the function f(x) = x⁴ - 10x² + 9 is shown below:1. The value of f(0) is required to be found. When x=0,f(0) = 0⁴ - 10(0)² + 9 = 9Therefore, the value of f(0) = 9.2. Increasing and Decreasing Intervals in interval notation are to be found. To find the increasing and decreasing intervals, we need to find the critical points of the function.f'(x) = 4x³ - 20x = 4x(x² - 5) = 0.4x = 0 or x² - 5 = 0.x = 0 or x = ±√5.The critical points are x = 0, x = -√5, and x = √5. In addition, we may use the first derivative test to see whether the intervals are increasing or decreasing. f'(x) is positive when x < -√5 and when 0 < x < √5.

It's negative when -√5 < x < 0 and when x > √5. Therefore, the function f(x) is increasing on the intervals (-∞,-√5) and (0,√5) and it is decreasing on the intervals (-√5,0) and (√5,∞).3. We need to find the intervals of concave up and concave down. (Interval Notation) f''(x) = 12x² - 20. The critical points are x = ±√(5/3). f''(x) is positive when x < -√(5/3) and it is negative when -√(5/3) < x < √(5/3) and when x > √(5/3).Therefore, f(x) is concave upward on (-∞, -√(5/3)) and ( √(5/3),∞), and it is concave downward on (-√(5/3), √(5/3)).

Point(s) of Inflection as ordered pairs.5. The domain is all real numbers (-∞,∞) and the range is [0,∞).6. We need to find the x- y-intercepts of the graph of the function. We already found the y-intercept above. To find the x-intercepts, we have to solve the equation f(x) = 0. This gives us\(:x⁴ - 10x² + 9 = 0x² = 1 or x² = 9x = ±1 or x = ±3\)Therefore, the x-intercepts are (-1,0), (1,0), (-3,0), and (3,0).Therefore, the final answer is:f(0) = 9Increasing intervals = (-∞,-√5) and (0,√5)Decreasing intervals = (-√5,0) and (√5,∞)

Concave up intervals =\((-∞, -√(5/3)) and ( √(5/3),∞)Concave down interval = (-√(5/3), √(5/3))Points of inflection are (-\(√(5/3),f(-√(5/3))) and (√(5/3),f(√(5/3)))Domain = (-∞,∞)\)

\(Range = [0,∞)X-intercepts = (-1,0), (1,0), (-3,0), and (3,0).Y-intercept = (0,9\))\)

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The combination of truth values for r and s that satisfy the given conditions and make the statement true can be any of the four combinations mentioned above.

To determine the combination of truth values for variables r and s that make the statement true, let's break down the given information step by step.

The statement "p implies negation r or s" can be represented as "p → ¬r ∨ s." This means that if p is true, then either ¬r or s must be true (or both).

The statement "negation s implies q" can be represented as "¬s → q." This means that if ¬s is true, then q must also be true.

Combining these two statements, we can conclude that if p is true, then either ¬r or s must be true (or both), and if ¬s is true, then q must also be true.

To find all possible combinations of truth values for r and s, we can create a truth table:

|  p  |  q  |  r  |  s  | p → ¬r ∨ s | ¬s → q |

|-----|-----|-----|-----|------------|--------|

|  T  |  T  |  T  |  T  |     F      |   T    |

|  T  |  T  |  T  |  F  |     T      |   T    |

|  T  |  T  |  F  |  T  |     T      |   T    |

|  T  |  T  |  F  |  F  |     T      |   T    |

|  T  |  F  |  T  |  T  |     F      |   F    |

|  T  |  F  |  T  |  F  |     T      |   T    |

|  T  |  F  |  F  |  T  |     T      |   T    |

|  T  |  F  |  F  |  F  |     T      |   T    |

|  F  |  T  |  T  |  T  |     T      |   T    |

|  F  |  T  |  T  |  F  |     T      |   T    |

|  F  |  T  |  F  |  T  |     T      |   T    |

|  F  |  T  |  F  |  F  |     T      |   T    |

|  F  |  F  |  T  |  T  |     T      |   T    |

|  F  |  F  |  T  |  F  |     T      |   T    |

|  F  |  F  |  F  |  T  |     T      |   T    |

|  F  |  F  |  F  |  F  |     T      |   T    |

From the truth table, we can see that there are multiple combinations of truth values for r and s that satisfy the given conditions. Therefore, the combination of truth values for r and s that make the statement true can be any of the following:

1. r = T, s = T
2. r = F, s = T
3. r = T, s = F
4. r = F, s = F

In all these cases, the statement "p implies negation r or s and negation s implies q" is true.

