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[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question Show that the statement “For any real numbers a and b, a^2 = b^2 implies that a = b” is not true by giving a counter-example, think step by step [/INST] We take two numbers a = -3 and b = 3. Here, a^2 = b^2 (9 = 9) but a ≠ b. Hence, the statement ‘a^2 = b^2 implies that a = b’ is not true in general. , The answer is The statement is not true as shown by the counter-example.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question Find the coordinates of the foci, vertices, length of major axis, length of minor axis, eccentricity, and length of latus rectum for the equation 16x^2 + y^2 = 16., think step by step [/INST] , The answer is {'foci': ['(0, √15)', '(0, -√15)'], 'vertices': ['(0, 4)', '(0, -4)'], 'major axis length': 8, 'minor axis length': 2, 'eccentricity': '√15/4', 'latus rectum length': '½'}

[INST] help me answer this question **Question**: Taking the set of natural numbers as the universal set, write down the complements of the following sets: (i) {x: x is an even natural number}, think step by step [/INST] , The answer is {x: x is an odd natural number}

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question Solve the equation for x: 2x + 3 = 7., think step by step [/INST] We isolate x by subtracting 3 from both sides and then dividing both sides by 2. , The answer is The solution is x = 2.

[INST] help me answer this question If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii., think step by step [/INST] , The answer is To find the ratio of the radii, we first need to convert the angles to radians and then use the ratio of the arc-lengths formula. The final answer would be a simplified ratio of the radii based on the given angles.

[INST] help me answer this question A – C, think step by step [/INST] , The answer is A – C = (1, 2, 3, 4, 5, 6) - (3, 6) = (1, 2, 4, 5)

[INST] help me answer this question According to the question, the entire students should have an average of at least 60 marks, think step by step [/INST] To find the minimum number of marks, we need to first find the total marks of all students and then divide it by the number of students. After simplification, we get x ≥ 35. , The answer is The minimum number of marks that each student should obtain is 35.

[INST] help me answer this question Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbola 9y2 – 4x2 = 36, think step by step [/INST] Given the equation 9y2 – 4x2 = 36 or y2/4 – x2/9 = 1, we can compare it with the standard equation of a hyperbola y2/a2 – x2/b2 = 1. By doing so, we find that a = 2 and b = 3. We then calculate c using a2 + b2 = c2, which gives us c = √13. The coordinates , The answer is The coordinates of the foci are (0, √13) and (0, -√13), the coordinates of the vertices are (0, 2) and (0, -2), the eccentricity is e = c/a = √13/2, and the length of the latus rectum is (9/2).

[INST] help me answer this question Ends of major axis (± 3, 0), ends of minor axis (0, ±2), think step by step [/INST] The major axis is along the x-axis, and the ends of the major and minor axes are given. So, the equation will be of the form x2/a2 + y2/b2 = 1. Here, a = 3, b = 2. So, the equation of the ellipse is x2/9 + y2/4 = 1. , The answer is The equation of the ellipse is x2/9 + y2/4 = 1

[INST] help me answer this question Let us make the table of the given data and append other columns after calculations., think step by step [/INST] Here, the user is required to make a table of given data and add other columns after performing some calculations. , The answer is In this question, the user is being asked to create a table of the given data and append other columns after calculations.

[INST] help me answer this question (sin 2x + cos x)(sin 2x - cos x), think step by step [/INST] Simplify the given expression using the formula (a - b)(a + b) = a^2 - b^2 and (sin^2 x + cos^2 x) = 1. , The answer is sin4 x + cos2 x - 1

[INST] help me answer this question A coin is tossed, and a die is thrown. Find the sample space., think step by step [/INST] , The answer is The sample space contains possible outcomes of the given experiment. Since either coin can turn up Head (H) or Tail (T), and let us assume that 1, 2, 3, 4, 5 and 6 are the possible numbers that come when the die is thrown. The total number of possible outcomes equals (2 × 6) = 12. Hence, the sample space is, S={(H,1),(H,2),(H,3),(H,4),(H,5),(H,6),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}

