2 years ago

Define and name two pairs of corresponding angles

Mathematics

1 answer:

Inga [223]2 years ago

4 0

Answer:

2 corresponding to 6

3 corresponding to 7

Step-by-step explanation:

Corresponding angles just make the letter F

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3 years ago

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3 years ago

The GCD(a, b) = 9, the LCM(a, b)=378. Find the least possible value of a+b.

denis-greek [22]

$\mathrm{gcd}(a,b)=9\implies9\mid a\text{ and }9\mid b\implies9\mid a+b$

which means there is some integer $k$ for which $a+b=9k$ .

Because $9\mid a$ and $9\mid b$ , there are integers $n_1,n_2$ such that $a=9n_1$ and $b=9n_2$ , and

$\mathrm{lcm}(a,b)=\mathrm{lcm}(9n_1,9n_2)=9\mathrm{lcm}(n_1,n_2)=378\implies\mathrm{lcm}(n_1,n_2)=42$

We have $42=2\cdot3\cdot7$ , which means there are four possible choices of $n_1,n_2$ :

1, 42
2, 21
3, 14
6, 7

which is to say there are also four corresponding choices for $a,b$ :

9, 378
18, 189
27, 126
54, 63

whose sums are:

387
207
153
117

So the least possible value of $a+b$ is 117.

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3 years ago