Coordinate system Questions and Answers

The function shown below is f(x). We are interested in the transformed function g(x) = -2f((x - 2)). a) Describe all the transformations g(x) has made to f(x) (shifts, stretches, etc). b) NEATLY sketch the transformed function g(z) and upload your graph as a PDF document below. You may use graph paper if you want. Be sure to label your vertical and horizontal scales so that I can tell how big your function is.

Imagine a circus tent in which the roof of the tent is shaped like a right circular cone, with the tip of the cone being the highest and center-most point of the tent. (a) The outside wall of the tent is 8 feet high. Six feet toward the center pole from the outside wall, the tent is 11 feet high. The center pole of the tent is 50 feet from the outside wall. Draw and label a picture which matches this scenario. (b) What is the slope of the line that follows the roof of the circus tent? (c) Use the slope to find the height of the tent at its center pole. (d) A rope is attached to the roof of the tent at the top of the outside wall and anchors the tent to a stake in the ground. The rope follows the line of the tent roof. How far away from the tent wall is the anchoring stake?

Simple Interest Application Simple interest is given by the formula A = P + Prt. Where A is the balance of the account after t years, and P is the starting principal invested at an annual percentage rate of r, expressed as a decimal. Noah is investing money into a savings account that pays 3% simple interest, and plans to leave it there for 20 years. Determine what Noah needs to deposit now in order to have a balance of $50,000 in his savings account after 20 years. Noah will have to invest $ now in order to have a balance of $50,000 in his savings account after 20 years. Round your answer to the nearest dollar.

You started this year with $384 saved and you continue to save an additional $22 per month. Write an equation to model this situation (use m for months and s for savings). Equation:

You have just bought a new Sony 55″ 3D television set for $1,600. The value of the television set decreases by $190 per year. How long before the television set is worth half of its original value? Round your answer to the nearest tenth as needed. It will take years for the television set to be worth half of its original value.

A city currently has 123 streetlights. As part of an urban renewal program, the city council has decided to install 4 additional streetlights at the end of each week for the next 52 weeks. Use this information to complete the following statements. Round to the nearest whole number as needed. streetlights at the end of 46 weeks. The city will have The city will have 263 streetlights at the end of weeks.

Emanuel's goal is to find a job that provides an income of $45,000 a year. Lauren's Furniture offers him a job paying a base salary of $23,000 a year, plus a commission of 4% of his sales. Determine what Emanuel's total sales will need to be for him to have a yearly income of $45,000 . If Emanuel takes the job with Lauren's Furniture, he will need to make $ _______ in total sales in order to have a yearly income of $45,000 per year. Round your answer to the nearest cent.

You started this year with $233 saved and you continue to save an additional $15 per month. Write an equation to model this situation (use m for months ands for savings). Equation:_________

What is the image (11, -5) after the R-00 T(11,-5)

The equation V = 16.2 + 3.8x gives the value (in thousands of dollars) of an investment after x months.Interpret the Slope in this situation.The value of this investment is Select an answer at a rate of________Select an answer

Paul is planning to sell bottled water at the local carnival. Paul's profit (in dollars) from selling b bottles of water is given by the formula P =1.556 - 281. Interpret the Slope in this situation. Paul's profit is increasing at a rate of Select an answer

Investment Application In the year 1981, an investment was worth $28600. In the year 1988, this investment was worth $37700. The value of this investment is Select an answer at a rate of Select an answer

Working with Percents The sales tax rate in a particular town is 9.4%. How much tax will you pay on a $3,100 purchase? You will pay $__________ Round your answer to the nearest cent.in sales tax for this purchase.

If 1300 dollars is invested in an account for 10 years. Find the value of the investment at the end of 10 years if the interest is: (a) 5% compounded annually: $ (b) 5% compounded semiannually: $ (c) 5% compounded quarterly: $ (d) 5% compounded monthly: $ (e) 5% compounded daily (ignore leap years): $

A lender requires a minimum down payment of 20% of the value of the home. You have $30,000 cash available to use as a down payment toward a home. Determine the maximum home value that you can finance. You can afford to finance a home worth at most $_________ Round your answer to the nearest dollar,

Prove the following 7. Let f: A = f(A) and ACX. Then f₁: A = f(A).

The fox population in a certain region has a relative growth rate of 5 percent per year. It is estimated that the population in the year 2000 was 21,000 foxes. a) Find an equation that models the population t years after 2000 (t=0 for2000). b) Use the equation from part (a) to estimate the fox population in the year 2009. Round to the nearest fox. ________ foxes

A shirt was originally priced at $20. The store is having a 25% off sale. How much will you pay for the shirt after the discount (not including tax)? Round your answer to the nearest cent A $20 shirt marked 25% off will cost $_______before tax

The value of a car dropped from $28,200 to $26,100 over the last year. Determine the absolute and relative change in this sitation. Absolute Change: This car's value decreased by $ _____ Last year Round your answer to the nearest dollar. Relative Change: This car's value decreased by ______% last year Round your answer to the nearest tenth of a percent. l

Consider the following products and conjecture and then answer the questions that follow. • 3 X5 X 7 = 105 • 3 X5 X 11 165 . 3 X5 X 13=195 • 3 X 7 X 11 = 231 Conjecture: The product of three prime numbers is odd. a. Was this conjecture achieved through inductive or deductive reasoning? Explain your answer. b. Is there a counterexample to this conjecture? If so, provide a counterexample.

