The dimensions of a small juice box are 11 cm by 4 cm by 7 cm. the super-size juice box has the same height of 11 cm but double the volume. give two sets of the possible dimensions of the super-size juice box and the volume.

Two sets of the dimensions may be 4cm×14cm×11cm or 7cm×8cm×11cm and the volume will be 616 cm³.

Step-by-step explanation:

Dimensions of a small juice box are 11cm×4cm×7cm.

Volume of the small juice box = 11×4×7 = 308 cm³

Height of the super size juice box is same as small juice box but volume is double.

Let length and width of the super size juice box are x and y cm.

So volume = 11xy cm³ = 2(Volume of small juice box)

11xy = 2×308

xy =

xy = 56

Therefore, two sets of the dimensions may be 4cm×14cm×11cm or 7cm×8cm×11cm and the volume will be 616 cm³.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!