Need help with 17 and 18

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)

the area of the piece of paper =   27- inch square.

so, the length of the square piece of paper = = .

the side of the triangle cut = =

also the side of the small square cut =

so, the area of each triangle cut = 1/2 * .

so, the area of 4 triangles cut =

area of a small square cut =

total area of 4 triangles cut and a small square cut = 6+3 = 9 square inches.

reaming area of the octagonal window   = 27 - 9 = 18 square inches.

x³ - 13x + 12

step-by-step explanation:

if you are familiar with the distributive property

a(b+c) = a·b + a·c

then you can apply this here with the binomials.

since multiplication over the real numbers is commutative, we can multiply these binomials in any order. suppose we want to focus on the product (x - 1)(x + 4)

using the distributive property, we can distribute (x - 1) into (x+4):

(x - 1)(x + 4) = x(x - 1)+ 4(x - 1)

and then we apply the distributive property again:

  = x² - x + 4x - 4

combining like terms -x and 4x, we get that

  = x² + 3x - 4

hence we have that (x - 1)(x + 4) = x² + 3x - 4. in this original product, this means that

  (x - 1)(x + 4)(x - 3) = (x² + 3x - 4)(x - 3)

now we can take (x - 3) to the front

  = (x - 3)(x² + 3x - 4)

and then distribute (x-3) inside

  = x²(x - 3) + 3x(x - 3) - 4(x - 3)

now distribute again

  = x³ - 3x² + 3x² - 9x - 4x + 12

and combine like terms to get a final answer of

  = x³ - 13x + 12