Basic Math Questions and Answers

Write your answers as integers or simplified fractions. (a) Write the function in vertex form. n(x) = 2x²+6x+9 Factor out the leading coefficient of the x term from the two terms containing x. The leading term within parentheses now has a coefficient of 1. n(x) =

Consider the function below. Which statement about the range of this function is true? f(x) =6/x -5 The range is all real numbers because the output of the function is not restricted The range is all real numbers except for 0 because the output of the function cannot be 0. The range is all real numbers except for 5 because the denominator of the function cannot be 0. The range is all real numbers equal to or greater than 6 because the denominator must be a positive numb

Tessa is making greeting cards, which she will sell by the box at an arts fair. She paid $20 for a booth at the fair, and the materials for each box of cards cost $3. She will sell the cards for $5 per box of cards. At some point, she will sell enough cards so that her sales cover her expenditures. How much will the sales and expenditures be? Write a system of equations, graph them, and type the solution.

14. Simplify the expression. Assume that variables represent positive real numbers. Use the properties of exponents to simplify (don't convert to radical form) and leave your answer in exponent form with no negative exponents. (27a³b-6/c9)(-1/3)

Enter the correct answer in the box. Write an expression to represent the given statement. Use n for the variable. three times the absolute value of the sum of a number and 6

A shelf has 4 books, of which 2 are of science and 2 are of social studies. In how many ways can we select 3 books from the shelf such that we have atleast one science book and atleast one social studies book ? A) 7 B) 8 C) 4 D) 6

Jolene invests her savings in two bank accounts, one paying 3 percent and the other paying 10 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 6880 dollars. How much did she invest at each rate? Amount invested at 3 percent interest is $ Amount invested at 10 percent interest is $

(a) Identify the horizontal asymptotes (if any). The degree of the numerator is n = The degree of the denominator is m = Since n< m, then Part: 1/5 Part 2 of 5 (b) If the graph of the function has a horizontal asymptote, determine the point (if any) where the graph crosses the horizontal asymptote. From part(a), the horizontal asymptote is y=0. set x+7/x2-5x-4 equal to

Juan was given a box of assorted chocolates for his birthday. Each night, Juan treated himself to some chocolates. Juan ate 2 chocolates each night and after 13 nights, there were 4 chocolates remaining in the box. Write an equation for C, in terms of t, representing the number of chocolates remaining in the box t days after Juan's birthday.

James invests a total of $16,500 in two accounts paying 10% and 4% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $1,350.00. was invested at 10% and was invested at 4%.

Solve the problem. Franco borrows a total of $5,000 in student loan from two lenders. One charges 4.1% simple interest and the other charges 6.1% simple interest. He is not required to pay off the principal for 3 yr. However, at the end of 3 yr, he will owe a total of $825.00 for interest from both loans. How much did he borrow from each lender? Select one: a. She borrowed $1,100 at 4.1% and $3,900 at 6.1%. b. She borrowed $3,900 at 4.1% and $1,100 at 6.1%. c. She borrowed $1,500 at 4.1% and $3,500 at 6.1%. d. She borrowed $3,500 at 4.1% and $1,500 at 6.1%.

Calculate the (modeled) probability P(E) using the given information, assuming that all outcomes are equally likely. n(S) = 16, n(E) = 8 P(E) =

Diana has 400 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area? (a) A(W) =

Consider the following relation. x = 2|y| - 3 Step 1 of 2: Find four points contained in the inverse. Express your values as an integer or simplified fraction.

DIAGONALS ARE EQUAL LENGTH GIVEN: THE RECTANGLE DEFG PROVE: DF-FG CONSTRUCTION: LABEL THE QUADRILATERAL AND MARK OPPOSITE SIDES PARALLEL, THEN DRAW THE DIAGONAL EG AND DF. SINCE THIS IS A RECTANGLE INSERT SMALL SQUARE TO INDICATE RIGHT ANGLES

Find the x-intercepts and y-intercept of the following function. f(x) = (x-6) (x − 3) (4x + 4) Write your answer in coordinate pairs of the form (x, y))

A photographer takes an average of 15 pictures per session. The total number of pictures p(s) is a function of the number of sessions s. a. Identify the independent and dependent variables. b. What values of the domain and range make sense for this situation? Explain. c. Write a function to represent the total number of pictures taken. Then determine the number of pictures taken in 22 sessions.

A total of 330 children and adults attended a school play. There were 21 times as many children in attendance as there were adults. This situation is modeled by the given system of equations, where a represents the number of adults and c represents the number of children. c=21a a+c=330

A recreation the summer. On the first day of the offering, a family paid $96 for 4 pool passes and 2 gy memberships. Later that day, an individual bought a pool pass for herself, a pool pass for a friend, and 1 gym membership. She paid $72. 1. Write a system of equations that represents the relationships between pool passes, gym memberships, and the costs. Be sure to state what each variable represents.

Mr. Lings has a plank of wood 118 inches long. He cuts it into two pieces such that the longer piece is 5.5 inches longer than twice the length of the shorter piece. What is the length of the longer piece? 37.5 inches 59 inches 80.5 inches 56.25 inches

A study shows that 77% of the population was vaccinated against the Venusian flu but 2% of the vaccinated population got the flu anyway. Of the total population, 12% got this flu. Let V be the event that a person was vaccinated. Let F be the event that a person gets the flu. Compute the following values. P(V) = P(F) = P(V∩F) P(V∪F) What percentage of the population either got the vaccine or got the disease?