[INST] help me answer this question Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them., think step by step [/INST] , The answer is A × B = {(1, 3), (1, 4), (2, 3), (2, 4)} The set A × B has 2^4 = 16 subsets. These are: {Φ}, {(1, 3)}, {(1, 4)}, {(2, 3)}, {(2, 4)}, {(1, 3), (1, 4)}, {(1, 3),(2,3)},{(1,3), (2,4)},{(1,4), (2,3)},{(1,4), (2,4)},{(2,3), (1,4)},{(2,3), (2,4)},{(1,3), (1,4), (2,3)},{(1,3), (1,4), (2,4)},{(1,4), (2,3), (2,4)},{(1,3), (2,3), (1,4), (2,4)}

[INST] help me answer this question (ii) {3, 4} ∈A is correct, think step by step [/INST] , The answer is {3, 4} is an element of A.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question Define a relation R on the set N of natural numbers by R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ∈ N}. Depict this relationship using roster form. Write down the domain and the range. , think step by step [/INST] , The answer is The relation R is given by R = {(1, 6), (2, 7), (3, 8)}

[INST] help me answer this question b = 3, c = 4, centre at the origin; foci on the x axis. What is the equation of the ellipse?, think step by step [/INST] The foci are on the x-axis, so the major axis is along the x-axis. The equation of the ellipse will be of the form x2/a2 + y2/b2 = 1. Since b = 3 and c = 4, a = 5. Using the formula a2 = b2 + c2, we get a2 = 25. Therefore, the equation of the ellipse is x2/25 + y2/9 = 1. , The answer is The equation of the ellipse is x2/25 + y2/9 = 1.

[INST] help me answer this question Factorize the given expression: 12x² + 16x, think step by step [/INST] , The answer is The factorized form of the given expression is 4x(3x + 4).

[INST] help me answer this question Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b^2}. Are the following true? (i) (a, a) ∈ R, for all a ∈ N, think step by step [/INST] , The answer is No, it is not true that (a, a) ∈ R, for all a ∈ N.

[INST] help me answer this question Prove that the coefficient of xn in the expansion of (1 + x)2n is twice the coefficient of xn in the expansion of (1 + x)2n – 1., think step by step [/INST] , The answer is The coefficient of xn in (1+x)2n is 2nCn and the coefficient of xn in (1+x)2n-1 is 2n-1Cn. We need to prove that 2nCn = 2 * 2n-1Cn.

[INST] help me answer this question 5.1) Make the table of the given data and append other columns after calculations., think step by step [/INST] This question is a subpart of question 1, and it is a instruction for the reader to create a table by calculating the mentioned values. , The answer is The answer is a table created by calculating mid-points, fixi, (xi – x̅), (xi – x̅)2, and fi(xi – x̅)2 for the given classes and their frequencies.

[INST] help me answer this question Major axis on the x-axis and passes through the points (4,3) and (6,2). What is the equation of the ellipse?, think step by step [/INST] The major axis is on the x-axis and the ellipse passes through the points (4,3) and (6,2). Using these two points, we can calculate the values of a and b and hence, the equation of the ellipse. , The answer is The equation of the ellipse is (x-5)2/16 + (y-3)2/1.5 = 1.

[INST] help me answer this question E ∩ F, think step by step [/INST] , The answer is E ∩ F = (6) ∩ (3, 4, 5, 6) = (6)

[INST] help me answer this question Select a point (0, 0)., think step by step [/INST] The solution region of the given inequality is below the line 3x + 4y = 12. (That is, the origin is included in the region.) , The answer is 3 × (0) + 4 × (0) ≤ 12

[INST] help me answer this question Find the equation of the parabola that satisfies the given conditions: Vertex (0, 0); focus (3, 0), think step by step [/INST] The vertex of the parabola is (0, 0), and the focus lies on the positive x-axis. The equation of the parabola is of the form y^2 = 4ax. Since the focus is (3, 0), a = 3. , The answer is y^2 = 12x.

