Finding the greatest common factor ( or G C F ):
G C F is the largest number that divides evenly into all the numbers.
270 : 90 = 3
360 : 90 = 4
G C F ( 270, 360 ) = 90
HCF=Highest Common Factor-HCF of two or more numbers is the greatest factor that divides the numbers. For example, 2 is the HCF of 4 and 6.
LCM=Least Common Multiple-LCM is the smallest positive number that is a multiple of two or more numbers.
Answers:
1) 6
2) 12
3) 5
4) 3
5) 26
6) 15
7) 88
1. Find the "opposite side," if the angle is 60 degrees and the hyp is 6:
opp opp sqrt(3)
sin 60 deg = ------- = -------- = ----------
hyp 6 2
Cross-multiplying, 2(opp) = 6sqrt(3), so that opp = 3 sqrt(3) (answer)
2. Use the Pyth. Thm. to find the "adjacent side:"
[3sqrt(3)]^2 + x^2 = 6^2, or 9(3) + x^2 = 36, or x^2 = 9, or x = 3.
The lengths of the legs of this 30-60-90 triangle are 3 and 3 sqrt(3).
check: Does 3^2 + [3sqrt(3)]^2 = 6^2?
Does 9 + 9(3) = 6^2? YES
Answer:
10. Ray ED and Ray EF (two rays)
11. DE and EF (two line segments)
Step-by-step explanation:
hope this helped
Let
x------> amount of pounds of apples
y------> amount of pounds of oranges
z-----> amount of pounds of peaches
we know that
x+y+z=127------> equation 1
x=4z-----> equation 2
y=7+z----> equation 3
substitute equation 2 and equation 3 in equation 1
x+y+z=127----> (4z)+(7+z)+z=127---> 6z=127-7---> 6z=120----> z=20 lb
x=4z---> x=4*20----> x=80 lb
y=7+z----> y=7+20---> y=27 lb
amount of pounds of apples----> 80 lb
amount of pounds of oranges----> 27 lb
amount of pounds of peaches---> 20 lb
