Algebra How Algebra Can Be Essay

Words: 477 Length: 2 Pages Document Type: Essay Paper #: 57146207By observing x on the graph, then we make the connection that the slope of x on the graph represents rate of change of the linear function.

Once we have done this, it is then possible to move to the development of a quadratic equation and see what the impact of the increase (or perhaps decrease) means to the data. Have we proven that the rate of change is linear? The graphical representation of the data may be misleading, so it would be good to be able to calculate the rate of change to see if it is significant.

We could assign to value of L1 to the year in which the students are enrolled collect this data in columnar form, still graphing it on our graph. We would then call L2 the number of students enrolled every year which corresponds to the year we have listed in L1. In this case, in order to define the degree to which the number of students changes in enrollment from year to year we could simply make the calculation as such: (our change being represented as L3)

L3 = ?List (L2)/?L1

Reference:

No Authors Listed. (1996) Achieving Mathematical Power. Mathematics Curriculum Framework. Accessed via the World Wide Web on July 17, 2005 at http://www.doe.mass.edu/frameworks/math/1996/patterns.html… [Read More]

No Authors Listed. (1996) Achieving Mathematical Power. Mathematics Curriculum Framework. Accessed via the World Wide Web on July 17, 2005 at http://www.doe.mass.edu/frameworks/math/1996/patterns.html

Algebra the Use of Scientific Essay

Words: 650 Length: 2 Pages Document Type: Essay Paper #: 21750542Those studying physics and astronomy, and perhaps other scientific disciplines as well, are accustomed to the use of scientific shorthand and in some fields it is essential -- the example above of distance between energy waves from supernovae is a good example. There is a high level of variation in these distances, so a shorthand like the one on financial statements would be apply, but the numbers are very small so the use of shorthand is necessary. It is interesting to note, however, that even those in fields accustomed to scientific notation sometimes avoid it, as is the case with distances between objects in space.

Another group that does something similar to astronomers is the archaeologists. They have found ways to talk about years without using scientific notation, even though events often date back millions or billions of years. Yet, when discussing the science behind dating their samples, they will often use scientific notation, because that process involves radiation, carbon and other elements of physics. It can be concluded, however, from these examples, that the use of scientific notation is uncommon, and only used in highly specialized scientific fields. Even within those fields, practitioners have often developed a number of workaround solutions to avoid using scientific notation.

Works… [Read More]

Hoflich, P.; Wheeler, J. & Khokhlov, A. (1997). Hard x-rays and gamma rays from type Ia supernovae. The Astrophysical Journal. Vol. 492 (1998) 228-245.

Lalho, J. (2010). Light quark physics from lattice QCD. The XXVIII International Symposium on Lattice Field Theory. Retrieved November 19, 2011 from http://docs.google.com/viewer?a=v&q=cache:gDvRm6TY1VMJ:arxiv.org/pdf/1106.0457+physics+1.5e+%2B+09&hl=en&gl=us&pid=bl&srcid=ADGEESj0lgK5NDCG9_6ieDz24CvN4cltyb2a6Rkcxewes9FXnLbXorx8egE4f6_a7wSR-YQXM9fvOSZ3D05z4ASakSK1f48HrDiYS0JnlOLNbF3-1-upjAM4N-DhnF8rUoEmdWRK-qQC&sig=AHIEtbQ5aUobZS_c9iSSgDQqnLuG1-Kw2Q

Lalho, J. (2010). Light quark physics from lattice QCD. The XXVIII International Symposium on Lattice Field Theory. Retrieved November 19, 2011 from http://docs.google.com/viewer?a=v&q=cache:gDvRm6TY1VMJ:arxiv.org/pdf/1106.0457+physics+1.5e+%2B+09&hl=en&gl=us&pid=bl&srcid=ADGEESj0lgK5NDCG9_6ieDz24CvN4cltyb2a6Rkcxewes9FXnLbXorx8egE4f6_a7wSR-YQXM9fvOSZ3D05z4ASakSK1f48HrDiYS0JnlOLNbF3-1-upjAM4N-DhnF8rUoEmdWRK-qQC&sig=AHIEtbQ5aUobZS_c9iSSgDQqnLuG1-Kw2Q

Algebra All Exponential Functions Have as Domain Essay

Words: 475 Length: 2 Pages Document Type: Essay Paper #: 31166656Algebra

All exponential functions have as domain the set of real numbers because the domain is the set of numbers that can enter the function and enable to produce a number as output. In exponential functions whatever real number can be operated. (-infinity, infinity)

You have ln (x+4) so everything is shifted by 4. The domain of ln (x+4) is now -4 < x < infinity (Shifting infinity by a finite number gives you infinity again.) So,-4 < x < infinity is the domain of ln (x+4).