[INST] help me answer this question Find R – Q, think step by step [/INST] R – Q represents the set of elements that are present in R but not in Q. Here, R is the set of real numbers and Q is the set of rational numbers. Therefore, R – Q is the set of irrational numbers. , The answer is Set of irrational numbers

[INST] help me answer this question If the area of a rectangle is 48 cm^2, and its length is 8 cm, find its breadth., think step by step [/INST] The formula for the area of a rectangle is A = l*b, where l is the length and b is the breadth. Plugging in the given value of A and l gives the breadth as b = A/l = 48/8 = 6 cm. , The answer is The breadth of the rectangle is 6 cm.

[INST] help me answer this question Question: The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour, and nth hour?, think step by step [/INST] Explanation: Given the situation, the sequence forms a G.P. To solve for the number of bacteria in each given case, we can use the properties of a G.P. , The answer is [{'part': 'At the end of the 2nd hour: 120 bacteria'}, {'part': 'At the end of the 4th hour: 480 bacteria'}, {'part': 'At the end of the nth hour: 30 * 2^n bacteria'}]

[INST] help me answer this question Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3)., think step by step [/INST] This is the equation of the line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3). Here, 'a' is the length of the intercept. , The answer is x/a + y/a = 1

[INST] help me answer this question What is a simple event?, think step by step [/INST] , The answer is An event that has only one sample point of a sample space is called a simple (or elementary) event.

[INST] help me answer this question Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbola y2/9 – x2/27 = 1, think step by step [/INST] Given the equation y2/9 – x2/27 = 1, we can compare it with the standard equation of a hyperbola y2/a2 – x2/b2 = 1. By doing so, we find that a = 3 and b = √27. We then calculate c using a2 + b2 = c2, which gives us c = 6. The coordinates of the foci are (0, ±c), so they are (0, 6) and (0, -6). The coordinates of the vertices are (0, ±a), so they are (0, 3) and (0, -3). The eccentricity is e = c/a = 6/3 = 2. The length of the latus rectum is given by 2b2/a = (2 × 27)/3 = 18. , The answer is The coordinates of the foci are (0, 6) and (0, -6), the coordinates of the vertices are (0, 3) and (0, -3), the eccentricity is e = c/a = 2, and the length of the latus rectum is 18.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question Find the variance for X., think step by step [/INST] , The answer is The variance for X is 35.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?, think step by step [/INST] , The answer is Let 'A' be the event of selecting a woman. n(A) = 6 P(A) = n(A)/n(S) = 6/10 = 3/5

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question Is it an order?, think step by step [/INST] None. , The answer is No, it is not an order.

[INST] help me answer this question In a group of 65 people, 40 like cricket, and 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?, think step by step [/INST] This is derived from n(C ∪ T) = n(C) + n(T) - n(C ∩ T) and n (T) = n (T - C) + n (T ∩ C). , The answer is 25 people like only tennis, and 35 people like tennis.

[INST] help me answer this question A coin is tossed, and then a die is rolled only in case a head is shown on the coin. Describe the sample space., think step by step [/INST] , The answer is When the head is encountered, the number of possible outcomes equals (1 × 6) = 6. So, the sample space when a head is encountered, SH, is {H1, H2, H3, H4, H5, H6}. If the tail is encountered, the sample space ST = {T}. Hence, the total sample space S = {H1, H2, H3, H4, H5, H6, T}.

[INST] help me answer this question What is the relationship between set B and set D?, think step by step [/INST] , The answer is Set B is equal to set D.

[INST] help me answer this question Clearly, √(x – 1) is defined for (x – 1) ≥ 0. So, the function f(x) = √(x – 1) is defined for x ≥ 1. Thus, the domain of f is the set of all real numbers greater than or equal to 1. Domain of f = [1, ∞)., think step by step [/INST] , The answer is The domain of the function f(x) = √(x – 1) is the set of all real numbers greater than or equal to 1.

[INST] help me answer this question How many 4-digit numbers are there with no digit repeated?, think step by step [/INST] , The answer is 9 × 9 × 8 × 7 = 4536

[INST] help me answer this question Verify the following: 3.1 (i) (0, 7, –10), (1, 6, –6), and (4, 9, –6) are the vertices of an isosceles triangle. 3.2 (ii) (0, 7, 10), (–1, 6, 6), and (–4, 9, 6) are the vertices of a right-angled triangle. 3.3 (iii) (–1, 2, 1), (1, –2, 5), (4, –7, 8), and (2, –3, 4) are the vertices of a parallelogram., think step by step [/INST] , The answer is 3.1 (i) The given points are the vertices of an isosceles triangle. 3.2 (ii) The given points are the vertices of a right-angled triangle. 3.3 (iii) The given points are not the vertices of a parallelogram.

