HW2 - MTH 140, section 002, Fall 2020 Web Assign PDF

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9/13/2020

HW2 - MTH 140, section 002, Fall 2020 | WebAssign

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MTH 140, section 002, Fall 2020 INSTRUCTOR

Nara Yoon

HW2 (Homework)

Adelphi University

Current Score

QUESTION

1

2

3

4

POINTS

1/1

2/2

2/2

1/1

5

6

7

8

9

1/1

2/2

1/3

2/2

2/2

10

2/2

11

3/3

12

1/1

13

2/2

14

2/2

15

6/6

16

2/2

17

3/3

18

1

5/5

TOTAL SCORE

66/69

95.7%

Due Date

MON, SEP 14, 2020 11:59 PM EDT Request Extension

Assignment Submission & Scoring Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score.

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HW2 - MTH 140, section 002, Fall 2020 | WebAssign

[1/1 Points] MY NOTES

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ASK YOUR TEACHER

SPRECALC7 1.4.001.

PRACTICE ANOTHER

Which of the following are rational expressions? (Select all that apply.) 2x x2 − 1 x+3 2x + 3 x(x2 − 1) x+2

2.

[2/2 Points] MY NOTES

DETAILS

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ASK YOUR TEACHER

SPRECALC7 1.4.006.

PRACTICE ANOTHER

Yes or No? (Disregard any value that makes a denominator zero.) (a) Is the expression

a 6+a equal to 1 + ? 6 6

Yes No

(b) Is the expression

2 1 2 equal to + ? x 2 4+x

Yes No

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HW2 - MTH 140, section 002, Fall 2020 | WebAssign

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SPRECALC7 1.4.005.

PRACTICE ANOTHER

Yes or No? (Disregard any value that makes a denominator zero.) (a) Is the expression

x(x + 8) (x + 8)2

equal to

x ? x+8

Yes No

(b) Is the expression

x2 + 25 equal to x + 5?

Yes No

4.

[1/1 Points] MY NOTES

DETAILS

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ASK YOUR TEACHER

SPRECALC7 1.4.010.

PRACTICE ANOTHER

Find the domain of the expression. 5t2 − 3 3t + 9 all real numbers t ≠ −3 t < −3 t≤0 t > −3

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HW2 - MTH 140, section 002, Fall 2020 | WebAssign

[1/1 Points] MY NOTES

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ASK YOUR TEACHER

SPRECALC7 1.4.008.

PRACTICE ANOTHER

Find the domain of the expression. −x4 + x3 + 2x x≥0 x0

6.

[2/2 Points] MY NOTES

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ASK YOUR TEACHER

SPRECALC7 1.5.004.

PRACTICE ANOTHER

x= 0,2

(a) The solutions of the equation x2(x − 2) = 0 are

. (Enter your answers as a comma-separated list.)

(b) To solve the equation x3 − 2x2 = 0, we factor

7.

[1/3 Points] MY NOTES

DETAILS

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ASK YOUR TEACHER

the left-hand side.

SPRECALC7 1.5.006.

PRACTICE ANOTHER

W= $$0

The equation (x + 1)2 − 6(x + 1) + 8 = 0 is of quadratic

type. To solve the equation, we set

.

The

resulting quadratic equation is $$3

.

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HW2 - MTH 140, section 002, Fall 2020 | WebAssign

DETAILS

[2/2 Points] MY NOTES

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ASK YOUR TEACHER

SPRECALC7 1.5.007.

PRACTICE ANOTHER

To eliminate the denominators in the equation

3 4 + = 5, we multiply each side by the lowest common denominator x x+5

x(x+5)

to get the equivalent equation 3(x+5)+4x=5x(x+5)

.

9.

[2/2 Points]

DETAILS

MY NOTES

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ASK YOUR TEACHER

SPRECALC7 1.5.010.MI.

PRACTICE ANOTHER

Determine whether the given value is a solution of the equation. 3 − [4 − (3 − x)] = 3x − (4 + x) (a)

x = −2 Yes No

(b)

x=2 Yes No

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HW2 - MTH 140, section 002, Fall 2020 | WebAssign

[2/2 Points]

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SPRECALC7 1.8.004.

