A number is three less than six times another numbers. The sum is 53. Find the numbers

1 answer:

3 0

X = 6y - 3
x + y = 53

6y - 3 + y = 53
7y - 3 = 53
7y = 53 + 3
7y = 56
y = 56/7
y = 8

x = 6y - 3
x = 6(8) - 3
x = 48 - 3
x = 45

ur numbers are : 8 and 45

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Find the orthocenter of the triangle with the given vertices: L(2, 2), M(-4, 2), N(-2, 6) a (-2, 4) b (3, -5) c (2, -4) d (-3, 5

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Answer:

(a) (-2, 4)

Step-by-step explanation:

The orthocenter is the point of concurrence of the altitudes of the triangle.

A plot of the triangle vertices shows the triangle to be acute. That means the orthocenter is inside. This eliminates choices B, C, D, which are all points outside the triangle.

Conveniently, side LM is horizontal. This means the orthocenter will have the x-coordinate of the vertical line through N, which is -2. Only one answer choice has an x-coordinate of -2:

a (-2, 4)