How high is the hand of the superhero balloon above the ground? The hand is _ feet above the ground.

the best estimate is 3 because   8 can only go into 24 3 times

b) yes

step-by-step explanation:

let the statements be named as,

statement 1: if the power has been cut, then the refrigerator does not work.

statement 2: the refrigerator does not work.

conclusion: the power has been cut

now, 'law of detachment states that if we have the statements given as,

1. if p, then q.

2. p

then, we get the true statement or conclusion as q'.

thus, on comparing, we get that,

p: if the power has been cut.

q: the refrigerator does not work.

so, the argument is true by the law of detachment.

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