Answer:
Number of small boxes shipped = 7
Number of large boxes shipped = 15
Step-by-step explanation:
Let the number of small boxes = s
And the number of large boxes = l
Weight of small box = 25 pound
Weight of the large box = 50 pounds
Total weight of the shipment = 925 pounds
Therefore, equation for the weight of shipment will be,
25s + 50l = 925
s + 2l = 37 ----- (1)
Total number of boxes shipped = 22 boxes
Therefore, equation will be,
s + l = 22 ------(2)
Subtract equation (2) from equation (1)
(s + 2l) - (s + l) = 37 -22
l = 15
From equation (2)
s + 15 = 22
s = 7
Therefore, number of small boxes shipped = 7
Number of large boxes shipped = 15
Answer:
The value of k is greater than or equal to 0, i.e. k≥7.
Step-by-step explanation:
The given equation is
The value of k must be a positive integer because k! is defined for k≥0, where k∈Z.
Subtract 48 from both the sides.
Using ![[\frac{r^m-1}{r-1}=r^{m-1}+r^{m-2}+...+1]](https://tex.z-dn.net/?f=%5B%5Cfrac%7Br%5Em-1%7D%7Br-1%7D%3Dr%5E%7Bm-1%7D%2Br%5E%7Bm-2%7D%2B...%2B1%5D)
, we get
Divide both sides by 48k.
Note: The value of m can be 0 or 1.
The value of k is positive integer, so the right hand side of the above equation must be a positive integer.
Since RHS of the equation is positive integer, therefore (k-1)! is completely divisible by 48.
Add 1 on both sides.
Therefore the value of k is greater than or equal to 0.
Answer:
x² + x - 12 = 0
Step-by-step explanation:
Given the solutions are x = - 4 and x = 3, then the factors are
(x + 4) and (x - 3) and the equation is the product of the factors, that is
(x + 4)(x - 3) = 0 ← expand factors using FOIL
x² + x - 12 = 0 ← in standard form
Set up the equation of two ratios:
3 racks 36 racks
----------- = --------------
15 min x
Solve this for x: 3x =540; x = 180 minutes, or 3 hours
It will be 20 cm I believe
Because AB is half of AC
if AB is 10 cm then the other half would be 10 cm
So just add those and you get 20cm
