Math Problem Statement

Solution

Let's re-evaluate the provided expression with the correct values from the latest image. The expression is:

[ \frac{15(21086) - (514)(429)}{\sqrt{[15(26550) - (514)^2] \times [15(26191) - (429)^2]}} ]

Step 1: Evaluate the Numerator

15×21086514×42915 \times 21086 - 514 \times 429

First, calculate each part:

15×21086=31629015 \times 21086 = 316290 514×429=220506514 \times 429 = 220506

Then subtract the results:

316290220506=95784316290 - 220506 = 95784

Step 2: Evaluate the Denominator

The denominator consists of two parts inside the square root which are then multiplied:

(15×265505142)×(15×261914292)\sqrt{(15 \times 26550 - 514^2) \times (15 \times 26191 - 429^2)}

First, calculate each part inside the parentheses:

15×26550=39825015 \times 26550 = 398250 5142=264196514^2 = 264196 15×26191=39286515 \times 26191 = 392865 4292=184041429^2 = 184041

Now subtract these results:

398250264196=134054398250 - 264196 = 134054 392865184041=208824392865 - 184041 = 208824

Then multiply these two results:

134054×208824=27998811496134054 \times 208824 = 27998811496

Finally, take the square root of the product:

27998811496167329.47\sqrt{27998811496} \approx 167329.47

Step 3: Calculate the Final Result

Divide the evaluated numerator by the evaluated denominator:

95784167329.470.5725\frac{95784}{167329.47} \approx 0.5725

Thus, the value of the given expression is approximately 0.57250.5725.

Would you like more details or have any questions about this calculation? Here are five more questions you might want to ask:

  1. How do you simplify complex fractions?
  2. Can you explain the steps for solving quadratic equations?
  3. What are the properties of logarithms?
  4. How do you find the derivatives of trigonometric functions?
  5. What is the process for solving systems of linear equations?

Tip: Always ensure to use precise values when performing mathematical operations to avoid errors in the final result.

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Math Problem Analysis

Mathematical Concepts

Algebra
Fraction operations
Square root operations

Formulas

Quadratic formula
Fraction calculation formula

Theorems

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Suitable Grade Level

Grades 10-12