[INST] help me answer this question 3x + 4y ≥ 12, , think step by step [/INST] , The answer is N/A

[INST] help me answer this question Find the coordinates of the point which divides the line segment joining the points (– 2, 3, 5) and (1, – 4, 6) in the ratio (i) 2: 3 internally, (ii) 2: 3 externally., think step by step [/INST] The formulas used for the coordinates of a point dividing two points internally and externally come directly from the section formula. The section formula gives the coordinates of a point that divides the line joining two points in a ratio, internally or externally. In this case, the two points are P (x1, y1, z1) = (– 2, 3, 5) and Q (x2, y2, z2) = (1, – 4, 6), and the given ratio is m : n = 2 : 3. Replacing these values in the section formula provides the required coordinates of the point dividing the two points in the given ratio, both internally and externally. , The answer is

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question What is the intersection of set B and set D?, think step by step [/INST] , The answer is (HHT, HTH)

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question x2 = -16y, think step by step [/INST] Since the coefficient of y is negative, the parabola opens downwards. On comparing the given equation with x2 = -4ay, we get -4a = -16, which gives a = 4. Thus, the coordinates of the focus are (0, a) = (0, -4), and the equation of directrix is y = a, which gives y = 4. The length of the latus rectum is 4a = 16. , The answer is The coordinates of the focus are (0, -4), the axis of the parabola is the y-axis, the equation of the directrix is y = 4, and the length of the latus rectum is 16.

[INST] help me answer this question Upon comparing, we have (x1 = -2, y1 = 3, z1 = 5); (x2 = 1, y2 = -4, z2 = 6) and (m = 2, n = 3). So, the coordinates of the point which divide the line segment joining the points P (– 2, 3, 5) and Q (1, – 4, 6) in the ratio 2: 3 externally are given by, think step by step [/INST] , The answer is ∴ The coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) are (-8, 17, 3).

[INST] help me answer this question c/a = 4/3, think step by step [/INST] , The answer is The eccentricity e is given as the ratio of c/a, where a = 7, so c = e × a = 4/3 × 7 = 28/3.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question Find the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8)., think step by step [/INST] , The answer is Hence, the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8) is 2:3.

[INST] help me answer this question We have x ≥ 0, , think step by step [/INST] , The answer is N/A

[INST] help me answer this question Prove that cos2 2x – cos2 6x = sin 4x sin 8x, think step by step [/INST] Using sum and difference formulas, cos 6x can be written as cos (2x + 4x) and cos 4x can be written as cos (2x + 2x). Then applying the formula for cos (a + b) and cos (a - b) and using some trigonometric identities, the result can be obtained. , The answer is cos2 2x – cos2 6x = sin 4x sin 8x

[INST] help me answer this question Does the equation of the circle becomes when h = -2?, think step by step [/INST] , The answer is (x + 2)2 + y2 = 25

[INST] help me answer this question Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5., think step by step [/INST] , The answer is The sum of such numbers is 99500.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question Evaluate<br>(i) 6C2<br>(ii) 9C5, think step by step [/INST] nCr = n! / {(n-r)! × r!} , The answer is {'part1': '15', 'part2': '126'}

[INST] help me answer this question Question: P (k + 1) is true whenever P (k) is true., think step by step [/INST] Explaination: N/A , The answer is Answer: Therefore, by the principle of mathematical induction, statement P (n) is true for all natural numbers, i.e., n.