The polygon below was a square with 20-meter sides before a triangle was removed. What is the new perimeter of the polygon, in meters? F. 66 G. 70 H. 76 J. 78 K. 80

A doctor sees between 7 and 12 patients each day. On Mondays and Tuesdays, the appointment times are 15 minutes. On Wednesdays and Thursdays, they are 30 minutes. On Fridays, they are one hour long. The doctor works for no more than 8 hours a day. Here are some inequalities that represent this situation. 0.25 ≤ y ≤ 1 7≤x≤ 12 xy ≤8 a. What does each variable represent? b. What does the expression xy in the last inequality mean in this situation?

Diana has 120 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area?

In a certain country, approximately 24 out of 100 people over the age of 12 smoke. How many smokers would you expect in a group of 550 people over the age of 12?

Find the remaining five trigonometic functions of θ. cot θ = 12/5, sin θ >0 Complete the following table. sin θ = cos θ = tan θ = csc θ = sec θ = cot θ = 12/5

In a product liability case, a company can settle out of court for a loss of $350,000, or go to trial, losing $800,000 if found guilty and nothing if found not guilty. Lawyers for the company estimate the probability of a not-guilty verdi be 0.8. Complete parts (a) through (b) below.

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equation dependent. -9x - 6z = 19 x - 3y = 35 Select one: a. {(0, -18, 16)} b. {(-19/2,2,0)} c. {(-3,2,4)} d. {(-3,-38/3, 4/3,)}

Choose the correct expression equal to sin x. A. sinx= ± √1- cos x B. sinx= 1/1- cos x C. sinx=(1- cos x)(1+ cos x) D. sinx= ± √1- cos^2 x

Diana has 440 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area?

A right circular cone is shown. The base of the cone is a circle with the center at point A. The distance from point A to point C is 16 inches. The distance from point to point B is 20 inches. What is the diameter, in inches, of the base of the cone?

It has been said that newspapers are disappearing, replaced by various electronic media. In 2001, newspaper circulation (the number of copies distributed in a day) in a country was about 58 million. In 2011, this ad dropped to 46 million. Assume that the relationship between time, x, and circulation, y, is a linear relationship. Write an equation describing the relationship between time and circulation. Use ordered pairs of the form (years past 2001, number of newspapers circulated in millions). Use this equation to predict newspaper circulation in 2015. The equation describing the relationship is type your answer in slope-intercept form. Use integers or decimals for any numbers in the equation.) million. In the year 2015, the newspaper circulation will be implify your answer. Type an integer or a decimal.)

The school that Imani goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 3 senior citizen tickets and 3 child tickets for a total of $69. The school took in $91 on the second day by selling 5 senior citizen tickets and 3 child tickets. What is the price each of one senior citizen ticket and one child ticket?

Solve the system by the method of your choice. x²+2y² = 36 x+y = 6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an ordered pair, using integers or simplified fractions for the coordinates. Use a comma to separate answers as needed.) B. There is no solution.

Lauren has dimes and nickels in her purse. The number of dimes is three more than seven times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.

The area of a parallelogram is 18 square units. One side of the parallelogram is 24 units long. The other side is 6 units long. Which could be the parallelogram's height? Select all that apply. A 3/4 units B 4/3 units C 3 units D 4 units E 12 units

A 300. L kiln is used for vitrifying ceramics. It is currently operating at 1065 °C, and the pressure is 0.9250 atm. How many moles of air molecules are within the confines of the kiln?

Determine if the conclusion follows logically from the premises. All children are energetic. Some actors are children. Therefore, some actors are energetic. Valid argument Invalid argument All flowers need water. Roses need water. Therefore, roses are flowers. Valid argument Invalid argument

When factoring, which of of the following is the rule we follow? We just guess until we get something that works. We find what multiplies to "c" and adds to "b" We find what multiples to "a" and adds to "b" We find what multiples to "b" and adds to "c"

Describe and correct the error a student made when graphing y +5=-3/4(x-8)

Find the roots of the quadratic function: f(k)= 2k² - 3k - 9.

Graph the line through the point (0, -3), having a slope of 3/4

The mathematics faculty at a college consists of 4 professors, 7 associate professors, 5 assistant professors, and 9 instructors. If one faculty member is randomly selected, find the probability of choosing a professor or an instructor.

Supply a conclusion to make each argument valid. 1. All shrimp are appetizing. Tiger is a shrimp. Therefore, Tiger is appetizing. 2. All flowers smell good. All things that smell good are tasty. Therefore, all flowers are tasty. 3. No New Yorker likes pecan pie. All Southerners like pecan pie. Select an answer 4. All sailors are big spenders. No big spenders are miserly. Select an answer 5. All violets are blue. Some flowers are violets. Select an answer

A company found that an experienced surveyor can survey a roadbed in 5 hours. An apprentice surveyor needs 8 hours to survey the same stretch of road. If the two work together, find how long it takes them to complete the job.

A figure containing STU is dilated by a scale factor of 2/3 to form a new figure which contains S'T'U'. STU measures 140°. What is the measure of S'T'U'?

Solve the system by the substitution method. x+y = - 12 y = - 4x Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. There are infinitely many solutions. C. There is no solution.

Maya arranges some tiles in different arrays. One array has 4 rows with 3 tiles in each row. The other array has 2 rows with 6 tiles in each row. Maya says that she can use the Commutative Property of Multiplication to show that the arrays both have 12 tiles. Is she correct? Explain.

A ferris wheel is 15 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? What is the Midline? y = What is the Period? How High are you off of the ground after 4 minutes?

Kimani plans to paint the background of a mural on a wall in her school's cafeteria. The mural will be in the shape of a parallelogram. One quart of paint covers 100 square feet. How many quarts of paint does Kimani need? Show your work.