Answer:
GCF < 2 : 2 and 7, 12 and 13
GCF = 2 : 2 and 6
GCF = 3 : 3 and 6
GCF > 3 : 4 and 12, 6 and 18
Step-by-step explanation:
The greatest common Factor (GCF) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
(a) 2 and 7: Both 2 and 7 are prime numbers, therefore the GCF of 2 and 7 is 1 which is less than 2.
(b) 2 and 6: Both 2 and 6 are even numbers, therefore the GCF of 2 and 6 is 2.
(c) 4 and 12: Both 4 and 12 are even numbers and multiple of 4, therefore the GCF of 4 and 12 is 4 which is greater than 3.
(d) 12 and 13: 13 is a prime number, therefore the GCF of 12 and 13 is 1 which is less than 2.
(e) 6 and 18: Both 6 and 18 are even numbers and multiple of 6, therefore the GCF of 6 and 18 is 6 which is greater than 2 and greater than 3.
(f) 3 and 6: Both are multiple of 3, therefore the GCF of 3 and 6 is 3.
Answer:
The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle
The Leg Rule (or Leg geometric mean theorem) relates the length of each leg of a right triangle with the segments projected by them on the hypotenuse.
Step-by-step explanation:
The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. Notice the triangle used with this rule. The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.
If you times it the answer is going to be 1,200
Answer:
The required drawing showing the cliff, river, and tower as well as the details in the question is attached, please find alongside the answer
The width of the river is approximately 51.55 meters
Step-by-step explanation:
The height of the observation tower = 11 meters
The angle of elevation of the cliff top and the opposite side of the river = 20°
The angle of elevation of the tower top and the opposite side of the river = 30°
Therefore, by sine rule, we have;
h/sin(20) = w/sin(60)
11/sin(10) = length, l/sin(60)
l = sin(60) ×11/sin(10) ≈ 54.86 meters
w = l × cos (20) = 54.86 meters × cos (20) ≈ 51.55 meters
The width, w, of the river is approximately 51.55 meters.
Answer:
X=½ or 3
Step-by-step explanation:
0=2x²-7x+3
0=(2x-1)(x-3)
0=2x-1 or 0=x-3
1=2x or 3=x
½=x
