For two numbers (let's call them a & b), the least common multiple is the smallest number that is an integer multiple of both a and b. For example, given the numbers 12 and 18, their least common multiple is 36, because of 3x12=36 and 2x18=36. A least common multiple can never be greater than the product of the two numbers because b times a is the b-the multiple of a, and the a the multiple of b. For example, the least common multiple of 7 and 11 is 77 because multiples of 7 are 14, 21, 28, 35, 42, 49, 56, 63, 70 and 77 and multiples of 11 are 22, 33, 44, 55, 66, 77, so 77 is the first one that is a multiple of both numbers. (BTW, 7 & 11 can be your first pair).The least common multiple of two numbers is the product of the two numbers when those numbers are relatively prime to each other, that is to say, that the two numbers do not share a factor in common (except for 1). For example, the least common multiple of 9 and 8 is their product 72. While neither 9 nor 8 are prime numbers, the factors of 9 are 3*3 and of 8 are 2*2*2. Since they share no factors in common, their product will be the least common multiple. (Multiples of 9 are 18, 27, 36, 45, 54, 63, and 72; Multiples of 8 are 16, 24, 32, 40, 48, 56, 64, and 72). (BTW, 8 & 9 could be your 2nd pair.So to construct a pair of numbers whose product is their least common multiple all you need to do is create two lists of prime factors, one for each number, where none of their factors overlap. While a number can be on one list multiple times (like the number 2 for 8 or the number 3 for 9), the same number cannot be on the list for both a and b. The first six prime numbers are 2, 3, 5, 7, 11, and 13. You can mix and match them however you'd like (following the rule above) to create your third pair of numbers. If you comment your choice, I'd be happy to confirm whether you have successfully constructed such a pair. -Hope this help #Hackerhelper
<span>1) if 2 times the wind speed is increased by 2, the wind speed is still less
than 46 km/h.
=> 2x + 2 < 46
2) Twice the wind speed minus 27 is greater than 11 km/h.
=> 2x - 27 > 11
Part A: Create a compound inequality to represent the wind speed range.
(3 points)
from 2x + 2 < 46
=> 2x < 44
=> x < 22
from 2x - 27 > 11
=> 2x > 11 + 27
=> 2x > 38
=> x > 19
The set of inequalities is
2x + 2 <46 2x - 27 > 11
The solution is x < 22 and x > 19, which is:
19 < x < 22 <----- answer
Part B: Can the wind speed in this town be 20 km/h? Justify
your answer by solving the inequalities in Part A. (3 points)
Yes, the wind speed can be 20 km/h, because the solution of the inequality is the range (19,22).
Part C:
The average wind speed in another town is 23 km/h, but the actual wind
speed is within 4 km/h of the average. Write and solve an inequality to
find the range of wind speed in this town.
If the x-6 is all under the sqrt, the last answer is right:
6<= x <= infinity
If only x is under the sqrt and - 6 is NOT under the sqrt, then:
0 <= x <= infinity is the correct answer.
Step-by-step explanation:
You can look at the equation and or graph to determine the domain of a function. The domain is all the x's that may go into the equation or all the x's on the graph of the function. Inside of a squareroot symbol the number inside there must be positive. While considering the equation, only x's that keep that inside positive can be used.