(2 [less than] t [less than] infinity)

For your function f (t) = 5.5exp (t) the function is continuous for all values of t as exp (t) is continuous for all values t, i.e. The domain of the function is -oo < t < oo

2a. subtracting 3 on the inside the function moves it 3 units to the right, that's the only transformation.

the vertical asymptote results from an invalid input to the function, like dividing by zero or taking the square root of a negative number, or in this case, taking the log of zero. so we need to find the value where x-3=0, thus the asymptote occurs at x=3. The x intercept is when y (or g (x) in this case)=0-0=g (x)=log (x-3) log (x-3)=0 x-3=10^0 x-3=1 x=4 so the intercept is at (4,0)

2b. We see that the right side of g (x), which is -log…… [Read More]

e^(75/40) = x

6.5208 = x

According to the model, at a time approximately 6.5 years after 2002, or some time in mid-2008, spam will account for 90% of all inbound email.

6.5208 = x

According to the model, at a time approximately 6.5 years after 2002, or some time in mid-2008, spam will account for 90% of all inbound email.

Words: 586 Length: 2 Pages Document Type: Essay Paper #: 24752073

Algebra -- Trig --

Writer's Note: The symbol "n" should really be referred to as "pi" or "?" To prevent confusion within the problem. Also, there is a difference between "squared" and "square root." The case in these problems is to use the square root, so "sqrt (number)." I've only managed the calculations because I have presumed the indicated changes.

Using the periodic properties of trigonometric functions, find the exact value of the expression

cos-

cos (8?/5) = cos (2? + (2?/5)) = cos (2?/5) = cos (72) = 0.31

cos (8?/5) = 0.31.

The point P. On the unit circle that corresponds to a real number t is:

{ 5-2 6 squared}

} Find csc (t)

P is on the unit circle, therefore the coordinates are (cos (t), sin (t)). This leads to the following calculations:

sin (t) = -2sqrt (6)/7, and csc (t) = 1/sin (t) = 1/(-2sqrt (6)/7) = 7/(-2sqrt (6)) = -7/2sqrt (6)

Answer: csc (t) = -7/2sqrt (6).

Use the reference to find the exact value of the expression

csc-

3

csc (4?/3) = csc (? + ?/3) -- csc (?/3) = -1/sin (?/3) = 1/sqrt (3/2) = -2/sqrt (3)

Answer: csc (4?/3) = -2/sqrt (3).

4. The point P. On the unit circle that corresponds to a real number t is:

{ 7 squared 3 }

{ - -, -- } Find the cot (t)

{ 4-4 }

P is on the unit circle, therefore coordinates are (cos (t), sin (t)). This leads to the following calculations:

cot (t) = cos (t)/sin (t) = x/y cos (t) = -sqrt (7)/4, sin (t) = -3/4

cot (t) = [-sqrt (7)/4] / (-3/4) = sqrt (7)/3

Answer: cot (t) = sqrt (7)/3.

5. What is the domain of the…… [Read More]

Algebra -- Trig Evaluate the Determinant Essay

Words: 668 Length: 2 Pages Document Type: Essay Paper #: 87391963Algebra -- Trig

Evaluate the determinant: | 3-9 |

Determinant of a square matrix can be solved by the following equation: A = ad -- bc, where a = 3, b = 9, c = 6, and d = 4. Therefore, A = (3)(4) -- (9)(6) = 12 -- 54 = -42

Solve the following system of equations using matrices:

y + 4z = 6, 2x + z = 1, x + 5y + z = -9

[ 1-5-1 | -9 ]