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The combination of truth values for r and s that satisfy the given conditions and make the statement true can be any of the four combinations mentioned above Negation.

The combination of truth values for variables r and s that make the statement true, let's break down the given information step by step.

The statement "p implies negation r or s" can be represented as "p → ¬r ∨ s." This means that if p is true, then either ¬r or s must be true (or both).

The statement "negation s implies q" can be represented as "¬s → q." This means that if ¬s is true, then q must also be true.

Combining these two statements, we can conclude that if p is true, then either ¬r or s must be true (or both), and if ¬s is true, then q must also be true.

To find all possible combinations of truth values for r and s, we can create a truth table:

|  p  |  q  |  r  |  s  | p → ¬r ∨ s | ¬s → q |

|-----|-----|-----|-----|------------|--------|

|  T  |  T  |  T  |  T  |     F      |   T    |

|  T  |  T  |  T  |  F  |     T      |   T    |

|  T  |  T  |  F  |  T  |     T      |   T    |

|  T  |  T  |  F  |  F  |     T      |   T    |

|  T  |  F  |  T  |  T  |     F      |   F    |

|  T  |  F  |  T  |  F  |     T      |   T    |

|  T  |  F  |  F  |  T  |     T      |   T    |

|  T  |  F  |  F  |  F  |     T      |   T    |

|  F  |  T  |  T  |  T  |     T      |   T    |

|  F  |  T  |  T  |  F  |     T      |   T    |

|  F  |  T  |  F  |  T  |     T      |   T    |

|  F  |  T  |  F  |  F  |     T      |   T    |

|  F  |  F  |  T  |  T  |     T      |   T    |

|  F  |  F  |  T  |  F  |     T      |   T    |

|  F  |  F  |  F  |  T  |     T      |   T    |

|  F  |  F  |  F  |  F  |     T      |   T    |

From the truth table, we can see that there are multiple combinations of truth values for r and s that satisfy the given conditions. Therefore, the combination of truth values for r and s that make the statement true can be any of the following:

1. r = T, s = T

2. r = F, s = T

3. r = T, s = F

4. r = F, s = F

In all these cases, the statement "p implies negation r or s and negation s implies q" is true.

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Answer:

b^7

Step-by-step explanation:

as long as the bases are the same, just add the exponents when multiplying and subtract them when dividing

Answer:

\( {b}^{7} \)

Step-by-step explanation:

\( {a}^{m} {a}^{n} = {a}^{m + n} \)

\( {b}^{3} \times {b}^{4} \)

\( {b}^{3 + 4} \)

\( {b}^{7} \)

Step-by-step explanation:

Image 1:

Blank 1: (0,5)

Blank 2: (5,0)

Blank 3: (0,-5)

Blank 4: (-5,0)

Image 2:

C, Both B and D only have one line of symmetry. Choice A has more than 2 because you can evenly split the kite by its vertices and its lengths.

Image 3:

B, a regular quadrilateral is named this way because it contains both the point and linear symmetry. By definition, a regular quadrilateral must have 4 equal sides and angles and must have its diagonals bisect each other.

Image 4:

B, Point symmetry only. This is because when flipped upside down, the shape would still look the same. This would not be rotational symmetry because it does not look 100% like the original after rotating it to a certain degree.

Answer:

It's 25

Step-by-step explanation:

ooposite angle of 40 is the one between 2x and the 90 degree angle.

if that is 40 and another angle is 90, then

2x + 40 + 90 = 180

2x = 180 - 130

2x = 50

50/2 = x

x = 25

Sue is an example of the law for "diminishing marginal utility" if she only buys apples if the price drops because each apple produces less additional satisfaction.