[INST] help me answer this question What are mRNA and rRNA? Define them., think step by step [/INST] Both mRNA and rRNA are essential for protein synthesis. mRNA carries the genetic information from DNA to the ribosomes, while rRNA plays a structural role in ribosomes and facilitates the protein synthesis process. , The answer is mRNA, or messenger RNA, is a type of RNA (ribonucleic acid) that plays a crucial role in biology. The primary function of mRNA is to carry genetic information from the DNA in the cell nucleus to the ribosomes in the cytoplasm, where protein synthesis occurs.<br><br>rRNA, or ribosomal RNA, is another type of RNA that is a major component of ribosomes. Ribosomes are cellular structures where protein synthesis takes place. rRNA is vital for the assembly and function of ribosomes, helping to decode the mRNA and facilitating the formation of peptide bonds during protein synthesis.

[INST] help me answer this question Evaluate the given limit:, think step by step [/INST] Given limit, substitute x = 1, we get (a + b + c) / (a + b + c) = 1 , The answer is 1

[INST] help me answer this question Is event D a compound event?, think step by step [/INST] , The answer is Yes, D = (HHH, HHT, HTH, HTT) is a compound event.

[INST] help me answer this question In ΔOAB, if OA = OB = 20 cm and AB = 20 cm, what type of triangle is ΔOAB?, think step by step [/INST] , The answer is ΔOAB is an equilateral triangle.

[INST] help me answer this question Find the slope of the line AB., think step by step [/INST] , The answer is The slope of the line AB (m1) = (5-4)/(3-4) = 1/-1 = -1

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question Find the 15th term of the arithmetic sequence., think step by step [/INST] The nth term of the arithmetic sequence is given by an = n + 10. To find the 15th term, substitute n = 15 into the formula to get a15 = 15 + 10 = 24. , The answer is The 15th term is 24.

[INST] help me answer this question (Explore – NCERT Class 11 Solutions), think step by step [/INST] The data contains a link to explore NCERT Class 11 Solutions, but does not include the solutions directly. , The answer is Not provided in the data.

[INST] help me answer this question If the coin shows Head, what is the sample space?, think step by step [/INST] , The answer is The sample space, denoted as SH, is {(H,1), (H,2), (H,3), (H,4), (H,5), (H,6)}.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question Solve the given inequality: (x - 2)(x - 3) > 0, think step by step [/INST] , The answer is The solution of the given inequality is x < 2 or x > 3.

[INST] help me answer this question If A = {–1, 1}, find A × A × A., think step by step [/INST] , The answer is The A × A × A for a non-empty set A is given by A × A × A = {(a, b, c): a, b, c ∈ A} Here, it is given A = {–1, 1} So, A × A × A = {(–1, –1, –1), (–1, –1, 1), (–1, 1, –1), (–1, 1, 1), (1, –1, –1), (1, –1, 1), (1, 1, –1), (1, 1, 1)}

[INST] help me answer this question How many sets are there in this exercise?, think step by step [/INST] There are 9 questions in the exercise, and each question (and its corresponding subparts) represents a set. , The answer is There are 9 sets in this exercise.

[INST] help me answer this question Foci (0, ±13), the conjugate axis is of length 24., think step by step [/INST] Given foci (0, ±13) are on the y-axis, and the conjugate axis is of length 24, so the equation of the hyperbola is of the form y2/a2 – x2/b2 = 1. Here, a = 12 and c = 13. We know that a2 + b2 = c2, so b2 = 25. , The answer is The equation of the hyperbola is y2/25 – x2/144 = 1.

[INST] help me answer this question What can you say about the given triangle?, think step by step [/INST] , The answer is The given triangle is right-angled at A (4, 4).

[INST] help me answer this question If sin x + sin 3x + sin 5x = 0, find the value of x., think step by step [/INST] We can write sin x + sin 3x + sin 5x = 0 as (sin x + sin 5x) + sin 3x = 0. Using the formula 2 sin A cos B = sin (A + B) + sin (A - B), we can simplify it to sin 3x (2 cos 2x + 1) = 0. Therefore, sin 3x = 0 or 2 cos 2x + 1 = 0. If sin 3x = 0, then x = nπ/3, where n ∈ Z. If 2 cos 2x + 1 = 0, then cos 2x = – 1/2 = – cos π/3 = cos (π – π/3), so 2x = 2π/3 or 4π/3, and x = π/3 or 2π/3. However, x = 2π/3 is not a solution because sin 3x is negative when x = 2π/3. , The answer is x = nπ/3, where n ∈ Z