The Sears Tower in Chicago is 1450feet high. A model of the tower is 24inches tall. What is the ratio of the height of the model to the height of the actual Sears Tower? O 725:1 O 1:725 O 725:12 O 12:725

3) The height of the tide in Ocean City on a summer day was recorded by a scientist. It was found that the tide was at its lowest height at 6 A.M., where the tide was measured at 1 foot. The highest tide height occurred at 6 P.M., where the tide was measured at 13 feet. The tide height on this day can be measured by a sinusoidal function. a) What is the amplitude and midline of the function described in this scenario? Amplitude (1 Point): Midline (1 Point):

The intensity of light on a sunny day is given by L(x) where x represents the number of hours since noon. A photographer can take his best pictures when the light intensity is 3 or greater. During what time interval can the photographer take his best pictures? (2 points)

Parallelogram UVWX is dilated by a scale factor of 2 to form parallelogram U'V'W'X'. Side UV measures 4. What is the measure of side U'V'?

An assembly line worker can expect to earn $36 000, with a raise of 5% each year. How much can the worker expect to earn after 10 years of working at the company? (i.e. what is his salary in year 10?)

The first four terms for the recursion formula t₁ = 8, t₁ = t-1+n² are A 8, 4, 9, 16 B 1, 4, 9, 16 C 1, 9, 17, 25 D 8, 12, 21, 37

Which formula is the general term of a geometric sequence with t₁ = 5 and t₂ = 10? A tn = 5(2)^n-¹ B tn= 5n C S₂ = 15 D Sn = 5(2^n-1)

Let A= 1 3 0 k 1 k 0 3 1 Find the values of k for which A is not invertible. NOTE: Enter all values exactly.

Find the equilibrium solutions and determine if they are stable or unstable. y-y²-y Give answers from least to greatest. yo yo y" (select) (select) (select)

Find the future value of the annuity. payments of $3000 at the end of each year for 20 years at 8% interest compounded annually What is the future value of the annuity? $ (Round to the nearest cent.)

Let A be a 3 x 3 matrix whose entries are 2 or 0. What is the largest possible value for det(A)? The largest possible value for det (A) is i 8192

Solve the following system 3x + 7y = 4 (mod 11) 8x + 6y = 1 (mod 11) Hint: Use Cayley's table to solve the system

Draw the following graph on the interval-240° < x < 480°: y = cos(x/2)

Find the value of x. The diagram is not to scale. 35 145 90 45

QUESTION 4 Find the number of sides of a regular polygon having an interior angle of 140° O a. 12 sides b. 9 sides O c. 8 sides O d.6 sides.

The image is an example of which type(s) of symmetry? A. Both rotational and reflectional B. Reflectional C. Neither rotational nor reflectional D. Rotational

Solve the following compound inequality. Write the solution set using interval notation and graph it. 1 3(x+3) >2 or 0<5-x Select the correct choice below, and fill in the answer box if necessary. OA. The solution set is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. The solution set is Ø.

You want to put a 3 inch thick layer of topsoil for a new 15 ft by 25 ft garden. The dirt store sells by the cubic yard. How many cubic yards will you need to order? You need to order 3.47 X cubic yards of topsoil.

Bernadette is making a quilt. She needs 4 square yards of green fabric, 3 square yards of purple fabric and 7 square yards of white fabric. How many square feet of fabric is this in total?

Given the ordered pair (5, -4), where will the transformed image be after the following composition: r(180, O) T(-1,2)

When finding the exact value of 4cos75 + 4cos15, the first three steps involved to get he final answer are:

Linear Application The equation C = 50400 2800q represents the balance in your college payment account after q quarters. Interpret the Slope in this situation. The balance in this account is increasing Interpret the Initial Value in this situation. After = You can pay for How many quarters will this account pay for? at a rate of quarters, the balance in this account is $ Select an answer î quarters before the money in this account is gone.

A 90 ft. long swimming pool is to be constructed. The pool will be 5 ft. deep at one end and 9 ft. deep at the other. To the nearest degree, what will be the measure of the acute angle the bottom of the pool makes with the wall at the deep end? 87° 84⁰ 86° 82° 89⁰

Bernadette is making a quilt. She needs 5 square yards of green fabric, 3 square yards of purple fabric and 11 square yards of white fabric. How many square feet of fabric is this in total?

The sum of the angle measures of a polygon with s sides is 2340. Find s. 17 14 13 15

A long year-end status report for work is 78 pages long. You need to print 15 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.71 each.

Convert the measurement. 5 square feet = _square inches

3. [8 pts] The Space Needle tower in Seattle, Washington, is 605 feet tall. From an observation point some distance away from the Space Needle, the angle of elevation to the tower base is 5° and to the top of the tower is 7º.find the distance between the observation point and the top of the Space Needle.

Convert 10 minutes, 37 seconds to seconds. 10 minutes, 37 seconds = ________seconds

Donna is a software saleswoman. Her monthly salary is $2000 plus an additional $80 for every copy of English is Fun she sells. Let S represent her total salary this month (in dollars), and let N represent the number of copies of English is Fun she sells. Write an equation relating S to N, and then graph your equation using the axes below.