Row 2: R2 -- 2R1 = [ 2-0-1 | 1 ] -- 2[ 1 -1-4 | 6 ] = [ 0-2 -7 | -11 ]

Row 3: R3 -- R1 = [ 1-5-1 | -9 ] -- [ 1 -1-4 | 6 ] = [ 0-6 -3 | -15 ]

New matrix:

[ 0-2 -7 | -11 ]

[ 0-6 -3 | -15 ]

Row 2: R2/2 = [ 0-1 -7/2 | -11/2 ]

Row 3: R3 -- 3R2 = [ 0-6 -3 | -15 ] -- 3[ 0-2 -7 | -11 ] = [ 0-0-18 | 18 ]

Converting back to system of equations:

x -- y + 4z = 6

y -- 7/2z = -11/2

18z = 18, where z = 1

Plugging in:

y -- 7/2(1) = -11/2 y = -11/2 + 7/2 = -4/2 = -2

x -- (-2) + 4(1) = 6 x = 6 -- 6 = 0

Answer: x = 0, y = -2, z = 1.

Write the augmented matrix for the following system of equations:

x -- 7y + z = 15, y +6z = 14, z = 11

Answer:

[ 1 -7-1 | 15 ]

[ 0-1-6 | 14 ]

[ 0-0-1 | 11 ]

4. Perform the matrix row operation(s) and write the new matrix [ 2, -4, 1| 4]

[ -5, 0, 1| -3]

[ -1, 5, -2| -1]

-3R1 + R2

-3R1 = -3[ 2 -4-1 | 4 ] = [ -6-12 -3 | -12 ]

-3R1 + R2…… [Read More]

Algebra Trig Solve the System 7x Essay

Words: 859 Length: 2 Pages Document Type: Essay Paper #: 98381696Algebra, Trig

Solve the system: 7x + 3y = -2, -7x -- 7y =

(7x + 3y) + (-7x -- 7y) = (-2 + 14) 7x + 3y -- 7x -- 7y = 12 -4y = 12 y = -3

Substituting y for the first equation: 7x + 3(-3) = -2 7x -- 9 = -2 7x = 7 x = 1

x = 1, y = -3.

Solve the system: x + y = -5, x -- y = 12

(x + y) + (x -- y) = (-5 + 12) x + y + x -- y = 7 2x = 7 x = 7/2

Substituting x for the first equation: 7/2 + y = -5 y = -5 -- (7/2) y = -17/2

x = 7/2, y = -17/2.

Solve the system: y -- 3z = -12, -2x + y + 2z = 5, 2x + 3z = 7

(y -- 3z) + (-2x + y + 2z) + (2x + 3z) = -12 + 5 + 7 y -- 3z -- 2x + y + 2z + 2x + 3z = 0

2z = 0 y + z = 0 y = -z

Substituting for y for the first equation: -z -- 3z = -12 -4z = -12 z = 3 y = -3

Substituting z for the third equation: 2x + 3(3) = 7 2x + 9 = 7 2x = -2 x = -1

Answer: x = -1, y = -3, z = 3.

Solve the system: y = 4x + 3, 4y -- 20x = -8

4y -- 20x = -8 4y = 20x -- 8 y = 5x --

4x + 3 = 5x -- 2 x = 5

Substituting x for the first equation: y = 4(5) + 3 = 20 + 3 = 23

Answer: x = 5, y = 23.

5. Solve the system: x -- y + z = 6, x + y + z = 2, x + y -- z =0

x + y -- z = 0 x + y = z

Substituting z for the second equation: x + y + 2 = 2 z + z = 2 2z = 2 z = 1

(x -- y + z) + (x + y -- z) = (6 + 0) 2x = 6 x = 3

Substituting x…… [Read More]

Algebra or Geometry Have No Use in Essay

Words: 529 Length: 2 Pages Document Type: Essay Paper #: 15974703algebra or geometry have no use in "real" life, many people think that statistical analyses have no possible real-world applications. However, as the following scenario should make clear, statistical analysis can be extremely helpful in assessing quality control issues in the workplace. Using a specific type of statistical analysis, the supervisor at a former workplace was able to reduce costs while increasing customer satisfaction.

