Step-by-step explanation:
so, we need to find the smallest common multiple of 36 and 42.
that is the smallest number I can divide both by 36 and 42 without remain.
let's use the method of basic prime factors (we start with the smallest fitting prime number - 2 is a prime number too - and divide as often as possible, then continue with the next bigger prime number, until there is nothing left to divide) :
36 / 2 = 18
18 / 2 = 9
9 / 3 = 3
3 / 3 = 1 finished
therefore,
36 = 2×2×3×3
42 / 2 = 21
21 / 3 = 7
7 / 5 does not work
7 / 7 = 1 finished
therefore,
42 = 2×3×7
to find the smallest common multiple (SCM) we check the maximum length of each prime factor sequence.
and we see 2 times 2, 2 times 3 and 1 time 7.
so, the SCM = 2×2×3×3×7 = 252.
there is no smaller number that can be divided by both 36 and 42 without remain.
so, the rod must be at least 252 cm long to cut it into equally long pieces of either 36 cm (7 pieces) or 42 cm (6 pieces).
Answer:
67.5 degrees
Step-by-step explanation:
The first angle is 45 and the second angle is x and the third angle is x (the second and third are equal)
We know the 3 angles of a triangle add to 180 degrees
45+x+x = 180
Combine like terms
45+2x=180
Subtract 45 from each side
45-45 +2x = 180-45
2x= 135
Divide by 2
on each side
2x/2 =135/2
x = 67.5
Answer:
1:3
Step-by-step explanation:
Both numbers are divisible by 25:
∴ The simplified ratio is 1:3
Hope this helps!
Answer:
Step-by-step explanation:
It is true because you can draw an edge to that vertex
