Given m ∠ Q P S = 4 7 ∘ m∠QPS=47 ∘ m, angle, Q, P, S, equals, 47, degrees m ∠ R P S = 3 x − 3 8 ∘ m∠RPS=3x−38 ∘ m, angle, R, P,
lukranit [14]
Answer:
Step-by-step explanation:
Given m ∠ Q P S = 4 7 ∘ m∠QPS=47 ∘ m, angle, Q, P, S, equals, 47, degrees m ∠ R P S = 3 x − 3 8 ∘ m∠RPS=3x−38 ∘ m, angle, R, P, S, equals, 3, x, minus, 38, degrees m ∠ Q P R = 7 x − 9 5 ∘ m∠QPR=7x−95 ∘
Sum of angles in a triangle = 180°
47° + 3 x − 3 8 ∘ + 7x - 95° = 180°
10x + 180° = 180°
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.
Learn more about gcd here:
brainly.com/question/16969353
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Answer:
B. {x| x > 2 or x < -4}
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Step-by-step explanation:
Given
![5(x - 2)(x + 4) > 0](https://tex.z-dn.net/?f=5%28x%20-%202%29%28x%20%2B%204%29%20%3E%200)
Required
Solve
![5(x - 2)(x + 4) > 0](https://tex.z-dn.net/?f=5%28x%20-%202%29%28x%20%2B%204%29%20%3E%200)
Start by dividing both sides by 5
![\frac{1}{5} * 5(x - 2)(x + 4) > \frac{0}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%20%2A%205%28x%20-%202%29%28x%20%2B%204%29%20%3E%20%5Cfrac%7B0%7D%7B5%7D)
![(x - 2)(x + 4) > 0](https://tex.z-dn.net/?f=%28x%20-%202%29%28x%20%2B%204%29%20%3E%200)
Find critical point of the inequality by changing the inequality to equality
![(x - 2)(x + 4) = 0](https://tex.z-dn.net/?f=%28x%20-%202%29%28x%20%2B%204%29%20%3D%200)
Split the above expression
![x - 2= 0\ or\ x + 4= 0](https://tex.z-dn.net/?f=x%20-%202%3D%200%5C%20or%5C%20x%20%2B%204%3D%200)
Make x the subject of formula in both
![x - 2+2= 0+2\ or\ x + 4-4= 0-4](https://tex.z-dn.net/?f=x%20-%202%2B2%3D%200%2B2%5C%20or%5C%20x%20%2B%204-4%3D%200-4)
![x = 0+2\ or\ x = 0-4](https://tex.z-dn.net/?f=x%20%3D%200%2B2%5C%20or%5C%20x%20%3D%200-4)
![x = 2\ or\ x = -4](https://tex.z-dn.net/?f=x%20%3D%202%5C%20or%5C%20x%20%3D%20-4)
Check the intervals in between the critical points
Set:
--- This works in the inequality
Set:
--- This doesn't work in the inequality
Set:
--- This doesn't works in the inequality
Set:
--- This works in the inequality
<em>Hence, the solution is: {x| x > 2 or x < -4}</em>
Answer:
YOUR MOM IS A NI**A
Step-by-step explanation:
First i had s3X with ur mom then i mast_turbated with ur mom and BOOM