Analysis of variance (more generally referred to as an ANOVA test) is one of the most basic statistical tests that can be applied to a data set. It is used to provide an accurate way to compare the results from different groups (defined in ways that are relevant to the issue at hand). Such comparisons are useful because they provide information that allows processes to become more efficient or to meet other goals, such as increasing customer satisfaction.

For a number of years I have worked in a family-owned pet grooming company. It is a relatively small company, with two shops and plans to expand to four locations after the economy settles down. The staff provides grooming and bathing services for dogs, cats, and some "exotic" mammals such as sugar gliders and hedgehogs. These services include nail care, bathing and hair cutting. Some of the staff also trims birds' nails and flight feathers. The owners are thinking of adding boarding services as well as dog-walking services but are currently waiting on adding these services also.

The company frequently receives samples of grooming products -- shampoo and conditioners -- for dogs and occasionally for cats. Some products are advertised…… [Read More]

Intermediate Algebra Background for Martha Essay

Words: 937 Length: 2 Pages Document Type: Essay Paper #: 87139823

3b. One method that can be utilized to help Martha with applying algebra to real world application is through interactions within her environment that will allow her to utilize these skills. Another method proven useful in building applicable skills and communication is online conferencing. This tool utilized in the class room can give Martha access to knowledge from other professors and learners that could not normally be possible in a standard classroom. A professor that may specialize in a specific method on how to understand certain terms or expressions would be able to share these applications with students globally through virtual conferences. Technological Horizons (1993), recant the significance of videoconferencing by reporting that the characteristics of videoconferencing may actually enhance the learning process. Teachers and administrators say that students who take distance education classes are scoring higher on basic skills tests than those who are in the same classroom with an instructor. One side benefit to delivering classes through interactive video is increased socialization among the students

4b. Fox (2006) discussed the significant impact that utilizing the internet as a resource can be to furthering comprehension of a subject matter for children and adults. The writer went further to explain that e-learning can also be an effective way of reaching and maintaining the guidelines created under the No Child Left Behind Law. E-learning has been utilized in Florida as well as other states as a supplement to current learning initiatives. Fox made a valid point to the significance of e-learning as a tool by explaining that not only does e-learning help states and districts meet certain mandates. Virtual courses have a positive effect on student engagement and achievement.… [Read More]

Fox, Christine. "Going virtual: online courses can get to people and places beyond the reach of the traditional school setting, serving the needs of students and teachers nationwide. (Using Technology to Expand Opportunity)." THE Journal (Technological Horizons In Education). 1105 Media, Inc. 2006. Retrieved September 10, 2010 from HighBeam Research: http://www.highbeam.com/doc/1G1-148856686.html

Olliges, Ralph; Sebastian Mahfood. "10. Resources.(Teaching and learning in the new millennium: transformative technologies in a transformable world)(Missouri Department of Education Commission)." Communication Research Trends. Centre for the Study of Communication and Culture. 2003. Retrieved September 10, 2010 from HighBeam Research: http://www.highbeam.com/doc/1G1-130975621.html

Olliges, Ralph; Sebastian Mahfood. "10. Resources.(Teaching and learning in the new millennium: transformative technologies in a transformable world)(Missouri Department of Education Commission)." Communication Research Trends. Centre for the Study of Communication and Culture. 2003. Retrieved September 10, 2010 from HighBeam Research: http://www.highbeam.com/doc/1G1-130975621.html

Representation in Algebra A Problem Essay

Words: 4074 Length: 12 Pages Document Type: Essay Paper #: 317523302007, p. 115). Likewise, a study by Wyndhamm and Saljo found that young algebra learners were more successful in their problem-solving efforts when collaborating in a group environment. According to these researchers, "An experiment involving 14 small groups of Swedish students (usually 3 per group) aged 10, 11, and 12 years shows that these students acting in groups and creating shared contextualizations were able to solve mathematics word problems calling for real-world knowledge. Research has shown students acting alone to have difficulty with the same types of problems" (Wyndhamm & Saljo 1997, p. 361). Other teachers report that algebra story problems can help make learning more relevant to young people's lives. For instance, according to Homann and Lulay, "Algebra story problems are an important practical application of mathematics since real-world problems usually do not arise in terms of equations but as verbal or pictorial representations. The problems are solved by understanding, abstraction, and transformation of these representations into symbolic equational forms which can be solved by algebraic algorithms" (1996, p. 1). Likewise, Laughbaum makes the point that, "Our students see relationships in their lives, but do not know that the study of functions is the tool for analyzing and understanding them. What our students must be taught is to recognize and understand these mathematical relationships in the world they live in now, and will live in as adults" (2003, p. 64). Even here, though, there are some constraints to learning. For example, Dillon and Sternberg emphasize that, "Problem solving involves building a representation of the words of the problem and finding the solution of the problem using the rules of algebra. A major difficulty in students' performance on word problems seems to involve representation of the problem, i.e., moving from the words in the problem to a coherent mental representation of the problem. One major subcomponent in the representation process for word problems in the translation of each sentence" (1986, p. 145).

