Find the missing length. Round to the nearest tenth, if necessary. A right triangle has legs measuring 8 units and x units and a
1 answer:
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Answer:
14 years old
Step-by-step explanation:
<u>Define the variable</u>
Let x be the actual age of Zeba (in years).
<u>Create an equation</u> using the give information and the variable x:
To find Zeba's age now, <u>solve the equation for x</u>.
Expand the brackets:
Subtract 5x from both sides:
Subtract 11 from both sides:
<u>Factor the found quadratic</u>
To factor a quadratic in the form <em>, </em>find two numbers that multiply to
and sum to
, then rewrite
as the sum of these two numbers:
Factor the first two terms and the last two terms separately:
Factor out the common term (x - 14):
Apply the <u>zero product property</u>:
Therefore, Zeba's age now is either 1 or 14 years.
As the question states "If Zeba were younger by 5 years" then 1 must be an <u>extraneous solution</u> since 1 - 5 = -4 and Zeba cannot be -4 years old.
Therefore, Zeba's age now is 14 years old.
<u>Check</u>
Given the actual age of Zeba is 14 years old.
Therefore, If Zeba were younger by 5 years, she would be 9 years old as: 14 - 5 = 9
The square of 9 is: 9² = 81.
5 times her actual age: 5 × 14 = 70
81 is 11 more than 70, hence verifying that her <u>actual age is 14 years old</u>.
Learn more about quadratic equations here: