A circular piece of fabric has a radius of 1.2 feet. The fabric sells for $5.40 per square foot. What is the total cost of the circular piece of fabric? A. $6.48 B. $20.35 C. $24.42 D. $40.69

Answer:

Inverse function: A function g is the inverse of a function f if whenever y=f(x) then x=g(y).

In other words, we can write this in terms of the composition of f and g as g(f(x))=x.

For any input x, the function corresponding to f spits out the value y=f(x)=4x+12.

Now, we want to find the inverse function g(x)=[tex]f^{-1}[/tex] that takes the value y as an input and spits out x as the output.

In other words, y=f(x) gives y as a function of x and we want to find [tex]x=f^{-1}(y)[/tex] that will give us x as a function of y.

Given,the expression y=4x+12 for y as a function of x and solve for x.

Subtract 12 from both sides we get;

y-12 = 4x+12-12

Simplify:

y-12 = 4x

Divide by 4 to both sides we get;

[tex]\frac{y-12}{4} =\frac{4x}{4}[/tex]

Simplify:

[tex]x=\frac{1}{4}y - 3[/tex]

therefore,  [tex]x = f^{-1}(y) = \frac{1}{4}y-3[/tex]

since, g(x) is the inverse of f(x)

⇒[tex] g(x)=\frac{1}{4}x-3[/tex]

Now, verify that g(x) is really the inverse of f(x), we should show that the composition of f and g doesn't do anything to the input.

[tex](g o f)(x) = g(f(x)) = g(4x+12) = \frac{1}{4}(4x+12) -3 = x+3 -3[/tex]

Simplify:

g(f(x)) = x                for all x

⇒  g(x) is the inverse of f(x)

Therefore, [tex] g(x)=\frac{1}{4}x-3[/tex]

Using inverse functions, it is found that that:

[tex]g(x) = \frac{x - 12}{4}[/tex]

To find the inverse function, we exchange x and y in the original function, then isolate f.

The function f(x) is given by:

[tex]f(x) = 4x + 12[/tex]

Function g(x) is the inverse of f(x), then:

[tex]y = 4x + 12[/tex]

[tex]x = 4y + 12[/tex]

[tex]4y = x - 12[/tex]

[tex]y = \frac{x - 12}{4}[/tex]

[tex]g(x) = \frac{x - 12}{4}[/tex]

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Step 1: Assign variable for the unknown that we need to find.

Let ' x ' be the number of applicants received by University Law School.

Step 2: Set up an equation based on the information given.

"University Law School accepts 2 out of every 15 applicants. If the school accepts 180 students, find how many applicants they received"

[tex] \frac{Accepted \; application}{Applied \; applicants} =\frac{2}{15} =\frac{180}{x} [/tex]

Step 3: Solving the equation

[tex] \frac{2}{15} =\frac{180}{x} \\ Cross \; Multiply\\ \\ 2x=15(180)\\ 2x=2700\\ Divide\; by\; 2\; on\; both\; sides\\ \\ \frac{2x}{2} =\frac{2700}{2} \\ Simplifying\; fraction\; on\; both\; sides\\ \\ x=1350 [/tex]

Conclusion:

The number of applicants received by University Law School is 1350.

Domingo made $14.25 per hour last year by dividing his annual income of $29640 by the total hours worked in the year, which is 2080 hours (40 hours/week  imes 52 weeks).

To calculate how much Domingo made per hour, divide his annual income by the total number of hours worked in a year. Domingo works 40 hours per week, and there are 52 weeks in a year, so the total hours worked in a year is 40 hours/week  imes 52 weeks/year = 2080 hours/year.

The formula to find the hourly wage is:

Hourly Wage = Annual Income / Total Hours Worked

Thus, Domingo's hourly wage would be:

$29640 / 2080 hours = $14.25 per hour.

Therefore, the correct answer is A. $14.25.

To laminate the cabinet, the total surface area is calculated and multiplied by the cost per square foot. The cabinet has a surface area of 62 square feet, and with a lamination cost of $2 per square foot, it will cost Rosalie $124.

To calculate the cost for laminating the outside of a cabinet, we first need to find the total surface area to be laminated. Since the cabinet is a rectangular prism, we can use the surface area formula for a rectangular prism: Surface Area = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. In this case, l = 3 ft, w = 2 ft, and h = 5 ft.

