Exam 3: Linear, Quadratic, Polynomial, and Rational Functions

Find a number t such that the line in the xy-plane containing the points (t, 7) and (-2, 8) is perpendicular to the line containing the points (6, 8) and (8, 24).

Free

(Short Answer)

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Question 1

Correct Answer:

Verified

Find the equation of the line that contains the points (7, 14) and (9, 40). Write the equation in slope-intercept form.

Free

(Short Answer)

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Question 2

Correct Answer:

Verified

y = 13x - 77

Find a number t such that the line containing the points (2, t) and (1, 3) is parallel to the line containing the points (2, 5) and (-2, 1).

Free

(Short Answer)

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Question 3

Correct Answer:

Verified

Find a formula for if and .

(Short Answer)

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Question 4

Suppose p(x) = x² + 3x + 1, r(x) = 6x³ + 3. Write the expression (p(x))²(r(x) - 3) as a sum of terms, each of which is a constant times a power of x.

(Short Answer)

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Question 5

Find the equation of the line that contains the point (2, 1) and that is parallel to the line containing the points (2, 4) and (-2, 2).

(Multiple Choice)

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Question 6

The point (-2, -4) lies on a circle centered at (6, 1). Find the equation of the circle in standard form.

(Multiple Choice)

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Question 7

Suppose that f is a function whose domain is the interval , with f(x) = x² + 2x + 7. What is the domain of f^-1?

(Short Answer)

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Question 8

Find all real numbers x such that satisfy the indicated equation.

(Short Answer)

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Question 9

Suppose and . Write the expression (p + q)(x) as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

(Short Answer)

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Question 10

Evaluate the indicated quantity.25^3/2

(Multiple Choice)

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Question 11

Solve using any method. Round to two decimal places if necessary.

(Short Answer)

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Question 12

Find the asymptotes of the graph of the function .

(Short Answer)

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Question 13

Write as a power of 3.

(Short Answer)

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Question 14

Find the asymptotes of the graph of the function .

(Multiple Choice)

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Question 15

Suppose p(x) = x² + 9x + 7, r(x) = 18x³ + 9. Write the expression (9p - 7r)(x) as a sum of terms, each of which is a constant times a power of x.

(Short Answer)

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Question 16

Find two positive numbers whose difference equals 8 and whose product equals 180.

(Short Answer)

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Question 17

Suppose p(x) = x² + 4x + 2, q(x) = 4x³ - 2x + 1, r(x) = 8x³ + 4. Write the expression as a sum of terms, each of which is a constant times a power of x.

(Short Answer)

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Question 18

is $x^8 - 1 = (x^4 + 1)(x^2 + 1)(x + 1)(x - 1)$ correct?

(True/False)

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Question 19

Suppose . Write the expression (r(x))² as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

(Multiple Choice)

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Question 20

Showing 1 - 20 of 166

Find a number t such that the line in the xy-plane containing the points (t, 7) and (-2, 8) is perpendicular to the line containing the points (6, 8) and (8, 24).

Find the equation of the line that contains the points (7, 14) and (9, 40). Write the equation in slope-intercept form.

Find a number t such that the line containing the points (2, t) and (1, 3) is parallel to the line containing the points (2, 5) and (-2, 1).

Find a formula for if and .

Suppose p(x) = x² + 3x + 1, r(x) = 6x³ + 3. Write the expression (p(x))²(r(x) - 3) as a sum of terms, each of which is a constant times a power of x.

Find the equation of the line that contains the point (2, 1) and that is parallel to the line containing the points (2, 4) and (-2, 2).

The point (-2, -4) lies on a circle centered at (6, 1). Find the equation of the circle in standard form.

Suppose that f is a function whose domain is the interval , with f(x) = x² + 2x + 7. What is the domain of f^-1?

Find all real numbers x such that satisfy the indicated equation.

Suppose and . Write the expression (p + q)(x) as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

Evaluate the indicated quantity.25^3/2

Solve using any method. Round to two decimal places if necessary.

Find the asymptotes of the graph of the function .

Write as a power of 3.

Find the asymptotes of the graph of the function .

Suppose p(x) = x² + 9x + 7, r(x) = 18x³ + 9. Write the expression (9p - 7r)(x) as a sum of terms, each of which is a constant times a power of x.