The phenomenon known as diminishing marginal utility describes how each extra unit of gain results in an ever-smaller rise in subjective value.

Thus, Sue is an example of the law for "diminishing marginal utility" if she only buys apples if the price drops because each apple produces less additional satisfaction.

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This question is incomplete because the options were not written properly.

Complete Question

On Tuesday Jack bought four boxes. On Wednesday half of all the boxes that he had were destroyed.

Write an expression for how many boxes Jack has now

A. 1/2b+4

B. 1/2+4b

C. 4b−1/2b

D. b+42/2

Answer:

C. 4b−1/2b

Step-by-step explanation:

Let the number of boxes that Jack has be represented by b

In the question, we are told that:

• On Tuesday, Jack bought 4 boxes

Since 1 box = b

4 boxes = 4b

• On Wednesday , half of the boxes where destroyed.

= 1/2 b

The expression for how many boxes Jack has now is given as

Number of boxes Jack bought in Tuesday - half of the boxes destroyers on Wednesday.

This is expressed mathematically as:

4b - 1/2b

By solving the equation, we conclude that Jada scored approximately 26 points in the video game.

What is equation?

An equation is a mathematical statement that indicates the equality of two expressions. It consists of mathematical symbols, variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.

To find out how many points Jada scored, we need to divide James' score by the factor by which James outscored Jada.

Given that James scored 182 points and he scored 7 times as many points as Jada, we can set up the following equation:

James' score = Jada's score * 7

182 = Jada's score * 7

To find Jada's score, we can divide both sides of the equation by 7:

182 / 7 = Jada's score

Jada's score ≈ 26

Therefore, Jada scored approximately 26 points in the video game.

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Answer:

Cost: $11.50, $13, $14.50, $16, $17.50

Step-by-step explanation:

the pizza's 10 + 1.50x

its always 10 plus the price of the toppings

(x is the amount of toppings)

Answer:

the answer is A

Step-by-step explanation:

Answer:

A. 4xy \(\sqrt[4]{3y}\)

Step-by-step explanation:

4√768x⁸y⁵

---> factor 768 --> 4x4x4x4x3

---> x⁸ = x⁴⁺⁴ = x⁴ . x⁴

---> y⁵ = y⁴⁺¹ = y⁴ . y¹

4√4⁴x3 x⁴ . x⁴ . y⁴ .y  

since is 4th root, all the numbers with power to 4 comes out of the root

4x.x.y\(\sqrt[4]{3y}\)

4x²y\(\sqrt[4]{3y}\)

Complete options are attached.

Answer:

Option D: y = (∛x + 3) + 3

Step-by-step explanation:

To solve this, let's plug in some values into each of the options given.

From the graph, we can see that when x = 0, y ≈ 4.45.

Thus,let's plug in 0 for x into each of the options;

A) y = (√x - 3) + 3

Put 0 for x into the equation.

y = (√0 - 3) + 3

y = (√-3) + 3

Thus will give us a complex root. Thus, it is not the correct answer.

B) y = (√x + 3) + 3

Put 0 for x into the equation.

y = (√0 + 3) + 3

y = (√3) + 3

y = 1.732 + 3

y = 4.732

Thus,this function is not the correct answer.

C) y = (∛x - 3) + 3

Put 0 for x into the equation

y = (∛0 - 3) + 3

y = (∛-3) + 3

y = -1 + 3

y = 2

y is not equal to 4.45 and thus the function is not correct

D) y = (∛x + 3) + 3

Put 0 for x into the equation

y = (∛0 + 3) + 3

y = (∛3) + 3

y = 1.44 + 3

y = 4.44

This is approximately equal to the approximate value of 4.45 on the graph. Thus, it's the correct function.

Answer:

D EDGE2022

Step-by-step explanation:

Answer:

a and c

Step-by-step explanation:

Answer:

0.67 and 0.665

Step-by-step explanation:

Answe1/5 of r = 15

Step-by-step explanation:

1/5 r=

Answer:

20.27

Step-by-step explanation:

\(\sqrt{411} =20.27\)

Answer:

The square root of 411 cannot be simplified. √411 is already in its simplest radical form.

