Please solve the quadratic equationx² - 2x - 10 = 0x² - 2x - 2 = 0
2 answers:
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Complete question is;
Jane is training for a triathlon. After swimming a few laps, she leaves the health club and bikes 16 miles south. She then runs 12 miles west. Her trainer bikes from the health club to meet jane at the end of her run. Use the pythagorean theorem to write an equation for the distance janes trainer bikes
Answer:
x = √(12² + 16²)
Step-by-step explanation:
We are told that;
She bikes from health club to South = 16 miles
From South to West = 12 miles
Her trainer bikes from the health club to meet her at the end which is west.
I have attached a diagram showing this movement in form of a triangle.
From the diagram I attached, I have depicted the distance the trainer bikes as x.
Using pythagoras theorem;
x² = 12² + 16²
x = √(12² + 16²)
<h2>Answer: </h2><h2>99/5</h2><h2>~</h2><h3>Convert to a mixed number by placing the numbers to the right of the decimal over 10. </h3><h3>Reduce the fraction. </h3><h3>Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator to get the new numerator. </h3><h3>Place this new numerator over the original denominator to get:</h3><h3>99/5</h3><h3>Or</h3><h3>
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Answer:
The length of the diagonal = 3.6 feet
Step-by-step explanation:
* Lets change the story problem to equation to solve it
- Diagonal in a rectangle is the line which joining two
opposite vertices in it
- The diagonal , the length and the width formed together right
angle triangle where the diagonal is the hypotenuse of the
triangle and the length, the width are the two legs of the
right angle
- The length of the diagonal d is √(l² + w²) ⇒ Pythagoras theorem
∴ d² = l² + w²
- The diagonal is 2 feet more than the width
∴ d = w + 2
- The length is twice the width
∴ l = w
* Lets substitute the value of d and l in the equation of Pythagoras
∴ (w + 2)² = (2w)² + w² ⇒ solve the bracket
∴ w² + 4w + 4 = 4w² + w² ⇒ collect them in one side and add like term
∴ 4w² + w² - w² - 4w - 4 = 0 ⇒ add the like term
∴ 4w² - 4w - 4 = 0 ⇒ divide all term by 4
∴ w² - w - 1 = 0 ⇒ solve the quadratic using the formula
- In ax² + bx + c = 0
∵ a = 1 , b = -1 , c = -1
∴
-The value of the width is 1.6 feet
∴ The length = 1.6 × 2 = 3.2 feet
∴ The length of the diagonal = 2 + 1.6 = 3.6 feet