***urgent*** ***50 points***
if you do answer, provide an explanation because i want to know how to solve these problems for the future and not just have the answer without an explanation.

27) 18 < P ≤ 18 + 6√2 ⇒ answer D

28) The sum of the degree measures these angles is 1080° ⇒ answer B

29) 3E minutes before A ⇒ answer B

30) The difference between the greatest possible values is 0 ⇒ answer E

31) r divided by s = 1/3 ⇒ answer A

Step-by-step explanation:

* Lets explain each problem

27)

∵ BE is a quarter circle

∵ The radius of the circle is 6

∵ Point c is on the arc BE

∴ The distance from D to C = 6 ⇒ not depends on the position of c

   because DC is a radius in the quarter circle BE

- In Δ BDE

∵ m∠ D = 90°

∵ DB = DE = 6 ⇒ radii of the quarter circle

- By using Pythagoras Theorem

∴ BE = √ (6² + 6²) = √(36 + 36) = √72 = 6√2

- The perimeter of the quadrilateral ABCD is the sum of the sides

∵ AB = 6 , AD = 6 , CD = 6

- Point C can move from B to E

∴ The length of side BC can b greater than 0(it can not be 0

   because the quadrilateral has 4 sides

∴ The length of BC can not exceed the length of BE because the last

   position of point C to be on the arc BE is point E

∴ The length of BC ⇒ 0 < BC ≤ 6√2

  equal 6√2

∵ P is the perimeter of the quadrilateral ABCD

∴ P = 6 + 6 + 6 + (0 < BC ≤ 6√)

∴ P = 18 + (0 < BC ≤ 6√)

- Add 18 to 0 and 18 to 6√2

∴ 18 < P ≤ 18 + 6√2

28)

- In the figure we have a quadrilateral

- All the arrows represent the exterior angles of the figures

- Use the fact that:

 The sum of all angles around a points is 360°

∵ There are 4 vertices (points) on the quadrilateral

∴ The sum of the all angles around the 4 vertices = 4 × 360 = 1440°

- Use the fact that:

 The sum of the interior angles of any quadrilateral is 360°

∵ The sum of the angles represented by the arrows is the difference

  between the sum of all angles around the 4 vertices and the sum

  of the interior angles of the quadrilateral

∴ The sum of these angles = 1440° - 360° = 1080°

* The sum of the degree measures these angles is 1080°

29)

- In any watch the short arrow-hand represents the hours and the long

 arrow-hand represents the minutes

- The numbers of the hours in the watch from 1 to 12

- The number of minutes between each two hours is 5 minutes, then

  at 1 o'clock the minutes number is 5 , at 6 o'clock the number of

  minutes is 30 , at 9 o'clock the number of minutes is 45 , so we can

  find the number of minutes at any number of hour by multiply the

  number of hour by 5

∵ The number of hours have been replaced by letters

∵ The time on the watch is 45 minutes after 12 o'clock OR

  15 minutes before 1 o'clock

∵ The short arrow-hand pointed between L and A

∵ L is the replacing of 12 o'clock and A is the replacing of 1 o'clock

∵ The long arrow-hand pointed at I

∵ I is the replacing of  9 o'clock

∵ The hour number 9 means 5 × 9 = 45 minutes

∴ The hour hand I has 5I minutes

∴ The time in letter is 5I minutes after L

- This answer is not in the choices

- But the answer of 3E minutes before A means:

∵ E is the replacing of 5 o'clock

∴ 3E = 3 × 5 = 15 minutes

∵ A is the replacing of 1 o'clock

∴ 3E minutes before A means 15 minutes before 1 o'clok

* The answer is ⇒ 3E minutes before A

30)

∵ r² = 9

∴ r = ± √9 = ± 3

∴ r has two values -3 and 3

∵ s² = 25

∴ s = ± √25 = ± 5

∴ s has two values -5 and 5

- To find the greatest value of s - r put s greatest and r smallest

∵ The greatest value of s is 5

∵ The smallest value of r is -3

∴ The greatest value of s - r = 5 - (-3) = 5 + 3 = 8

- To find the greatest value of r - s put r greatest and s smallest

∵ The greatest value of r is 3

∵ The smallest value of s is -5

∴ The greatest value of r - s = 3 - (-5) = 3 + 5 = 8

∴ The difference between the greatest possible values of s - r

   and r - s = 8 - 8 = 0

* The difference between the greatest possible values is 0

31)

- There are 27 cubes each of side length r

- The 27 cubes are arranged to form on single large cube of side

  length s

∵ The volume of any cube is V = L³ , where L is the length of its side

∵ The large cube formed from the 27 small cubes

∴ The volume of the large cube = the volume of the 27 small cubes

∵ The side of the small cube is r

∴ The volume of the small cube is r³

∵ The side of the large cube is s

∴ The volume of the large cube is s³

∴ s³ = 27 r³

- Divide both sides by s³ and 27

∴ s³/(27 s³) = (27 r³)/(27 s³)

∴ 1/27 = r³/s³

- Take ∛  for both sides

∴ ∛(r³/s³) = ∛(1/27)

- The cube root canceled by the power 3 and the cube root of

  1/27 is 1/3

∴ r/s = 1/3

* r divided by s = 1/3

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:

the answer is 21%.