Andy used a scale of Inch - 2 feet for a drawing of his house. On the drawing, a rectangular room measures 3 inches by 2 inches. Andy wants to purchase new carpet for the room that costs $4.89 per square foot. Before sales tax, how much will the new carpet cost?

$ 117.36

Step-by-step explanation:

On the drawing, the rectangular room measures 3 inches by 2 inches, we can convert to feet (using a scale of Inch - 2 feet )

(3 inches ×2) by (2 inches ×2)

= 6 feet by 4 feet

The Area of the room can now be calculated as

Area=( 6 feet × 4 feet)

= 24 ft^2

how much will the new carpet cost?

we know that the carpet costs $4.89 per square foot, then the cost by the area of the room= (Area× $4.89 per square foot)

=24 ft^2 x $4.89

=$ 117.36

Hence, the new carpet cost is $ 117.36

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.