Step-by-step explanation:

To find a basis for the subspace W spanned by set S, we can perform Gaussian elimination on the matrix formed by the vectors in S. The basis vectors will be the non-zero rows in the reduced row-echelon form of the matrix.

a) s = [1 1 -2], [-1 -2 3], [1 0 -1], [2 -1 0]

Let's form a matrix using the given vectors:

```

[1  1  -2]

[-1 -2  3]

[1  0  -1]

[2 -1  0]

```

Perform Gaussian elimination to obtain the reduced row-echelon form:

```

[1  0  -1]

[0  1  -1]

[0  0  0]

[0  0  0]

```

The non-zero rows correspond to the basis vectors:

[1 0 -1] and [0 1 -1].

Therefore, the basis for W is {[1 0 -1], [0 1 -1]}.

The dimension of W (dim(W)) is equal to the number of basis vectors, which in this case is 2.

b) s = [1 2 -1 1], [3 1 1 2], [-1 1 -2 2], [0 -2 1 2]

Let's form a matrix using the given vectors:

```

[1  2 -1  1]

[3  1  1  2]

[-1 1 -2  2]

[0 -2  1  2]

```

Perform Gaussian elimination to obtain the reduced row-echelon form:

```

[1  0  1  0]

[0  1 -1  0]

[0  0  0  1]

[0  0  0  0]

```

The non-zero rows correspond to the basis vectors:

[1 0 1 0], [0 1 -1 0], and [0 0 0 1].

Therefore, the basis for W is {[1 0 1 0], [0 1 -1 0], [0 0 0 1]}.

The dimension of W (dim(W)) is equal to the number of basis vectors, which in this case is 3.

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Answer: 25%

Step-by-step explanation:

Given

Total students on a field trip are 68

Out of 68, only brings the camera

The percentage of students that bring the camera is given by

\(\Rightarrow \dfrac{17}{68}\times 100\\\\\Rightarrow \dfrac{1}{4}\times 100=25\%\)

Thus, only 25% of students bring a camera.

While writing the coordinates in the coordinate plane the coordinate that comes first coordinate is represented by x-coordinate.

As given in the question,

In the coordinate plane:

Therefore, the first coordinate in the coordinate plane is represented by x-coordinate.

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Answer:

Continuous.

Step-by-step explanation:

In Mathematics, a random variable can be defined as any variable whose values are determined by the outcome of a random experiment.

Basically, random variables are classified into two (2) main categories and these are;

1. Discrete random variable: a discrete random variable is a data set in which the number of possible values are either finite or countable. For instance, the value of a fair die, number of sweets in a jar, number of eggs in a crate etc.

2. Continuous random variable: a continuous random variable is a data set having infinitely many possible values and those values cannot be counted, meaning they are uncountable. Any quantity such as height, volume, weight, density, length, pressure, temperature, speed, distance, time are generally a continuous random variable.

Hence, the weight of a rock is continuous random variable because it has an infinite number of possible values such as 1kg, 20kg, 10kg, 50kg etc.

According to the combination method, the number of elements in the sample space for this experiment is 3060

Combination method:

Basically, the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter

Given,

A person eating at a cafeteria must choose 4 of the 18 vegetables on offer.

Here we have to calculate the number of elements in the sample space for this experiment.

While we looking into the given question, we have identified the following things,

They are

Total number of available vegetables = 18

Number of choices we have made = 4

Therefore, here the value of n = 18 and the value of x = 4,

Therefore, according to the ncx formula, it can be written as,

=> ¹⁸n₄ = 18! / 4! (18 - 4)!

=> ¹⁸n₄ = 18! / 4! (14)!

=> ¹⁸n₄ = 3060.

Therefore, there are 3060 number of elements in the sample space for this experiment.

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the correct option is D. 3 ln∣x - 7∣ + 4 ln∣x + 5∣ + C.

