Answer:
Equation of the line in question: 
.
Step-by-step explanation:
Start by finding the intersection of the two straight lines. The equation for both lines shall hold at their intersection. (Using the idea of the Gaussian Elimination.)
.
Add -3 times the first equation to the second:
.
Add the second equation 
to the first:
.
Hence the intersection of the two lines will be 
.
Now, find the slope of that straight line. 
is equivalent to 
. The slope of that line is equal to 1. So will be the slope of the line in question.
Apply the point-slope form of a line on a Cartesian plane:
- Point: ,
- Slope:
.
Equation of the line:
.
Simplify to obtain:
.
Answer
Find out the original side length of the square .
To prove
Let us assume that the original length of the square be x.
Formula
As given
The dimensions of a square are altered so that 8 inches is added to one side while 3 inches is subtracted from the other.
Length becomes = x + 8
Breadth becomes = x -3
The area of the resulting rectangle is 126 in²
Put in the formula
(x + 8) × (x - 3) = 126
x² -3x + 8x -24 = 126
x ²+ 5x = 126 +24
x² + 5x - 150 = 0
x² + 15x - 10x - 150 = 0
x (x + 15) -10 (x +15) =0
(x + 15)(x -10) =0
Thus
x = -15 , 10
As x = -15 (Neglected this value because the side of the square cannot be negative.)
Therefore x = 10 inches be the original side of the square.
Answer:
The probability that none of the 10 calls result in a reservation is 0.60%. In turn, the probability that at least one call results in a reservation being made is 99.40%.
Step-by-step explanation:
Since approximately 40% of the calls to an airline reservation phone line result in a reservation being made, supposing an operator handles 10 calls, to determine what is the probability that none of the 10 calls result in a reservation, and what is the probability that at least one call results in a reservation being made, the following calculations must be performed:
0.6 ^ 10 = X
0.006 = X
0.006 x 100 = 0.60%
Therefore, the probability that none of the 10 calls result in a reservation is 0.60%.
100 - 0.60 = 99.40
In turn, the probability that at least one call results in a reservation being made is 99.40%.
Answer:
294 or 6
Step-by-step explanation:
if he has 7 bags and 42 marbles in each then the answer will be 294
but if ur tryna say that there are a total of 42 marbles combined, then there are 6 marbles in each bag
