Marecek & Anthony-Smith - Elementary Algebra 1/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 8 / 16

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving... ()

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Question

Points

1	2	3	4	5	6	7
1/1	4/4	2/2	1/1	0/1	–/1	–/6

Total

8/16 (50.0%)

Instructions

Elementary Algebra, 1st edition, written by Lynn Marecek and MaryAnne Anthony-Smith and published by OpenStax is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

Question 1 allows the student an opportunity to use mathematics in a real-world application using the Pythagorean Theorem.

Question 2 demonstrates how images can be randomized in addition to the standard practice of randomized numbers for problem solving.

Question 3 enforces the answer in simplified form including prompts for specific form using only positive or negative exponents for rational expressions.

Question 4 includes prompts to direct the student to enter either a comma-separated list of values or enter NO SOLUTION.

Question 5 features grading for exact answers for solving rational equations.

Question 6 shows simplifying and rationalizing grading for square roots.

Question 7 is a step-by-step question that walks students through on how to find the axis of symmetry, the vertex, x- and y-intercepts, and graph a quadratic equation. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

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.

1. 1/1 points | Previous Answers OSElemAlg1 3.4.253. My Notes

Brian borrowed a 17–foot extension ladder to use when he paints his house. If he sets the base of the ladder five feet from the house, how many feet up the side of the house will the top of the ladder reach? (Round your answer to one decimal place.)


		17'
	5'

16.2

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2. 4/4 points | Previous Answers OSElemAlg1 5.6.319. My Notes

Translate to a system of inequalities and solve.

Jocelyn is pregnant and needs to eat at least 400 more calories a day than usual. When buying groceries one day with a budget of $15 for the extra food, she buys bananas that have 90 calories each and chocolate granola bars that have 150 calories each. The bananas cost $0.45 each and the granola bars cost $2.50 each.

(a)

Write a system of inequalities to model this situation. (Let b represent the bananas bought and let g represent the number of granola bars bought. Enter your answers as a comma-separated list of inequalities.)

.45b+2.5g≤15, 90b+150g≥400

$webMathematica generated answer key$

(b)

Graph the system.

(c)

Could she buy 6 bananas and 6 granola bars?

Yes

(d)

Could she buy 5 bananas and 3 granola bars?

Yes No

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3. 2/2 points | Previous Answers OSElemAlg1 6.5.937.Tut. My Notes

Consider the following expression.

m⁹n²p⁵

m⁸n⁴

(a) Simplify the expression. (Give your answer using only positive exponents.)

mp5n2

$webMathematica generated answer key$

(b) Rewrite the simplified expression using only negative exponents.

n−2m−1p−5

$webMathematica generated answer key$

Tutorial

Solution or Explanation

Part 1 of 3

(a) Simplify the expression.

The numerator and the denominator of the given quotient contain exponential expressions that share a common base. Simplify by applying the quotient rule to those exponential expressions.

Notice that the exponential expressions in the numerator and denominator have like bases m and n. Divide them by keeping the bases the same and subtracting their exponents.

m⁹n²p⁵
m⁸n⁴
= m^{(9 − 8)}n^{2 − 4}p⁵

= mn^-2p⁵
Part 2 of 3

Simplify by changing the negative exponent to a positive exponent. Remember that for any nonzero real number x and integer n,
xⁿ =
1
x⁻ⁿ
.

Write
n⁻²
using a positive exponent. Think of
mn⁻²p⁵
as the following.

mn⁻²p⁵
1

Change the sign of the exponent on
n⁻²,
and then move the expression to the denominator.

mn⁻²p⁵
1
=
mp⁵
${\color{red}n^2}$

Thus, the simplification process results in the following expression.
$\frac{mp^{{\color{red}5}}}{n^{{\color{red}2}}}$
Part 3 of 3

(b) Rewrite the simplified expression using only negative exponents.

Change the positive exponents to negative exponents. Remember that for any nonzero real number x and integer n,
xⁿ =
1
x⁻ⁿ
.

Write
n²,
m, and
p⁵
using negative exponents. Remember that the exponent 1 is understood on m. Change the signs of the exponents on m and
p⁵,
and then move the expressions to the denominator. Change the sign of the exponent on
n²
and move the expression to the numerator.

mp⁵
n²
=
n⁻²
$m^{-1}p^{-{\color{red}5}}$

Thus, rewriting the simplified expression using only negative exponents gives the following result.
$\frac{n^{-{\color{red}2}}}{m^{-1}p^{-{\color{red}5}}}$

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4. 1/1 points | Previous Answers OSElemAlg1 7.6.294. My Notes

Solve. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

(5b + 1)(3b + 1) = 0

b =

−15, −13

$webMathematica generated answer key$

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5. 0/1 points | Previous Answers OSElemAlg1 8.6.356. My Notes

Solve.

= 6

for p

p =

1q−6

$webMathematica generated answer key$

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6. –/1 points OSElemAlg1 9.5.464. My Notes

Simplify and rationalize the denominator.

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7. –/6 points OSElemAlg1 10.5.920.Tut. My Notes

For the quadratic equation, state the axis of symmetry, vertex, and any intercepts.

y = x² − 4x − 5

axis of symmetry

vertex

(x, y) =

y-intercept

(x, y) =

x-intercept

(x, y) =

(smaller x-value)

x-intercept

(x, y) =

(larger x-value)

Graph the quadratic equation.

Tutorial

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Marecek & Anthony-Smith - Elementary Algebra 1/e (Homework)

Current Score : 8 / 16

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving... ()

Instructions

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Assignment Scoring

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