To express the integral (x² - 2x - 35)/(7x - 13) as a sum of partial fractions, we first factor the denominator:

7x - 13 = 7(x - 7) + 4(x + 5)

Now, we can write the integrand as:

(x² - 2x - 35)/(7x - 13) = A/(x - 7) + B/(x + 5)

To find the values of A and B, we multiply both sides of the equation by the denominator:

(x² - 2x - 35) = A(x + 5) + B(x - 7)

Expanding and simplifying, we get:

x² - 2x - 35 = (A + B)x + (5A - 7B)

Comparing the coefficients of x on both sides, we have:

1 = A + B

And comparing the constant terms, we have:

-35 = 5A - 7B

Solving this system of equations, we find A = 3 and B = 4.

Now, we can rewrite the integrand using the partial fraction decomposition:

(x² - 2x - 35)/(7x - 13) = 3/(x - 7) + 4/(x + 5)

To evaluate the integral, we integrate each term separately:

∫(3/(x - 7)) dx = 3 ln|x - 7| + C1

∫(4/(x + 5)) dx = 4 ln|x + 5| + C2

Combining these results, the integral becomes:

∫(x² - 2x - 35)/(7x - 13) dx = 3 ln|x - 7| + 4 ln|x + 5| + C

Therefore, the correct option is D. 3 ln∣x - 7∣ + 4 ln∣x + 5∣ + C.

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all the three terms on the right-hand side are positive and hence dy/dx is negative. Thus, this satisfies all the properties given. Therefore, the required autonomous differential equation is:dy/dx = a (y - 3) (y) (y - b).

We can obtain the autonomous differential equation having all of the given properties as shown below:First of all, let's determine the equilibrium solutions:dy/dx = 0 at y = 0 and y = 3y' > 0 for 0 < y < 3For -∞ < y < 0 and 3 < y < ∞, dy/dx < 0This means y = 0 and y = 3 are stable equilibrium solutions. Let's take two constants a and b.a > 0, b > 0 (these are constants)An autonomous differential equation should have the following form:dy/dx = f(y)To get the desired properties, we can write the differential equation as shown below:dy/dx = a (y - 3) (y) (y - b)If y < 0, y - 3 < 0, y - b < 0, and y > b. Therefore, all the three terms on the right-hand side are negative and hence dy/dx is positive.If 0 < y < 3, y - 3 < 0, y - b < 0, and y > b. Therefore, all the three terms on the right-hand side are negative and hence dy/dx is positive.If y > 3, y - 3 > 0, y - b > 0, and y > b. Therefore, all the three terms on the right-hand side are positive and hence dy/dx is negative. Thus, this satisfies all the properties given. Therefore, the required autonomous differential equation is:dy/dx = a (y - 3) (y) (y - b).

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Lizzie's divisibility test works for numbers that are multiples of 11.

Lizzie's divisibility test for a number m works as follows: break a positive integer n into two-digit chunks, find the alternating sum of these two-digit numbers, and if the result is divisible by m, then n is also divisible by m.

For example, if we have a number n = 354764, we would break it into the two-digit chunks 64, 47, and 35, then find the alternating sum of these numbers (64 - 47 + 35 = 52).

If we want to test if n is divisible by m = 4, we check if 52 is also divisible by 4. If 52 is divisible by 4, then we can conclude that 354764 is also divisible by 4.

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If  0010 belongs to each of the following regular sets

a. 0(01)0: 0010 belongs.

b. (000) (10): 0010 does not belong.

c. (00) 1 (00): 0010 does not belong.

d. (001)*0*: 0010 belongs.

e. 00(11) (01)*: 0010 does not belong.

To determine if 0010 belongs to each of the following regular sets, we will analyze the patterns and rules of each set.

a. 0(01)0: This set consists of strings that start and end with 0, with the sequence 01 in between. Since 0010 starts with 0, has 01 in the middle, and ends with 0, it belongs to this set.

b. (000) (10): This set consists of strings that have three consecutive 0's followed by 10. Since 0010 does not have three consecutive 0's, it does not belong to this set.

c. (00) 1 (00): This set consists of strings that have two 0's followed by 1 and then two more 0's. Since 0010 has two 0's followed by 1 and then only one more 0, it does not belong to this set.

d. (001)*0*: This set consists of strings that have any number of occurrences of 001 followed by any number of 0's. Since 0010 starts with 001 and is followed by 0, it belongs to this set.

e. 00(11) (01)*: This set consists of strings that start with 00, followed by 11, and then have any number of occurrences of 01. Since 0010 starts with 00, is followed by 11, and does not have any occurrence of 01, it does not belong to this set.