Critical Evaluation from Own Experience

The argument has been made that some subjects, such as Shakespeare, should not be taught until students reach…… [Read More]

Barry, D. (1989) Dave Barry Slept Here: A Sort of History of the United States. New York:

Random House.

Random House.

Coding Relational Algebra Operations Varies From School Essay

Words: 988 Length: 4 Pages Document Type: Essay Paper #: 46545920Coding relational algebra operations varies from school to school. I wrote it according to my training, but there are variations. Review and rewrite in own words so as to preclude plagiarism.

What is a relation schema? What is the difference between a relation, a relation schema, and a relational schema?

A relation schema is the basic information that describes a table or a relation. This includes the set of column names, the data within the columns, or the name associated with the entire table.

For example 'Students' would be the relation (I..e category) name.

The relation schema for students may be expressed as following:

Students (sid: string, name: string, login: string, age: integer, gpa: real)

It has five fields or columns each having names or types.

The relation, in other words, is the topic / category (e..g 'student'), the relations schema is the property categories of the relation, or of the 'student' table.

A relational schema refer to the meta-data elements which are used to describe the way that the Table is laid out. It describes the lay out and the constraints of the data in that particular SQL domain, or, in other words, it is a logical description of the design of the database. For instance, if a relation account would possess the categories of account_number, branch_name and balance, the algorithm of the relational schema would be thusly:

Account_schema= (account_number, branch_name, balance)

The primary key is the tag in the relational table that gives each record in the table its own identifier. The primary key can refer to either unique data such as a person's social security number or it can be globally unique data.

Primary keys can consist of a single unique attribute or they can be a combination of attributes.

As an example, we have the relational scheme of the Table that has each student's name. The ID number is a good choice for a primary key since it is unique. Their first and last name would not be a good choice as primary key since these can always be duplicated. There can be only one primary key in a database and this is the difference between…… [Read More]

Blaha, M. Referential Integrity Is Important For Databases http://www.odbms.org/download/007.02%20Blaha%20Referential%20Integrity%20Is%20Important%20For%20Databases%20November%202005.PDF)

What is a relation schema | Answerbag http://www.answerbag.com/q_view/730085#ixzz1ncwaYsPz

SQL Authority. SQL SERVER -- Difference Between Candidate Keys and Primary Key. http://blog.sqlauthority.com/2009/05/30/sql-server-difference-between-candidate-keys-and-primary-key/

What is a relation schema | Answerbag http://www.answerbag.com/q_view/730085#ixzz1ncwaYsPz

SQL Authority. SQL SERVER -- Difference Between Candidate Keys and Primary Key. http://blog.sqlauthority.com/2009/05/30/sql-server-difference-between-candidate-keys-and-primary-key/

Intermediate Algebra the Formula Is C 4D -1 3B Essay

Words: 372 Length: 1 Pages Document Type: Essay Paper #: 83530964Intermediate Algebra

The formula is C=4d^-1/3b

D= 23,245 because it is the pounds

B= 13.5 because that is the height of the mast

C=4(23,245)^-1/3(13.5)

Because the exponent was negative it needed to be dropped down to the numerator. The fact that it was a fraction meant that 92980 needed to be cubed, since it was a 1/3 exponent. Then it could be multiplied with the B. value, which was 13.5 / This left the final answer to be 283.693745115.