Find two positive numbers whose difference equals 8 and whose product equals 180.

Suppose p(x) = x² + 4x + 2, q(x) = 4x³ - 2x + 1, r(x) = 8x³ + 4. Write the expression as a sum of terms, each of which is a constant times a power of x.

is $x^8 - 1 = (x^4 + 1)(x^2 + 1)(x + 1)(x - 1)$ correct?

Suppose . Write the expression (r(x))² as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

The Real Numbers

Functions and Their Graphs

Exponential Functions, Logarithms, and E

Trigonometric Functions

Trigonometric Algebra and Geometry

Sequences, Series, and Limits

Polar Coordinates, Vectors, and Complex Numbers

Prelude to Calculus

Filters

Exam 3: Linear, Quadratic, Polynomial, and Rational Functions

Find a number t such that the line in the xy-plane containing the points (t, 7) and (-2, 8) is perpendicular to the line containing the points (6, 8) and (8, 24).

Find the equation of the line that contains the points (7, 14) and (9, 40). Write the equation in slope-intercept form.

Find a number t such that the line containing the points (2, t) and (1, 3) is parallel to the line containing the points (2, 5) and (-2, 1).

Find a formula for if and .

Suppose p(x) = x2 + 3x + 1, r(x) = 6x3 + 3. Write the expression (p(x))2(r(x) - 3) as a sum of terms, each of which is a constant times a power of x.

Find the equation of the line that contains the point (2, 1) and that is parallel to the line containing the points (2, 4) and (-2, 2).

The point (-2, -4) lies on a circle centered at (6, 1). Find the equation of the circle in standard form.

Suppose that f is a function whose domain is the interval , with f(x) = x2 + 2x + 7. What is the domain of f -1?

Find all real numbers x such that satisfy the indicated equation.

Suppose and . Write the expression (p + q)(x) as a ratio, with the numerator and denominator each written as a sum of terms of the form cxm.

Evaluate the indicated quantity.253/2

Solve using any method. Round to two decimal places if necessary.

Find the asymptotes of the graph of the function .

Write as a power of 3.

Find the asymptotes of the graph of the function .

Suppose p(x) = x2 + 9x + 7, r(x) = 18x3 + 9. Write the expression (9p - 7r)(x) as a sum of terms, each of which is a constant times a power of x.

Find two positive numbers whose difference equals 8 and whose product equals 180.

Suppose p(x) = x2 + 4x + 2, q(x) = 4x3 - 2x + 1, r(x) = 8x3 + 4. Write the expression as a sum of terms, each of which is a constant times a power of x.

is x8−1=(x4+1)(x2+1)(x+1)(x−1)x^8 - 1 = (x^4 + 1)(x^2 + 1)(x + 1)(x - 1)x8−1=(x4+1)(x2+1)(x+1)(x−1) correct?

Suppose . Write the expression (r(x))2 as a ratio, with the numerator and denominator each written as a sum of terms of the form cxm.

The Real Numbers

Functions and Their Graphs

Exponential Functions, Logarithms, and E

Trigonometric Functions

Trigonometric Algebra and Geometry

Sequences, Series, and Limits

Polar Coordinates, Vectors, and Complex Numbers

Prelude to Calculus

Filters

Suppose p(x) = x² + 3x + 1, r(x) = 6x³ + 3. Write the expression (p(x))²(r(x) - 3) as a sum of terms, each of which is a constant times a power of x.

Suppose that f is a function whose domain is the interval , with f(x) = x² + 2x + 7. What is the domain of f^-1?

Suppose and . Write the expression (p + q)(x) as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

Evaluate the indicated quantity.25^3/2

Suppose p(x) = x² + 9x + 7, r(x) = 18x³ + 9. Write the expression (9p - 7r)(x) as a sum of terms, each of which is a constant times a power of x.

Suppose p(x) = x² + 4x + 2, q(x) = 4x³ - 2x + 1, r(x) = 8x³ + 4. Write the expression as a sum of terms, each of which is a constant times a power of x.

is $x^8 - 1 = (x^4 + 1)(x^2 + 1)(x + 1)(x - 1)$ correct?

Suppose . Write the expression (r(x))² as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.