9514 1404 393
Answer:
17/99
Step-by-step explanation:
Replace the digits 23 in your example with the digits 17 and you have your answer:
_____
In general, a 2-digit repeat will have 99 as its denominator. If the digits are a multiple of 3 or 11, then the fraction can be reduced. 17 is prime, so the fraction cannot be reduced.
If you're only provided with the lengths of a triangle, and you're asked to determine whether or not the triangle is right or not, you'll need to rely on the Pythagorean Theorem to help you out. In case you're rusty on it, the Pythagorean Theorem defines a relationship between the <em>legs</em> of a right triangle and its <em>hypotenuse</em>, the side opposite its right angle. That relationship is a² + b² = c², where a and b are the legs of the triangle, and c is its hypotenuse. To see if our triangle fits that requirement, we'll have to substitute its lengths into the equation.
How do we determine which length is the hypotenuse, though? Knowledge that the hypotenuse is always the longest length of a right triangle helps here, as we can clearly observe that 8.6 is the longest we've been given for this problem. The order we pick the legs in doesn't matter, since addition is commutative, and we'll get the same result regardless of the order we're adding a and b.
So, substituting our values in, we have:
(2.6)² + (8.1)² = (8.6)²
Performing the necessary calculations, we have:
6.76 + 65.61 = 73.96
72.37 ≠ 73.96
Failing this, we know that our triangle cannot be right, but we <em>do </em>know that 72.37 < 73.96, which tells us something about what kind of triangle it is. Imagine taking a regular right triangle and stretching its hypotenuse, keeping the legs a and b the same length. This has the fact of <em>increasing the angle between a and b</em>. Since the angle was already 90°, and it's only increased since then, we know that the triangle has to be <em>obtuse</em>, which is to say: yes, there's an angle in it larger than 90°.
Answer:
The table of Henry's family will be at (4, -4)
Step-by-step explanation:
The problem states that the initial coordinates of Henry's family is at the coordinates (-4, 4). Each 15 minutes the restaurant will rotate 90° every 15 minutes. If we follow the Cartesian plane and the center of the restaurant being at (0, 0) we know that the table will be situated at the (4, 4) coordinates of the restaurant after the first rotation. After the 30 minute mark, the restaurant rotates one more time and moves the table of Henry's family at the (4, -4) coordinates of the restaurant as the center of the restaurant will never move.