C=4d^-1/3b

d=64b3/c3

In order to solve for D. you needed to move 4 and the variable D. To the other side. Then you have to log both sides, which leaves an exponent of 3 instead of -1/3.

This formula could definitely be very important in the real world. For one, it is needed to be able to properly sail a boat in various conditions. It is extremely important to understand the conditions in which any boat can capsize. As such, it is important to use the formula in the real world to understand o much weight can be utilized in a boat of various length without the…… [Read More]

Words: 354 Length: 1 Pages Document Type: Essay Paper #: 57495388

College Algebra

Individual Project

Solve the following algebraically. Trial and error is not an appropriate method of solution. You must show all your work.

Solve algebraically and check your potential solutions:

x = -4 does not satisfy the equality. So the answer is only x = 5

Show the steps that you would take to solve the following algebraically:

Show your work here:

c) What potential solution did you obtain? Explain why this is not a solution.

This is not a solution because it makes the original equation indefinite. It makes the denominator zero.

The following function computes the cost, C (in millions of dollars), of implementing a city recycling project when x percent of the citizens participate.

a)

Using this model, find the cost if 60% of the citizens participate?

Answer:

million dollars

b)

Using this model, determine the percentage of participation that can be expected if $4 million is spent on this recycling project. Set up an equation and solve algebraically. Round to the nearest whole percent.

Answer: 74%

4)

a)

If

, fill in…… [Read More]

Words: 777 Length: 3 Pages Document Type: Essay Paper #: 17669883

College Algebra

Graphing Transformations

a) Given the function f (x) = x^2 complete the following table. Must show all work for full credit.

f (x)

Show Work:

When x = 0, f (x) = f (0) = (0)^2 = 0.

When x = 1, f (x) = f (1) = (1)^2 = 1.

When x = 4, f (x) = f (4) = (4)^2 = 16.

When x = 9, f (x) = f (9) = (9)^2 = 81.

When x = 16, f (x) = f (16) = (16)^2 = 256.

b) Using the table from part a, graph the function f (x) = x^2 . For a tutorial on creating graphs in Excel and inserting graphs of functions please see the Assignment List.

c) Given the function f (x) = (x +1)^2 complete the following table. Must show all work for full credit.

f (x)

Show Work or Explain in Words:

When x = -1, f (x) = f (-1) = (-1 + 1)^2 = (0)^2 = 0.

When x = 0, f (x) = f (0) = (0 + 1)^2 = (1)^2 = 1.

When x = 3, f (x) = f (3) = (3 + 1)^2 = (4)^2 = 16.

When x = 8, f (x) = f (8) = (8 + 1)^2 = (9)^2 = 81.

When x = 15, f (x) = f (15) = (15 + 1)^2 = (16)^2 = 256.

d) Using the table from part c, graph the function f (x) = (x +1)^2 . For a tutorial on creating graphs in Excel and inserting graphs of functions please see the Assignment List.

Answer:

e) Given the graph of y=f (x) describe in words the transformation of y=f (x+1).

Answer:

The function f (x+1) is the transformation of f (x) where f (x) is moved one unit to the left.

2) Find the domain of the function and express the answer in interval notation. Explain in words or show the calculations for full credit.

a) f (x) = 3x - 1

Answer: The domain of…… [Read More]

Business Math and Algebra Essay

Words: 1247 Length: 5 Pages Document Type: Essay Paper #: 2302411Managerial Math

Solve each of the following equations for the unknown variable.

a) 15x + 40 = 8x -

15x +49 = 8x

49= -7x

b) 7y - 1 = 23-5y

Y=

c) 9(2x + 8) = 20 - (x + 5)

= 15-x

d) 4(3y - 1) - 6 = 5(y + 2)

Y = (20/7)

Bob Brown bought two plots of land for a total of $110,000. On the first plot, he made a profit of 16%. On the second, he lost 4%. His total profit was $9,600. How much did he pay for each piece of land?

X= price of the first plot

Y= price of the second plot

X+Y= 110,000

.16x-.04y=9600

x=110,000-y

.16(110,000-y)-.04y=9600

17600-.16y-.04y=9600

y=40,000

x=110,000-40,000=70,000

A major car rental firm charges $57 a day with unlimited mileage. A discount firm offers a similar car for $24 a day plus 22 cents per mile. How far must you drive in a day in order for the cost to be the same at both firms?

