For line B to AC: y - 6 = (1/3)(x - 4); y - 6 = (x/3) - (4/3); 3y - 18 = x - 4, so 3y - x = 14
For line A to BC: y - 6 = (-1)(x - 0); y - 6 = -x, so y + x = 6
Since these lines intersect at one point (the orthocenter), we can use simultaneous equations to solve for x and/or y:
(3y - x = 14) + (y + x = 6) => 4y = 20, y = +5; Substitute this into y + x = 6: 5 + x = 6, x = +1
<span>So the orthocenter is at coordinates (1,5), and the slopes of all three orthocenter lines are above.</span>
Answer:
If you take 32 percent of a number and get 64, then what is that number? In other words, you know that 32 percent of a number is 64 and you want to know what that initial number is. Therefore, the answer to "64 is 32 percent of what number?" is 200, and you can also derive that 32 percent of 200 equals 64.
Step-by-step explanation:
Answer:
LAST OPTION: 
Step-by-step explanation:
For this exercise it is important to remember the Power of a power property, which states that:
The expression given in the exercise is:
Therefore, in order to simplify it, you must apply the Power of a power property explained before.
Then, you get the following expression:
As you can notice, the expression obtained matches with the expression provided in the last option.
To find the ratio, we must find the total amount of days (31) and the number of days that are either a Saturday or a Sunday (10). Since in the sentence, the number of Saturdays and Sundays is mentioned first, the 10 would precede the 31 in the ratio.
Final Answer - 10:31
Answer:3x-2/6
Step-by-step explanation:When you multiply 1/2 by 6 you would get 3, so 6x is turned to 3x, and when you multiply 1/2 by -2/3, you get -2/6, so your new equation is, (3x-2/6)
