A daycare center has 30 ft of dividers with which to enclose a rectangular play space in a corner of a large room. The sides against the wall require no partition. Suppose the play space is x feet long. Answer the following questions. Express the area A of the play space as a function of x. A(X)- (Do not simplify.) What is the domain of the function? O A. [0, 15] Ов. (0, 15) Ос. [0, 30] O D. (0, 30) What is the graph of the function? OA. OB. 400 400-- 40

Q: A certain airine company is offering a promotion for a year, where you pay a one-time fee of $5000,…

A: We will use simple formula for average

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A: To find: The point of inflection and discuss the concavity of the graph of the function. Given: The…

Q: Let f(x) be the function 12x – 2x + 12. f(9 + h) – f(9) - can be simplified to ah h a =

A: We have to find

Q: 2- Find the domain of the following functions:

A: Domain of a function is defined as the set of all possible inputs.

Q: The owner of a small restaurant can prepare a particular meal at a cost of 100 won. He estimates…

A:

Q: From a 18-cm by 18-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: From a 18 cm by 18 cm piece of cardboard, square corners are cut so that the sides can be folded up…

Q: - Find and classify the discontinuities of the function f(x) x2 - 1

A:

Q: An open box is to be made from a square piece of cardboard of side 12 inches by cutting out squares…

A: To find the size of squares cut out of the box for maximum volume.

Q: A college has a financial aid formula that applies to applicants whose family's income is below a…

A: Given, f(x)=25000+5000x  , where x is the number of siblings and f(x) is the financial aid of the…

Q: The value of Mr. Dulaney's car x years after its purchase is given by the function V(x) = 15,…

A: The value of Mr. Dulaney's car x years after its purchase is given by the function:…

Q: Find and interpret the given function values and determine an appropriate domain for the function.

A: Given: The financial aid can be determined by the function, f(x)=10000+2000x Where x is the number…

Q: Express the function graphed on the axes below as a piecewise function. 10 8 4 -10 -8 -6 -4 -2 4 8…

A:

Q: Is the function f(x) even, odd, or neither? 2x + 1

A: When -x is substituted for x in a function f(x) and the same function is obtained then the function…

Q: From a 24-cm by 24-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: in this first we will find side of the box and then  Volume of the box = length × breath× height

Q: From a 12-cm by 12-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: Given, Cardboard of size 12 cm  by 12 cm in which square corner of sides x cm is cut out. We have to…

Q: From a 18-cm by 18-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: Solution is provided below

Q: What type of discontinuity does the function f(x)=xsecx have?

A:

Q: A rectangle has a length of 16 inches and a width of 9 inches. If the length is increased by x…

A:

Q: Ivanna has 240 meters of fencing and wishes to form three sides of a rectangular field. The fourth…

A: Given: Ivana has 240 meters of fencing and wishes to from three side of a rectangular field. The…

Q: homeowner's insurance in a particular year can be described by the function ​f(x)=414.84(1.033)x​,…

A: Given query is to find after how many years average homeowners premium will be 1500.

Q: Is the function g(x) = x2 one-to-one?

A: Take x=2. g(2)=22=4. Take x=-2. g(-2)=(-2)2=4

Q: From a 27-cm by 27-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A:

Q: Determine whether  the following statement is true or false, and explain why. If ƒ″(c) = 0, the…

A: The given statement is true.

Q: Find the value of k, if the constant k that makes the function continuous:

A: Given,          f(x)=x2+k2if x≤4kx+12if x>4

Q: find a function that satisfies the following conditions: f'=3x^2+6x+4, f(2)=13

A: Given :  f'=x2+6x+4,  f(2)=13

Q: Determine whether the function is one-to-one. h(x) = x2 - 2x

A: Given: h(x)=x2-2x Determine the value of the function at x=0. h(0)=02-2(0)=0

Q: A wire of length 8x is bent into the shape of a circle. A. Express the circumference of the circle…

A:

Q: A videoke machine can be rented for P 1000 for 3 days, but the fourth day onwards, an additional…

A: Given:  A videoke machine can be rented for P 1000 for 3 days, but the fourth day onwards, an…

Q: Determine where the following function is continuous. х-5 M(x) = 4x2 - 9

A:

Q: Find the inflection point, if any, of the function. 9 f(x) = 8 + (х, у) 3D

A: We have to find the inflection point.

Q: Investigate when, historically, the use of the function notation y=f(x) first appeared.

A: Given, Investigate when, historically, the use of the function notation y=f(x) first appeared.

Q: An open-top box with a square base is to be constructed by taking a 36 by 36 square piece of…

A: The dimension of the square base is 36 by 36. Since a square of side length x in is cut out from…

Q: Which of the following equivalent forms of the function  f(x)=4x2+4x−24f(x)=4x2+4x-24 is the most…

A: This question is based on middle term splitting.

Q: show the function is continous dis continou or 2=(2x+3 3メ→1」Xハz F(x)ニ

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

A: Given that, The function changes concavity at the inflection point. To find inflection point, solve…

Q: 2. Determine whether the function is one-to-one. (a) y = 4x2 + 3 %3D (b) y = Vx + 3 – 5

A:

Q: 2. Determine if the following function is differentiable. x² +10, x <4 f(x) = 8x-6, x24 wwww

A:

Q: Determine whether the function has a concave up and/or concave down. f(x)=x/5+x^2

A:

Q: From a 18-cm by 18-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: A square card board is of 18cm by 18cm side of a card board is 18cm find the volume of the box

Q: Find the domain of the function in interval notation: f(x) = V + 17 %3D

A: Domain is the set of x values for which the function is defined We know that square root (negative…

Q: Express the function graphed on the axes below as a piecewise function. 10 4 2 -10 -8 -6 -4 -2 2 4 8…

A:

Q: From a 12-cm by 12-cm piece of cardboard, square comers are cut out so that the sides can be folded…

A: The length side of the box is 12-x-x =12-2x cm So the area of the box is (12-2x)2 cm2 Here height of…

Q: An electric company charges its customers $0.0577 per kilowatt-hour (kWh) for the first 1000 kWh…

A: We have to write the piecewise-defined function C for a customer’s bill where x is per kWh.  First,…

Q: Make a plot of the piecewise function below, and comment on its shape. x<0 Osx<1 f(x) = { -x + 3x-…

A: The plot of the given piecewise-defined function is

Q: Evaluate the piecewise defined function at the indicated values. if xs 5 5x – 6 if x > 5 f(x) •…

A:

Q: Write a function y =h Ex) and state domain. and ronge. Plecewise definition for y=h Lx) 2.

A:

Q: Suppose that the revenue from selling x radios is R(x) = 75x - dollars. Use the 10 function R' (x)…

A: Here, the given revenue function is: Rx=75x-x210

Q: a. The value of x that makes the function discontinuous. 3x f(x)= 3x-81 O 4 O -4

A: A function f(x) in an interval (a,b) is discontinuous if it is undefined at x=c where a&lt;c&lt;b.…

Q: A builder uses the function g defined by g(2) = 80x + 10000 to estimate the cost g(x), in dollars,…

A: Given:- A builder uses the function g defined by g(x) = 80x+10000 to estimate the cost g(x), in…