Kathleens's ice cream cone has a diameter of 9 cm and a slant height of 7.5cm, what is the height of the ice cream cone

  6 cm

Step-by-step explanation:

The triangle formed by the slant height, the height, and the radius is a right triangle with one leg 4.5 cm and hypotenuse 7.5 cm. These dimensions are in the ratio ...

  4.5 : 7.5 = 3 : 5

so suggests that the dimensions are similar to those of a 3-4-5 right triangle with a scale factor of 1.5 cm.

That is, the height of the cone will be 1.5 cm · 4 = 6 cm.

Comment on 3-4-5 right triangle

Triangles with dimensions of these ratios often show up in algebra problems because they work out nicely, avoiding irrational numbers. It is easy enough to show that a triangle with legs 3 and 4 will have a hypotenuse of 5, according to the Pythagorean theorem:

  5^2 = 3^2 + 4^2

  25 = 9 + 16 . . . . . . true

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: