Math Problem Statement

Risolvi

Translate into words the following expressions: 1) 25 + 8 = 5² + 8 2) (15 − 2)² ÷ 5 + 2 = 2 3) 1 + x + (14 − 4) ÷ 8³

Solution

The image you uploaded contains three expressions that need to be translated into verbal (word) form. Let's solve them one by one:

  1. 25 + 8 = 5² + 8

    • This is a simple equation where the sum of 25 and 8 is equal to the sum of 525^2 (which is 25) and 8.
    • Verbal translation: "The sum of twenty-five and eight is equal to the sum of the square of five and eight."
  2. (15 − 2)² ÷ 5 + 2 = 2

    • First, evaluate 152=1315 - 2 = 13. Then square the result: 132=16913^2 = 169. The equation simplifies to: 169÷5+2=2169 ÷ 5 + 2 = 2
    • Simplifying further, 169÷5=33.8169 ÷ 5 = 33.8, and adding 2 gives 35.835.8, which does not equal 2. This equation appears to have a typo or inconsistency, as it doesn't hold true.
    • Verbal translation: "The square of the difference of fifteen and two, divided by five, plus two equals two."
  3. 1 + x + (14 − 4) ÷ 8³

    • Simplify 144=1014 - 4 = 10, and compute 83=5128^3 = 512. The equation becomes: 1+x+105121 + x + \frac{10}{512}
    • This expression simplifies to 1+x+0.01951 + x + 0.0195, and there is no further simplification unless x is given.
    • Verbal translation: "One plus a variable x plus the result of the difference of fourteen and four divided by the cube of eight."

Would you like further details or clarification on any of these translations?

Here are some related questions to expand on the topic:

  1. How do you evaluate the cube and square of numbers?
  2. What are common pitfalls in solving equations with fractions and exponents?
  3. Can you explore how to verify the correctness of an equation?
  4. What strategies can be used to simplify complex algebraic expressions?
  5. How do word problems translate into algebraic expressions?

Tip: Always double-check your arithmetic, especially when dealing with squared and cubed numbers, as small mistakes can affect the final result.

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Math Problem Analysis

Mathematical Concepts

Algebra
Arithmetic
Exponents

Formulas

Square: a^2
Cube: a^3
Basic Arithmetic Operations

Theorems

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Suitable Grade Level

Grades 6-8