[INST] help me answer this question Write the following sets in the set-builder form. (i) (3, 6, 9, 12) (ii) {2, 4, 8, 16, 32} (iii) {5, 25, 125, 625} (iv) {2, 4, 6 … } (v) {1, 4, 9 … 100}, think step by step [/INST] In each case, I have described the sets using the set-builder notation, where x is the element of the set defined by a rule or condition. , The answer is (i) {x: x = 3n, n ∈ N and 1 ≤ n ≤ 4} (ii) {x: x = 2n, n ∈ N and 1 ≤ n ≤ 5} (iii) {x: x = 5n, n ∈ N and 1 ≤ n ≤ 4} (iv) {x: x is an even natural number} (v) {x: x = n^2, n ∈ N and 1 ≤ n ≤ 10}

[INST] help me answer this question Vertex (0, 0); focus (–2, 0), think step by step [/INST] , The answer is The equation of the parabola is y2 = -8x

[INST] help me answer this question Solve the quadratic equation -x2 + x - 2 = 0, think step by step [/INST] Comparing the given equation with ax2 + bx + c = 0, we have a = -1, b = 1, and c = -2. The discriminant (D) is calculated as D = b2 - 4ac = 12 - 4 × (-1) × (-2) = 1 - 8 = -7. Since D < 0, there is no real solution for this equation. , The answer is There is no real solution for this equation

[INST] help me answer this question What is the Perimeter of a square?, think step by step [/INST] The Perimeter is the distance around a shape. For a square, it is found by adding up all the side lengths, which are equal. So, 4 times the length of one side gives the perimeter. , The answer is The Perimeter of a square is calculated by the formula 4 multiplied by the side length.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question sin x = 1/4, x in quadrant II, think step by step [/INST] N/A , The answer is cos x/2 = ± √[(1 + cos x)/2]

[INST] help me answer this question (iii) Subsets of {1, 2, 3} are, think step by step [/INST] , The answer is Φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, and {1, 2, 3}.

[INST] help me answer this question What is the universal set for the set of right triangles?, think step by step [/INST] , The answer is The set of triangles or the set of polygons.

[INST] help me answer this question 3 (2 – x) ≥ 2 (1 – x), think step by step [/INST] The solutions of the given inequality are defined by all the real numbers greater than or equal to 4. Hence, the required solution set is [-∞, 4]. , The answer is x ≤ 4

[INST] help me answer this question What is the value of x in the following equation: 3x - 7 = 20?, think step by step [/INST] To find the value of x, we need to isolate it on one side of the equation. We can do this by adding 7 to both sides of the equation to get 3x = 27, and then dividing both sides by 3 to get x = 9. , The answer is The value of x is 9.

[INST] help me answer this question Find C – A, think step by step [/INST] C – A represents the set of elements that are present in C but not in A. , The answer is {2, 4, 10, 14}

[INST] help me answer this question Checking for the origin (0, 0) 0 ≤ 3, this is true. , think step by step [/INST] 0 ≤ 3, this is true. , The answer is The solution area would be on the left of the line graph

[INST] help me answer this question Find the value of tan (1050°)., think step by step [/INST] We know that the values of tan x repeat after an interval of π or 180°. Therefore, tan (1050°) = tan (900° + 150°) = tan 150° = tan (180° - 30°) = -tan 30°. Hence, tan (1050°) = -1/√3 = √3. , The answer is The value of tan (1050°) is √3.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question Is the origin included in the solution area for the second inequality?, think step by step [/INST] , The answer is No, the origin is not included in the solution area for the second inequality.

[INST] help me answer this question Expand (101)4 using the binomial theorem., think step by step [/INST] The binomial theorem is applied with 101 expressed as 100 + 1. , The answer is 104060401

[INST] help me answer this question (1/3 + 3i)3, think step by step [/INST] Not available in the text , The answer is -242/27 – 26i

[INST] help me answer this question Find the points on the x-axis whose distances from the line x/3 + y/4 = 1 are 4 units., think step by step [/INST] N/A , The answer is The required points on the x-axis are (-2, 0) and (8, 0).