Surface Area = 2(3 ft)(2 ft) + 2(3 ft)(5 ft) + 2(2 ft)(5 ft)
Surface Area = 2(6) + 2(15) + 2(10)
Surface Area = 12 + 30 + 20
Surface Area = 62 square feet

Now to find the total cost, we multiply the surface area by the cost per square foot: Total cost = Surface Area times Cost per square foot.
Total cost = 62 sq ft times $2/sq ft
Total cost = $124

Therefore, it will cost Rosalie $124 to get the cabinet laminated.

In each case, the x-values are equally-spaced. Thus looking at second differences will tell you if the relation is quadratic. If the second differences are non-zero and constant, then the values have a quadratic relationship.

A. First differences are 2-4 = -2, 1-2 = -1, 0.5-1 = -0.5. Second differences are -1-(-2) = 1, -0.5-(-1) = 0.5. Since 1 ≠ 0.5, this relation is not quadratic. (It is exponential with a base of 1/2.)

B. First differences are 128-135 = -7, 105-128 = -23, 72-105 = -33. Second differences are -23-(-7) = -16, -33-(-23)=-10. Since -16 ≠ -10, this relation is not quadratic. (It is cubic, since 3rd differences are constant at +4.)

C. First differences are -23.2-(-23.4) = 0.2, -23.0-(-23.2) = 0.2, -22.8-(-23.0) = 0.2. Second differences are zero, so this is not a quadratic relation. (It is linear, with a slope of 0.2.)

D. First differences are 56-90 = -34, 26-56 = -30, 0-26 = -26. Second differences are -30-(-34) = 4, -26-(-30) = 4. These are constant (=4), so the relation is quadratic.

The appropriate choice is ...

... D. x -1 0 1 2 3 4

... f(x) 90 56 26 0 -22 -40

Answer:  D. x -1 0 1 2 3 4

f(x) 90 56 26 0 -22 -40

Step-by-step explanation:

Answer:

240 cubic cm

Step-by-step explanation:

Volume of the box before increament in sides = length*width*height

Length= 5 in.

Width=5 in.

Height = 10 in.

Putting these vales in formula

Volume of box = 5*5*10

                        =[tex]250cm^{3}[/tex]

Now  If the side lengths of the square faces are changed to 7 inches,

So, Length will be 7 in.

Width will be 7 in.

So, new volume = 7*7*10

                          =[tex]490cm^{3}[/tex]

Thus increase in volume = 490-250 =240

Hence by 240 cubic cm  will this increase the volume of the box

The measure of the given angle in degrees is:

                          246 degrees

We are given a  angle measure in radians.

We have to convert the given angle measure to degrees.

We know the conversion that:

 π radians= 180°

⇒  1 radians= 180°/π

Hence, the value of 4.3 radians will be, we multiply both side of the equation by 4.3 :

   4.3 radians=246.372°

Hence, to the nearest degree i.e. to the whole number of a degree we get the value of:

    4.3 radians= 246°

Answer: 1.2

Step-by-step explanation:

The formula for inverse variation  is given by :-

[tex]x_1y_1=x_2y_2[/tex]

The given points : (1.6, 6) and (8, y)

It means at x = 1.6 , y=6 .

To find the value of y at x=8 , we substitute [tex]x_1=1.6,\ y_1=6\, \text{ and}\ x_2=8,\ y_2=y[/tex] in the above formula , we get

[tex]1.6\times6=8y\\\\\Rightarrow\ y=\dfrac{1.6\times6}{8}\\\\\Rightarrow\ y=1.2[/tex]

Thus, the missing value = 1.2

The measure of angle x is 40 degrees and this can be determined by using the formula of the sum of interior angles of a polygon.

Given :

A regular nonagon.

The sum of interior angles of a polygon is given by the equation:

= (n - 2)180   --- (1)

where 'n' is the total number of sides of the polygon.

Given that the polygon is the regular nonagon that means the total number of sides is 9.

Now, substitute the value of 'n' in the equation (1).

= (9 - 2)180

= [tex]1260^\circ[/tex]

Now, divide the above expression by 9 in order to get the value of one interior angle.

[tex]= \dfrac{1260}{9}[/tex]

= [tex]140^\circ[/tex]

Now, the sum of one interior angle and the angle x is equal to 180 degrees that means:

140 + x = 180

x = [tex]40^\circ[/tex]

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