Answer:
numbers are 24 and 210
Step-by-step explanation:
the number are : 24(2x2x2x3) and 210 (3x2x5x7)
GCF of 24 and 210 is 6
LCM of 24 and 210 is 840
6(2m - 1) - 4(m + 8)
We can use the distributive property here.
12m - 6 - 4m - 32
Simplify.
<h3><u>8m - 38 is the simplified form of the original expression. </u></h3>
Answer:

![x\in [5.55,6.45]](https://tex.z-dn.net/?f=x%5Cin%20%5B5.55%2C6.45%5D)
Step-by-step explanation:
<u>Absolute Value Inequality</u>
Assume the actual width of a safety belt strap for a certain automobile is x. We know the ideal width of the strap is 6 cm. This means the variation from the ideal width is x-6.
Note if x is less than 6, then the variation is negative. We usually don't care about the sign of the variation, just the number. That is why we need to use the absolute value function.
The variation (unsigned) from the ideal width is:

The question requires that the variation is at most 0.45 cm. That poses the inequality:

That is the range of acceptable widths. Let's now solve the inequality.
To solve an inequality for an absolute value less than a positive number N, we write:

This is a double inequality than can be easily solved by adding 6 to all the sides.

Operating:

That is the solution in inequality form. Expressing in interval form:
![\boxed{x\in [5.55,6.45]}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%5Cin%20%5B5.55%2C6.45%5D%7D)
Answer:
a = 2.5
b = 4.33
Step-by-step explanation:
a = sin(30 degrees) = o/5 = 2.5
b = cos(30 degrees) = a/5 = (5root3) / 2 or about 4.33
verify using Pythagorean theorem
2.5^2 + 4.33^2 = 5^2
6.25 + 18.75 = 25
25 = 25
Answer:

Step-by-step explanation:
Distance Formula: 
Simply plug in your 2 coordinates into the distance formula to find distance <em>d</em>:



