Answer:
56 cm
Step-by-step explanation:
We need ro find the GCD of these numbers. In finding the GCD, we list the multiples of the number, beginning with the smallest number. Here, the
The factors of 616=2*2*2*7*11
The factors of 448 =2*2*2*2*2*2*7
Common factors in both are 2*2*2*7=56
Therefore, the greatest possible length is 56 cm
Answer: THE GRAPH IS ATTACHED.
Step-by-step explanation:
We know that the lines are:

Solving for "y" from the first line, we get:

In order to graph them, we can find the x-intercepts and the y-intercepts.
For the line
the x-intercepts is:

And the y-intercept is:

For the line
the x-intercepts is:

And the y-intercept is:

Now we can graph both lines, as you can observe in the image attached (The symbols
and
indicates that the lines must be dashed).
By definition, the solution is the intersection region of all the solutions in the system of inequalities.
Complete Question:
On a number line, the coordinates of X, Y, Z, and W are −8, −5, 4, and 6, respectively. Find the lengths of the two segments below. Then tell whether they are congruent.
and 
Answer:


They are not congruent
Step-by-step explanation:
Length of segment XY:
Coordinate of X = -8
Coordinate of Y = -5
= |-8 -(-5)| = |-8 + 5| = 3
Length of ZW:
Coordinate of Z = 4
Coordinate of W = 6
= |4 - 6| = 2
≠
, therefore, they are not congruent.
The system of inequalities would be:
L+M >= 500 (greater than or equal to)
2L + 0.5M <= 850 (less than or equal to)
The first inequality deals with the total number of balloons. She wants the total to be at least 500, so add the variables and set it greater than or equal to 500.
The second inequality deals with the helium. 2L comes from each latex balloon using 2 ft^3 of helium. 0.5M comes from each Mylar balloon using 0.5 ft^3. Together they can use no more than 85% of the 1000 ft^3 tank; 85% = 0.85; 0.85×1000=850. "No more than" tells us it must be less than or equal to.