Answer:
B
Step-by-step explanation:
We are given the function:
And we want to determine the value of:
Let this value equal <em>a</em>. In other words:
Then by the definition of inverse functions:
Hence:
Solve for <em>a: </em>
By the Zero Product Property:
Hence:
Thus, f(9) = 225. Consequently, f⁻¹(225) = 9.
In conclusion, our answer is B.
The correct answer is: [D]: " 7.2 units" .
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Explanation:
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Use the Pythagorean theorem:
a² + b² = c² ;
in which: "6 units" and "4 units" equal the lengths of the right angle (formed by the rectangle); and "c" is the length of the diagonal of the rectangle, or the "hypotenuse", of the right triangle formed by the rectangle; We wish to solve for "c" ;
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6² + 4² = c² ; Solve for "c" ;
↔ c² = 6² + 4² ;
= (6*6) + (4*4) ;
= 36 + 16 ;
= 52 ;
c² = 52 ;
Take the "positive square root" of each side of the equation; to isolate "c" on one side of the equation; and to solve for "c" ;
√(c²) = √52 ;
c = √52 ;
At this point, we know the 7² = 49 ; 8² = 64 ; so, the answer is somewhere between "7" and "8" ; yet closer to "7" ; so among the answer choices given;
The correct answer is: [D]: " 7.2 units" .
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However, let use a calculator:
c = √52 = 7.2111025509279786 ; which rounds to "7.2" ;
which corresponds to:
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Answer choice: [C]: " 7.2 units" .
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Trick question — it’s a right triangle. Here’s why:
23 + 67 = 90. All triangles have an interior angle sum of 180. 180 - 90 = 90. 90 degrees is right, and therefore, having a right angle, this is a right triangle.
