Two positive integers have gcd (a, b) = 15 and lcm (a, b) = 90. Those two numbers are 15 and 90 or 30 and 45.
Suppose we have 2 positive integers, a and b, then:
gcd (a, b) = the greatest common divisor = common prime factors of a and b
lcm (a, b) = the least common multiple = multiplication of the greatest common prime factors of a and b
In the given problem:
gcd (a, b) = 15
prime factorization of 15:
15 = 3 x 5
Hence,
a = 3 x 5 x ....
b = 3 x 5 x ....
lcm (a, b) = 90
prime factorization of 90:
90 = 3 x 5 x 2 x 3
Therefore the possible pairs of a and b are:
Combination 1:
a = 3 x 5 = 15
b = 3 x 5 x 2 x 3 = 90
Combination 2:
a = 3 x 5 x 2 = 30
b = 3 x 5 x 3 = 35
We can conclude the two integers are 15 and 90 or 30 and 45.
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Answer:
slope = - 
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 9, - 4) and (x₂, y₂ ) = (- 3, - 6)
m =
=
= - 
Answer:
SP = 43 units
Step-by-step explanation:
Given question is incomplete: find the complete question in the attachment.
From the figure attached,
Length of LN = (5x - 14)
Length of SP = (2x + 3)
By the mid-segment theorem,
"Segment connecting the mid points of two sides of a triangle is parallel and half the length of the third side."
SP = 
(2x + 3) = 
4x + 6 = 5x - 14
5x - 4x = 14 + 6
x = 20
SP = (2x + 3)
= (2×20) + 3
= 43 units
Therefore, measure of SP = 43 units is the answer.