PRACTICE ANOTHER

(a) The set of all points on the real line whose distance from zero is less than 8 can be described by the absolute value inequality: |x| > 8 |x| < 8 |x| ≤ 8 |x| ≥ 8

(b) The set of all points on the real line whose distance from zero is greater than 8 can be described by the absolute value inequality: |x| > 8 |x| ≤ 8 |x| ≥ 8 |x| < 8

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HW2 - MTH 140, section 002, Fall 2020 | WebAssign

[3/3 Points]

MY NOTES

DETAILS

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ASK YOUR TEACHER

SPRECALC7 1.8.006.

PRACTICE ANOTHER

What is a logical first step in solving the inequality? (a)

3x ≤ 8 Divide both sides of the inequality by 3. Multiply both sides of the inequality by 8. Multiply both sides of the inequality by 3. Divide both sides of the inequality by 8. Subtract 3 from both sides of the inequality.

(b)

5x − 2 ≥ 1 Add 2 to both sides of the inequality. Subtract 1 from both sides of the inequality. Subtract 2 from both sides of the inequality. Subtract 5 from both sides of the inequality. Add 1 to both sides of the inequality.

(c)

|3x + 2| ≤ 6 Rewrite the inequality as 3x + 2 ≤ 6. Subtract 2 from both sides of the inequality. Consider the two cases |3x + 2| = 6 and |3x + 2| = −6. Consider the two cases |3x + 2| = 3x + 2 and |3x + 2| = −(3x + 2). Divide both sides of the inequality by 3.

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HW2 - MTH 140, section 002, Fall 2020 | WebAssign

DETAILS

[1/1 Points]

MY NOTES

Let S =

PREVIOUS ANSWERS

ASK YOUR TEACHER

−2, −1, 0,

1 , 1, 2

SPRECALC7 1.8.010.

PRACTICE ANOTHER

2 , 2, 4 . Determine which elements of S satisfy the inequality. (Enter your answers as a comma-

separated list.) −3 ≤ 4 − x < 3 $${√2, 2, 4}

13.

[2/2 Points]

MY NOTES

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ASK YOUR TEACHER

SPRECALC7 1.9.002.

PRACTICE ANOTHER

The distance between the points (a, b) and (c, d) is √(c−a)2 + (d−b)2

. So the distance between (5, 3) and (8, 7) is 5

14.

[2/2 Points]

MY NOTES

DETAILS

.

PREVIOUS ANSWERS

ASK YOUR TEACHER

SPRECALC7 1.9.003.

PRACTICE ANOTHER

(x, y) =

a+c2,b+d2

The point midway between (a, b) and (c, d) is

.

So the point midway between

(9, 10) and (7, 2)

(x, y) =

8,6

is

.

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[6/6 Points]

MY NOTES

HW2 - MTH 140, section 002, Fall 2020 | WebAssign

DETAILS

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ASK YOUR TEACHER

SPRECALC7 1.9.005.

PRACTICE ANOTHER

(a) To find the x-intercept(s) of the graph of an equation, we set y .

equal to 0 and solve for x

. So the

(b) To find the y-intercept(s) of the graph of an equation, we set x

equal to 0 and solve for y

. So the

x-intercept of 8y = x + 3 is -3

y-intercept of 8y = x + 3 is 0.375

16.

[2/2 Points]

MY NOTES

DETAILS

.

PREVIOUS ANSWERS

ASK YOUR TEACHER

SPRECALC7 1.9.006.

PRACTICE ANOTHER

(x, y) =

2,1

2 2 The graph of the equation (x − 2) + (y − 1) = 16 is a circle with center

and radius 4

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.

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[3/3 Points]

HW2 - MTH 140, section 002, Fall 2020 | WebAssign

DETAILS

PREVIOUS ANSWERS

SPRECALC7 1.9.007.

MY NOTES

ASK YOUR TEACHER

a,−b

(a) If a graph is symmetric with respect to the x-axis and (a, b) is on the graph, then

is also on the

graph.

−a,b

(b) If a graph is symmetric with respect to the y-axis and (a, b) is on the graph, then

is also on the

graph.

−a,−b

(c) If a graph is symmetric about the origin and (a, b) is on the graph, then

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is also on the graph.

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HW2 - MTH 140, section 002, Fall 2020 | WebAssign

DETAILS

[5/5 Points]

PREVIOUS ANSWERS

MY NOTES

SPRECALC7 1.9.008.

ASK YOUR TEACHER

The graph of an equation is shown below.