Answer:

57=24+.22X

.22X=57-24

.22X=

X=33/.22

X=150 MILES.

Algebraic Operations and Applications

When solving the following questions, show each step of the solution along with the final results. If there is no work to show, be sure to fully explain your solution method.

1. Simplify the following algebraic operations:

a) 7x -- 2(x-2) + 5(x+3)

7x-2x+4 + 5x +15

10x + 19

b) (x+2)(x-4) + 3x + 1

x^2 + x -7

2. Suppose a student has earned the following grades on her first four quizzes: 83, 72, 89, 78. What must she score on her fifth quiz in order to have a mean of 80 on all of her quizzes?

322 + x = 400

3. The perimeter of a rectangle is twice the length plus twice the width. The area of a rectangle is the product of its length and width. Suppose we let l represent the length and w represent the width of a rectangle.

a) Write an algebraic expression that represents the perimeter.

b) Write an algebraic expression…… [Read More]

Words: 604 Length: 2 Pages Document Type: Essay Paper #: 14053823

Solve the following quadratic equation by factoring:

A) X2 + 6x -16 = 0

(x-2) (x+8)= 0

(x+2) (x-8) = 0

x=-2, x-8

b) solve the quadratic equation 6x2 +3x-18 = 0 using the quadratic formula x= - b +/- ?(b2- 4ac)

+/- ?[32- (4*6*-18c)]

x = 3/2; x= 2

c) Compute the discriminant of the quadratic equation 2x2-3x - 5 = 0 and then write a brief sentence describing the number and type of solutions for the equation.

If x= - b +/- ?(b2- 4ac), then (b2- 4ac) is the discriminant b2- 4ac= -32- (4*2*-5) = 49

There are two solutions for the equation, 1 and 2 1/2, which one gets by plugging the discriminant into the quadratic formula and solving for x.

Use the graph of y=x2+4x-5 to answer the following:

a) Without solving the equation or factoring, determine the solution(s) to the equation, x^2 + 4x - 5 = 0, using only the graph. Answer: x= 0, x = -5. I obtained the answers by looking at the situation where y=0 and finding the value for x in those locations.

b) Does this function have a maximum or a minimum? The graph has a minimum, y= -9, because nothing on the graph goes below that point.

c) What are the coordinates of the vertex in (x, y) form?

(-2,-9)

See below to check:

x= - b +/- ?(b2- 4ac)

2a

y=x2+4x-5

h= -b/2a

h=-4/(2*1)= -2

k= 4ac-b2

4a

k= 4ac-b2 = (4*1*-5) - 42 = -20 -16 = -36/4 = -9

4a

4*1

4

d) What is the equation of the line of symmetry for this parabola? Answer: x= -2

3) The profit function for Wannamaker Trophies is P (x) = -0.4x2 + fx - m, where f represents the design fee for a customer's awards and…… [Read More]

Business Algebra and Math Essay

Words: 496 Length: 2 Pages Document Type: Essay Paper #: 72945915Financial Polynomials

Solution for the problem: (-9x3 + 3x2 -- 15x)

The division process for the polynomial above can be approached in the same way as dividing whole numbers. The polynomial (-9x3 + 3x2 -- 15x) is the dividend, while (-3x) is the divisor. To easily facilitate the division process, the whole equation will be multiplied by "-1." The new equation is: (9x3 -- 3x2 + 15x) / (3x). Writing the question in long division form, begin dividing (9x3) first by (3x), which is equal to (3x2). To cancel the first part of the equation, the first part of the quotient must be negative. Thus, 3x2 becomes (-3x2). Place (-3x2) above the division bracket as shown below.