In summary:

a. 0(01)0: 0010 belongs.

b. (000) (10): 0010 does not belong.

c. (00) 1 (00): 0010 does not belong.

d. (001)*0*: 0010 belongs.

e. 00(11) (01)*: 0010 does not belong.

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Step-by-step explanation:

\( \sf \pink{ ii) a boy is selected}\)

Answer:

Um Sorry I Didn't Understand

The slope of the line as shown in the diagram attached below = rise/run = 3/5.

The rise of a line over the run of a line would give us the slope of a line on a coordinate plane.

With the given line in the diagram, the image attached below shows the rise as represented by a red line while the run is represented by the blue line.

Therefore, we have:

Run = 10 units

Rise = 6 units

Slope (m) of the line = rise/run = 6/10

Simplify

Slope (m) of the line =  3/5

Therefore, the slope of the line as shown in the diagram attached below = rise/run = 3/5.

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The equilibrium of this game is {s1 = 1/2, s2 = 1/4} and Player 2 plays A if sA2 = 3/4 and plays B if sB2 = 1/2.

Consider the following two-player game. Si = [0, 1], for i = 1, 2. Player 2 is equally likely to be type A or type B, and the realization of her type is private information to her.

Payoffs are as follows:

u1(s1,s2)=1−[s1 −(1/2)s2]^4

uA2(s1,sA2)=100−[sA2 −s1−1/4]^2

uB2 (s1,sB2 )=100−[sB2 −s1]^2.

To find a Bayes-Nash equilibrium of this game, we need to solve this problem by backwards induction.

The equilibrium of this game is {s1 = 1/2, s2 = 1/4} and Player 2 plays A if sA2 = 3/4 and plays B if Subs = 1/2.

A Bayes-Nash equilibrium is a pair of strategies, one for each player, such that each player's strategy is optimal given the other player's strategy and her private information about the game.

This is a refinement of the Nash equilibrium that takes into account the players' information about the game.

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Answer:

Option C.

Step-by-step explanation:

The given absolute value inequality is

\(|x+12|+5<27\)

Isolate the absolute value by subtracting 5 from both sides.

\(|x+12|+5-5<27-5\)

\(|x+12|+0<22\)

\(|x+12|<22\)

Therefore, the correct option is C.

We can further solve this, to find the solution of the given inequality.

\(-22<x+12<22\)

Subtract 12 from each sides.

\(-22-12<x+12-12<22-12\)

\(-34<x<10\)

The solution of given inequality is \(-34<x<10\).

Answer:

x=2

Step-by-step explanation:

To test when the function f(x) over takes the function g(x)

I just plugged in the x values

X f(x) g(x)

1 6 6

2 12 16

3 18 30

4 24 48

We can see from this table that f(x) is greater than g(x) starting from x=2

Therefore I think x=2 is your answer.

Hope this helps! :)

Answer: She will not make at least $200

Step-by-step explanation: To get Gabbys pay after her raise you find what 20% of 7 by multiplying 7 by .20 You should get 1.r which you then add to 7 to get her pay of 8.4 Next we must multiply that by 18 to get 151.2.

A(n) focus indicates when an object sends or receives a message and is identified by a narrow vertical shape that covers the lifeline. A) focus.

A focus, in the context of UML, is a graphical element that represents the point in time when an object is actively sending or receiving a message. It is indicated by a narrow vertical shape that covers the lifeline of the object in a sequence diagram.

The other options, subclass and instance, do not refer to elements used in sequence diagrams. Subclass refers to a type of object that inherits attributes and behaviors from a parent class, while instance refers to a specific occurrence of an object with its own unique set of attribute values. Activity is a type of diagram used to model business processes or workflows.

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