(x, y) =

(x, y) =

−3,0

(smaller x-value)

(a) The x-intercept(s) are (x, y) =

3,0

and

(smaller y-value)

0,2

and

(larger y-value).

(b) The graph is symmetric about the y-axis

[2/2 Points]

MY NOTES

DETAILS

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ASK YOUR TEACHER

.

SPRECALC7 2.1.002.

PRACTICE ANOTHER

For a function h, the set of all possible inputs is called the domain the range

and the y-intercept(s) are

(x, y) =

0,−1

19.

(larger x-value)

of h, and the set of all possible outputs is called

of h.

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HW2 - MTH 140, section 002, Fall 2020 | WebAssign

DETAILS

[5/5 Points]

MY NOTES

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ASK YOUR TEACHER

SPRECALC7 2.1.004.

PRACTICE ANOTHER

A function is given algebraically by the formula f(x) = (x − 2)2 + 3. Complete these other ways to represent f: (a) Verbal: "Subtract 2, then square the result

and add 3

.

(b) Numerical:

21.

[2/2 Points]

MY NOTES

x

f(x)

0

7

2

3

4

7

6

19

DETAILS

PREVIOUS ANSWERS

ASK YOUR TEACHER

SPRECALC7 2.1.006.

PRACTICE ANOTHER

Yes or No? If No, give a reason. Let f be a function. (a) Is it possible that f(5) = 3 and f(6) = 3? Yes. No. A function assigns each value of x in its domain to exactly one value of f(x). No. A function assigns each value of f(x) in its range to exactly one value of x. No. A function expecting a variable cannot be called with a constant argument. No. There is no possible function operations that would yield 3 from 6.

(b) Is it possible that f(5) = 3 and f(5) = 4? Yes. No. A function assigns each value of x in its domain to exactly one value of f(x). No. A function assigns each value of f(x) in its range to exactly one value of x. No. A function expecting a variable cannot be called with a constant argument. No. There is no possible function operations that would yield 4 from 5.

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HW2 - MTH 140, section 002, Fall 2020 | WebAssign

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[6/6 Points]

MY NOTES

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ASK YOUR TEACHER

SPRECALC7 2.1.076.

PRACTICE ANOTHER

A verbal description of a function is given. Let V(d) be the volume of a sphere of diameter d. To find the volume, take the cube of the diameter, then multiply by π and divide by 6. (a) Find an algebraic representation for the function. V(d) = d3π6

(b) Find a numerical representation for the function. d

V(d)

8π6 2

27π6 3

64π6 4

125π6 5

(c) Find a graphical representation for the function.

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HW2 - MTH 140, section 002, Fall 2020 | WebAssign

DETAILS

[1/2 Points]

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ASK YOUR TEACHER

SPRECALC7 2.1.077.

PRACTICE ANOTHER

Find the domain and range of f. f(x) =

1 7

if x is rational if x is irrational

Domain: {1, 7} all rational numbers all irrational numbers {1, all irrational numbers} all real numbers

Range: {1, 7} all rational numbers all irrational numbers {1, all irrational numbers} all real numbers

24.

[3/3 Points]

MY NOTES

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SPRECALC7 2.1.085.MI.

PRACTICE ANOTHER

In a certain country, income tax T (in dollars) is assessed according to the following function of income x: T(x) =

0 0.03x 600 + 0.11x

if 0 ≤ x ≤ 10,000 if 10,000 < x ≤ 20,000 if 20,000 < x

Find T(5,000), T(12,000), and T(25,000). T(5,000) = $ 0 T(12,000) = $ 360 T(25,000) = $ 3350

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HW2 - MTH 140, section 002, Fall 2020 | WebAssign

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[1/1 Points]

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SPRECALC7 2.1.091.

PRACTICE ANOTHER

Temperature readings T (in °F) were recorded every 2 hours from midnight to noon in Atlanta, Georgia. The time t was measured in hours from midnight. Sketch a rough graph of T as a function of t. t

0

2

4

6

8

10

12

T

63

57

56

50

53

54

59

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HW2 - MTH 140, section 002, Fall 2020 | WebAssign

[6/6 Points]

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SPRECALC7 2.1.510.XP.

PRACTICE ANOTHER

Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.) f(x) = 6x + 1 7 f(1) =

−11 f(−2) =

f

1 2

4 =

6a+1 f(a) =

−6a+1 f(−a) =

6a−6+1 f(a − 1) =

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