) 9x3-3x2 + 15x

Multiply (3x) by (-3x2), which is equal to 9x3. Placing 9x3 below (-9x3) then subtract them, resulting to zero. The remaining parts of the equation must be divided in a descending order. Bring down the next term, (-3x2), and divide again by the divisor 3x. Dividing (-3x2) by 3x will give the quotient x. This is placed above the division bracket and added to the equation, resulting to the yet unfinished quotient:

____- 3x2 + x

3x

) 9x3-3x2 + 15x

-9x3

- 3x2

Subtracting 3x2 from (-3x2) will result to a difference of 0. Bring down the last term, 15x, and divide again by the divisor 3x. The quotient is 5. Again, 5 is placed above the division bracket and added to the final quotient:

____-…… [Read More]

Algebra in Daily Life it Essay

Words: 718 Length: 2 Pages Document Type: Essay Paper #: 41568888There are many other variables that would affect real-world riding speed, and the effort variable would also be far more complicated than represented here, but this should suffice for now. Several equations can be written using the variables defined here. For instance, to calculate the effort needed to go one kilometer (it's easier to go kilometers than miles, at least mathematically), or a thousand meters, in a given gear, the equation would look like this:

T) / G = E, where M. is the distance (in meters) of the journey, T is the circumference of the tire -- and therefore also the linear distance, G is the number of revolutions the tire goes per push of the pedal, which changes from gear to gear, and E. is the number of times the pedals have to go around, which is representative of the effort needed to push the bike forward for the given distance Plugging some numbers into this equation allows us to see how it works more clearly. Let's assume that the tires are 1.5 meters, and that in third gear they go around three times for every revolution. If the journey is one kilometer, the equation becomes: (1000 / 1.5) / 3 = E. Simplifying, we get 666.6 / 3 = E, and solving for E. we get 222.2. If we changed to first gear, which we will assume turns the tires once per push, the equation would become (1000 / 1.5) / 1 = E. This would mean that the effort in first gear to go the same distance is 666.6 (unintentionally Satanistic, I swear).

It might at first seem counterintuitive (strange) that it would take more effort to go the same distance in first gear than in third, but that is the mathematical purpose (comforting) of the harder gears -- though each push requires more effort (which I simply…… [Read More]

Words: 361 Length: 1 Pages Document Type: Essay Paper #: 54259558

Algebra, Trig

Algebra-Trig

Find the slope of the line that goes through the following points: (-4, 6), (-8, 6)

Slope: m = (y2 -- y1) / (x2 -- x1) = (6 -- 6) / (-8 -- (-4)) = 0 / (-4) = 0

m = 0.

Determine whether the given function is even, odd or neither: f (x) = 5x^2 + x^

To test a function for even, odd, or neither property, plug in -- x for x, and simplify.

f (-x) = 5(-x)^2 + (-x)^4 = 5x^2 + x^4.

Because the final expression remains the same for -- x, it stands that the function is even.

f (x) is even.

Find the slope of the line that goes through the following points: (-1, 1), (-2, -5)

Slope: m = (y2 -- y1) / (x2 -- x1) = ((-5) -- 1) / ((-2) -- (-1)) = (-6) / (-1) = 6

Answer: m = 6.

Evaluate: f (x) = -5x + 8 at f (-3)

f (-3) = -5(-3) + 8 = 15 + 8 = 23

Answer: f (-3)…… [Read More]

Algebra Suppose You Have a Essay

Words: 355 Length: 1 Pages Document Type: Essay Paper #: 57595437f (x) = 3 if x>2 otherwise f (x) = -2 Function: every x value corresponds to only one f (x) value

c. f (x) = 7 if x>0 or f (x) = -7 if x… [Read More]

Algebra Trig Find the Radian Measure of Essay

Words: 342 Length: 1 Pages Document Type: Essay Paper #: 92153160Algebra, Trig

Find the radian measure of the central angle of a circle of radius r = 4 inches that intercepts an arc length s = 20 inches.

The formula for an arc length is a = r?, where'd is the arc length, ? is the central angle in radians, and r is the radius. That said, s = 20, r = 4, and ? is unknown.

= 5 radians

The central angle is 5 radians.

In which quadrant will the angle 100 degrees lie in the standard position?

The angle of 100 degrees will lie in Quadrant II.

In which quadrant will the angle -305 degrees lie in the standard position?

The angle of -305 degrees will lie in Quadrant I.

Find the length of the arc on a circle of radius r = 5 yards intercepted by a central angle 0 = 70 degrees.

The formula for an arc length is a = r?, where'd is the arc length, ? is the central angle in radians, and r is…… [Read More]