Question

The distance between points ( (x_1, y_1) ) and ( (4,8) ) is the square root of ( (x_1-8)^2 + (y_1-4)^2 ).

Question 4882: Given: ( 1=2, 3=4, TS=TR ). Name the postulate or theorem you can use to prove ( TKS=TLR ).
Question 4883: 16. Mr. Shyam wishes to make his work efficient and use some logical attributes to maintain consistency in his documents. Suggest some ways to do so? 17. While analyzing a spreadsheet, a formula =sum(SALES!B5:B8) is entered in sheet1 of a workbook. What do you think is referred to with this formula? Why do you think this formula is used in spreadsheets and how is it an effective way of doing calculations?
Question 4884: Warm-Up
Simplify the number into simplest radical form. Use the factor tree to help determine the factors.

Select the correct factor for (96):
A) (5)
B) (28)
C) (47)
D) (4/5)

Answer 1

The given distance formula is a form of the Pythagorean theorem. Postulates such as SSS or SAS might be used to prove geometric congruence, and spreadsheet formulas like '=sum(...)' streamline calculations. The correct factor for simplifying 96 using a factor tree is (4/5).

Step-by-step explanation:

The distance formula given is a variation of the Pythagorean theorem, typically used to measure the direct straight-line distance between two points in a coordinate plane. To answer the questions posed, various mathematical concepts such as postulates, efficient logical methods for documentation, and the interpretation of spreadsheet formulas are used.

For Question 4882, without additional context, it's difficult to provide a postulate or theorem. However, with geometric proofs, postulates such as the Side-Side-Side (SSS) Congruence Postulate or the Side-Angle-Side (SAS) Congruence Theorem might apply if the given information pertains to triangle congruence.

In the context of Question 4883, suggestions for maintaining consistency in documents may include using consistent nomenclature, formatting consistently, and applying logical structures. Spreadsheet formulas like =sum(SALES!B5:B8) can efficiently calculate the sum of values from the cells B5 to B8 on a sheet named 'SALES', demonstrating how formulas can automate and streamline calculations, reducing the potential for human error.

For Question 4884, regarding the factor tree of 96, the correct factor to simplify the number into simplest radical form is Option D) (4/5).