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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 851. |
Find equations of the tangent lines to the curve y = (x - 1)/(x + 1) that are parallel to the line x - 2y = 4 |
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Answer» Find equations of the tangent lines to the curve y = (x - 1)/(x + 1) that are parallel to the line x - 2y = 4 Solution: |
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| 852. |
What is the difference of the polynomials? (5x3 + 4x2) - (6x2 - 2x - 9) - (x3 + 6x2 + 9) - (x3 + 2x2) - (5x3 - 2x2 - 2x - 9) - (5x3 - 2x2 + 2x + 9) |
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Answer» What is the difference of the polynomials? (5x3 + 4x2) - (6x2 - 2x - 9) - (x3 + 6x2 + 9) - (x3 + 2x2) - (5x3 - 2x2 - 2x - 9) - (5x3 - 2x2 + 2x + 9) Solution: |
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| 853. |
Write the point-slope form of the line passing through (2, -12) and perpendicular to y = 3x. |
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Answer» Write the point-slope form of the line passing through (2, -12) and perpendicular to y = 3x. Solution: |
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| 854. |
Find an explicit rule for the nth term of the sequence. 2, -8, 32, -128, … |
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Answer» Find an explicit rule for the nth term of the sequence. 2, -8, 32, -128, … Solution: |
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| 855. |
Solve the following system of equations: x - 2y = 14, x + 3y = 9 |
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Answer» Solve the following system of equations: x - 2y = 14, x + 3y = 9 Solution: |
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| 856. |
Identify the 31st term of an arithmetic sequence where a1 = 26 and a22 = -226. |
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Answer» Identify the 31st term of an arithmetic sequence where a1 = 26 and a22 = -226. Solution: |
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| 857. |
Identify the 12th term of a geometric sequence where a1 = 8 and a6 = -8,192. |
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Answer» Identify the 12th term of a geometric sequence where a1 = 8 and a6 = -8,192. Solution: |
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| 858. |
What is the sum of the arithmetic sequence 3, 9, 15..., if there are 36 terms? |
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Answer» What is the sum of the arithmetic sequence 3, 9, 15..., if there are 36 terms? Solution: |
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| 859. |
What is the equation in point-slope form of the line passing through (1, 9) and (-1, 11)? y + 9 = -(x - 1) y - 9 = 1(x + 1) y + 9 = 1(x + 1) y - 9 = -(x - 1) |
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Answer» What is the equation in point-slope form of the line passing through (1, 9) and (-1, 11)? Solution: |
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| 860. |
How do you express intervals in inequalities such as [-2,9]? |
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Answer» How do you express intervals in inequalities such as [-2,9]? Solution: |
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| 861. |
Which function in vertex form is equivalent to f(x) = x2 + 6x + 3? |
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Answer» Which function in vertex form is equivalent to f(x) = x2+ 6x + 3? Solution: |
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| 862. |
If g(x) = 2(x -4), find the value of x if g(x) = 20. |
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Answer» If g(x) = 2(x -4), find the value of x if g(x) = 20. Solution: |
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| 863. |
Identify the type of conic section whose equation is given. x2= 4y - 2y2. Find the vertices and foci. |
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Answer» Identify the type of conic section whose equation is given. x2= 4y - 2y2. Find the vertices and foci. Solution: |
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| 864. |
What is the slope of the line that passes through (3, -7) and (-1, 1)? |
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Answer» What is the slope of the line that passes through (3, -7) and (-1, 1)? Solution: |
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| 865. |
Evaluate the integral by making the given substitution. (Use C for the constant of integration.)? sin5(θ) cos(θ) dθ, u= sin(θ) |
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Answer» Evaluate the integral by making the given substitution. (Use C for the constant of integration.)? sin5(θ) cos(θ) dθ, u = sin(θ) Solution: |
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| 866. |
Which system of equations can be used to find the roots of the equation 4x5 - 12x4 + 6x = 5x3 - 2x? |
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Answer» Which system of equations can be used to find the roots of the equation 4x5 - 12x4 + 6x = 5x3 - 2x? Solution: |
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| 867. |
The graph of the function f(x) is shown below. When f(x) = 0, determine x |
