On a winter evening at sundown, a Kansas City news station reports that the temperature is [tex]$-2^{\circ} F$[/tex] and will drop by [tex]$2^{\circ} F$[/tex] per hour until sunrise. At the same time, a Chicago news station reports that the temperature is [tex]$6^{\circ} F$[/tex] and will drop by [tex]$4^{\circ} F$[/tex] per hour.
Which equation can you use to find [tex]$h$[/tex], the number of hours it will take the cities to reach the same temperature?
[tex]\begin{array}{l}
2 h-2=6 h-4 \\
-2-2 h=6-4 h
\end{array}[/tex]
How long will it take for the cities to reach the same temperature?
Simplify any fractions.
Answer (3)
Well, 10<49.5+50.5, 49.5<10+50.5 and 50.5<10+49.5 Because these conditions are obeyed, you have a triangle. A right triangle requires that 50. 5 2 = 1 0 2 + 49. 5 2 2550.25 = 100 + 2450.25 which is true. So, the triangle has a right angle.
To determine if the side lengths of 10 cm, 49.5 cm, and 50.5 cm form a right triangle, apply the Pythagorean theorem. Confirming the sum of the squares of the two shorter sides equals the square of the longest side, these lengths do form a right triangle.
The question is asking whether the given side lengths of 10 cm, 49.5 cm, and 50.5 cm can form a right triangle. To determine this, we apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Step-by-step, first we identify the longest side, which could be the potential hypotenuse, in this case, 50.5 cm. We then square each side length:
10 cm squared = 100
49.5 cm squared = 49.5 x 49.5 = 2,450.25
50.5 cm squared = 50.5 x 50.5 = 2,550.25
Next, we add the squares of the two shorter sides:
100 + 2,450.25 = 2,550.25
This sum is equal to the square of the longest side, which confirms that these side lengths can indeed form a right triangle.
The side lengths 10 cm, 49.5 cm, and 50.5 cm do form a right triangle, as verified by the Pythagorean theorem. The calculation shows that the square of the longest side equals the sum of the squares of the other two sides. Therefore, these lengths satisfy the condition for a right triangle.
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