The figure (see attached) shows an open box with a square base. The box is to have a volume of 10 cubic feet. Express the amount of material needed to construct the box, A, as a function of the length of a side of its square base, x.

Q: Consider the graph of the function f (2) as shown on the coordinate grid. Which correctly describes…

A: Basically the question is based on the transformation of graphs ..

Q: write the length L of the rectangle as a function of y.

A: Given a figure. We need to find the distance 'L' in terms of 'y'.  Let's find out.

Q: You have 600 feet of fencing to enclose a rectangular field. Express the area of the field, A, as a…

A: Let the length of the rectangular area=x and the width=ySo, perimeter=2(x+y)=600or, x+y=300or,…

Q: in a Washington town the charge for commercial ways collection is $694.55 for 5 tons of waist and…

A:

Q: Find the formula for a linear function f that models the data in the table exactly -2 4 f(x) 13 6 -1…

A: GivenHere e find the linear function f(x)

Q: A rectangular building lot is three times as long as it is wide. Find a function that models its…

A: A rectangular building lot is three times as long as it is wide. Let w be the width of the…

Q: The function

A: Given, the function f : ℂ→ℂ defined by                   f(z)=ez+e-zhas

Q: A cell phone plan charges $49.95 per month plus $14.02 in taxes, plus $0.40 per minute for calls…

A:

Q: Find the domain and sketch the graph of the function. f(1) = 21 + t?

A: Given: ft=2t+t2

Q: What is the domain of the function? Vx+2

A: Solution: The objective is to find the domain of the given function

Q: If the function y = e4x is vertically compressed by a factor of 5, reflected across the x-axis, and…

A: Given function:

Q: coming year. Total profit from planting xj acres at farm j is expressed by the function P(x,, X2,…

A: profit = 235x1 + 540x2 + 252x3 - 525000 we are given that x1 = 300 x2 = 600 x3 = 450

Q: In the theory of relativity, the mass of a particle is mo m where m, is the rest mass of the…

A: The mass of the particle is given.

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: The elevation of a valley above sea level (in feet) is modeled by the function f(x, y) = -2000 +…

A: Given the function, f(x,y)=-2000+0.004(x-1000)2+0.001(y+1000)2 in the direction u→=(0,-1000) The…

Q: Use the form to create a cubic function that (a) passes through the point and rises to the right and…

A:

Q: Graph the function using translations. f(x) 3*+1 4

A: Given, y= 3x+1 Let y=0, 3x+1=0 Therefore, x-intercept doesn't exist.   Let x=0, y= 31+0=31 y= 3…

Q: Assume a box has a square base and the length of a side of the base is equal to twice the height of…

A: Volume of cuboid= lbh  surface Area=2(lb+bh+hl)

Q: Explain why the function f(2) = 2:² – 3 – ze² + e¯² is entire? %3D

A:

Q: A function is modeled by the equation f(x)=2x+5f(x)=2x+5.

A:

Q: A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length…

A: We have to write the total cost C of construction as a function of h.

Q: A rain gutter is made from sheets of aluminum that are 20 inches wide. As shown in the figure, the…

A: We know that the aluminum sheets are rectangular in shape. The cross sectional area of the gutter is…

Q: The number of bacteria in a lab experiment can be modeled by the function P(t) = 43(3)2t+3, write an…

A:

Q: If the function y=e−2x is vertically compressed by a factor of 3, reflected across the y-axis, and…

A: given y=e-2x

Q: Write the most specific name of the function f(x) = ax + b.

A: A linear function has a standard form ax+b, where a, b are real numbers. The equation on the graph…

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the…

A:

Q: Write a function for the blue graph of a quadratic function in a form: f(x) = a ( b (x + c))² + d…

A: The given parent graph is shown by red and transformed graph shown by blue in the question.

Q: If the function y=e−3x is vertically stretched by a factor of 4, reflected across the y-axis, and…

A:

Q: A rain gutter is made from sheets of aluminum that are 20 inches wide. As shown in the figure…

A: Width of aluminium sheet is 20 inches The edges are turned from both sides by x inches. The cross…

Q: Express the side length of a square as a function of the length d of the square's diagonal Then…

A:

Q: Rick's lumberyard has 380 yd of fencing with which to enclose a rectangular area. If the enclosed…

A: The lumberyard is having 380 yd of fencing which means the perimeter of lumberyard is 380 yd. Length…

Q: Find the point of the graph of the function that is closest to the given point: f(x) = 2x+9 ;…

A:

Q: Find, if they exist, the extrema of the function:

A: Given that  f(x,y) = x2+y2-1 Subject to x - y = 2 ⇒g(x,y)=x-y-2 Let us find  <fx,fy> Finding…

Q: 3) Write the function whose graph is the graph of y = Vx, but is stretched vertically by a factor of…

A:

Q: Write a function that reflects f（x）= 2x^3 + 1 across the x-axis and shifts it 3 units down.

A:

Q: The elevation of a valley above sea level (in feet) is modeled by the function f(x, y) =…

A: Given,  The elevation of a valley above sea level (in feet ) is modeled by the function,…

Q: The triangular holes have a base of 3 inches and a height of h inches, and the other dimensions are…

A:

Q: 1² – 1 f(r) : 1² + 4°

A: We have to sketch the curve of given f(x)

Q: If the function y=e−x is vertically compressed by a factor of 2, reflected across the y-axis, and…

A:

Q: Express the side length of a square as a function of the length d of the square’s diagonal. Then…

A: Let x be the length of a side, d be the length of the diagonal and A be the area of the square.Now…

Q: What is the area A of a circle expressed as a function of its circumference C?

A: Our Aim is to express the area A of a circle as a function of its circumference C=?

Q: Rick's lumberyard has 240 yd of fencing with which to enclose a rectangular area. If the enclosed…

A:

Q: -20 in.- 14 in.

A: Question is solved.

Q: Find the point on the graph of the function that is closest to the given point: f(x)= 2x+8; (0,18)

A: We have given f(x)= 2x+8; (0,18)

Q: An open-top box is made by cutting equal squares of side x out of the corners of a piece of carboard…

A: Given that an open top box is made by cutting equal squares of side x out of the corners of a piece…

Q: Express the area A of a circle as a function of its radius, r. Determine the area of a circle whose…

A:

Q: 4 f(x) 3 1. V/1.57|V]3.14 V4.71|V6.28 -2

A: (a) f(x) is a wave with f(0)=1.5≠0.So the graph can be represented as a cosine function. Let f(x)=A…

Q: The function below has the form 14+ 12

A:

Q: What is a function? A linear function? A quadratic function?A rational function?

A: Function - A function is  a rule that associates every element in a set A a unique element in a set…

Q: The figure shows a package whose front is a square. The length plus girth of the package is 108…

A: Given figure is,

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.