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Answer» The graph of the function f(x) is shown below. When f(x) = 0, determine x
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| 868. |
An isosceles triangle has an area of 150 ft2. If the base is 12 ft, what is the length of each leg? Round the answer to the nearest tenth. |
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Answer» An isosceles triangle has an area of 150 ft2. If the base is 12 ft, what is the length of each leg? Round the answer to the nearest tenth. Solution: |
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| 869. |
What is the average (arithmetic mean) of 8, 7, 7, 5, 3, 2, and 2? |
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Answer» What is the average (arithmetic mean) of 8, 7, 7, 5, 3, 2, and 2? Solution: |
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| 870. |
Solve the given differential equation by separation of variables. dy/dx = (x - 1)/(y + 2). |
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Answer» Solve the given differential equation by separation of variables. dy/dx = (x - 1)/(y + 2). Solution: |
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| 871. |
How many positive integers not exceeding 100 are divisible either by 4 or by 6? |
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Answer» How many positive integers not exceeding 100 are divisible either by 4 or by 6? Solution: |
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| 872. |
What is the coefficient of the x9y-term in the binomial expansion of (2y + 4x3)4? |
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Answer» What is the coefficient of the x9y-term in the binomial expansion of (2y + 4x3)? Solution: |
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| 873. |
The correct simplification of the expression 4 over y to the power of negative 3? |
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Answer» The correct simplification of the expression 4 over y to the power of negative 3? Solution: |
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| 874. |
Consider the function f(x) = (√5x − 5) + 1.Which inequality is used to find the domain? |
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Answer» For the function f(x) = (√5x − 5) + 1, the domain isDf(x) ∈ [1,∞). Greater than equal to inequality is used to find the domain of the given function. The mathematical expressions in which both sides may or may not be equal are called inequalities. In inequality, unlike equations, we compare two values. The equal sign in between is replaced byless than,greater than,ornot equal tosign. |
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| 875. |
The x- coordinate of the point which lies on the line represented by 5x - y - 7 = 0 and whose y - coordinate is 13, is |
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Answer» The x- coordinate of the point which lies on the line represented by 5x - y - 7 = 0 and whose y - coordinate is 13, is Solution: |
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| 876. |
Using the completing-the-square method, rewrite f(x) = x2 + 10x + 7 in vertex form. |
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Answer» Using the completing-the-square method, rewrite f(x) = x2+ 10x + 7 in vertex form. Solution: |
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| 877. |
Find the derivative of f(x) = -10x2 + 4x at x = 11. |
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Answer» Find the derivative of f(x) = -10x2 + 4x at x = 11. Solution: |
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| 878. |
Consider the functions f(x) = (4/5)x and g(x) = (4/5)x + 6. What are the ranges of the two functions? |
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Answer» Consider the functions f(x) = (4/5)xand g(x) = (4/5)x + 6. What are the ranges of the two functions? Solution: |
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| 879. |
What is the equation for the line of reflection that maps the trapezoid onto itself? |
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Answer» What is the equation for the line of reflection that maps the trapezoid onto itself?
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| 880. |
The value of (1.02)2 + (0.98)2 correct to the 3 decimal place is? |
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Answer» The value of (1.02)2 + (0.98)2correct to the 3 decimal place is? Solution: |
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| 881. |
Solve open parentheses square root of 7 close parentheses to the 6 x power = 49x - 6. |
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Answer» Solve open parentheses square root of 7 close parentheses to the 6 x power = 49x - 6. Solution: |
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| 882. |
Given f(x) = the quantity of 4x plus 1, divided by 3, solve for f-1(3). |
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Answer» Given f(x) = the quantity of 4x plus 1, divided by 3, solve for f-1(3). Solution: |
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| 883. |
Two parallel lines are crossed by a transversal. What is the value of x? x = 45,x = 65,x = 95,x = 115 |
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Answer» Two parallel lines are crossed by a transversal. What is the value of x?
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| 884. |
Given f(x) = the quantity of x plus 7, divided by 5, solve for f-1(3). |
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Answer» Given f(x) = the quantity of x plus 7, divided by 5, solve for f-1(3). Solution: |
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| 885. |
What is the angle between the given vector and the positive direction of the x-axis? i + √3j |
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Answer» What is the angle between the given vector and the positive direction of the x-axis? i + √3j Solution: |
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| 886. |
Find the maximum and minimum values attained by the function f along the path c(t). f(x, y) = xy; c(t) = (cos(t), sin(t)); 0 ≤ t ≤ 2π maximum value minimum value. f(x, y) = x2 + y2; c(t) = (cos(t), 4 sin(t)); 0 ≤ t ≤ 2π maximum value minimum value. |
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Answer» Find the maximum and minimum values attained by the function f along the path c(t). Solution: |
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| 887. |
Write an equation for the parabola with focus at (0, -2) and directrix x = 2. |
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Answer» Write an equation for the parabola with focus at (0, -2) and directrix x = 2. Solution: |
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| 888. |
Find the equation of the plane tangent to the surface at a given point 7xy + yz + 4xz - 48 = 0; (2,2,2) |
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Answer» Find the equation of the plane tangent to the surface at a given point 7xy + yz + 4xz - 48 = 0; (2,2,2) Solution: |
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| 889. |
If x > 2, then x2 - x - 6/x2 - 4 = |
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Answer» If x > 2, then x2- x - 6/x2- 4 = Solution: |
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| 890. |
Evaluate the function rule for the given value. f(x) = 15x for x = 3 |
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Answer» Evaluate the function rule for the given value. f(x) = 15xfor x = 3 Solution: |
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| 891. |
Explain why the function is discontinuous at the given point a. For the function f(x) = 1 / ( x - 3 ), find the point of discontinuity. |
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Answer» The functionf(x) = 1 / (x - 3) is discontinuous at x = 3. The explanation for the discontinuity of a function at a point is given below. We will use the concept of limits, continuity, and differentiability to find out why a function is discontinuous at a given point a. |
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| 892. |
Find an equation for the plane consisting of all points that are equidistant from the points (1, 0, -2) and (3, 4, 0) . |
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Answer» Find an equation for the plane consisting of all points that are equidistant from the points (1, 0, -2) and (3, 4, 0). Solution |
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| 893. |
Find the value of x. The diagram is not to scale. Given RS = ST, m RST = 7x - 54, mSTU = 8x |
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Answer» Find the value of x. The diagram is not to scale. Given RS = ST, m RST = 7x - 54, mSTU = 8x
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| 894. |
What is the equation of the horizontal line that passes through the point (-5, 1). |
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Answer» What is the equation of the horizontal line that passes through the point (-5, 1). Solution: |
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| 895. |
Find f + g, f − g, fg, and f/g and their domains:f(x) = x - 6 and g(x) = 5x2. |
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Answer» For f(x) = x - 6 and g(x) =5x2, we get:f(x) + g(x) = x - 6 + 5x2,f(x) - g(x) = x - 6 - 5x2,f(x).g(x) = 5x3- 30x2,f(x) / g(x) = (x - 6) / 5x2. Functions are very important concepts in mathematics that form the backbone of topics like calculus. The fundamental operations can be performed on two or more functions to give a new function as a result. |
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| 896. |
Determine whether the function f(x) = 3x4 is even or odd. |
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Answer» Determine whether the function f(x) = 3x4 is even or odd. Solution: |
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| 897. |
Divide 3x3 - 2x2 - 61x - 20 by x - 5. |
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Answer» Divide 3x3 - 2x2 - 61x - 20 by x - 5. Solution: |
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| 898. |
The fraction 325/790 converted to a decimal and rounded to the nearest hundredths place is? |
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Answer» The fraction 325/790 converted to a decimal and rounded to the nearest hundredths place is? Solution: |
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| 899. |
If p + 2q = 8 and 2p - q = 11, then p =? |
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Answer» If p + 2q = 8 and 2p - q = 11, then p =? Solution: |
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| 900. |
Which best represents the center of the data set below? Mean,median,range,mode |
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Answer» Which best represents the center of the data set below?
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