"The sum of two numbers is 20" can be translated mathematically into the equation:
x + y = 20.
"... and their difference is 10" can be translated mathematically as:
x - y = 10
We can now find the two unknown numbers, x and y, because we now have a system of two equations in two unknowns, x and y. We'll use the Addition-Subtraction Method, also know as the Elimination Method, to solve this system of equations for x and y by first eliminating one of the variables, y, by adding the second equation to the first equation to get a third equation in just one unknown, x, as follows:
Adding the two equations will eliminate the variable y:
x + y = 20
x - y = 10
-----------
2x + 0 = 30
2x = 30
(2x)/2 = 30/2
(2/2)x = 15
(1)x = 15
x = 15
Now, substitute x = 15 back into one of the two original equations. Let's use the equation showing the sum of x and y as follows (Note: We could have used the other equation instead):
x + y = 20
15 + y = 20
15 - 15 + y = 20 - 15
0 + y = 5
y = 5
CHECK:
In order for x = 15 and y = 5 to be the solution to our original system of two linear equations in two unknowns, x and y, this pair of numbers must satisfy BOTH equations as follows:
x + y = 20 x - y = 10
15 + 5 = 20 15 - 5 = 10
20 = 20 10 = 10
Therefore, x = 15 and y = 5 is indeed the solution to our original system of two linear equations in two unknowns, x and y, and the product of the two numbers x = 15 and y = 5 is:
xy = 15(5)
xy = 75
Answer:
<h2>b. -3</h2>
Step-by-step explanation:
The common difference in an arithmetic sequence:
27 - 30 = -3
24 - 27 = -3
21 - 24 = -3
18 - 21 = -3
CORRECT :)
It's constant.
Answer:
The new volume is 
.
Step-by-step explanation:
We are given with the volume of a gas varies inversely as the pressure upon it.
Initial volume is 160 cubic centimetres and initial pressure is 108 Pa. It is required to find the volume when the pressure is 87 centimetres.
According to given condition,
is new volume
So, the new volume is .
Step-by-step explanation:
for part a
initial means starting point and starting point is always 0
so the question means number of thousands of bacteria in 0 hours, your n being the number of hours. so in part a u will simply just put 0 as n in equation
2^(0+3)
2³=8 thousands of bacteria
in part b
2^(n+3) means total number of bacteria
2^(n-1) is number of groups
its asking for number of bacteria in each group
so u will simply divide number of bacteria by groups
its like u have 30 candies and there are 5 groups and they ask u to find number of candies in each group so u simply divide 30 by 5
so 2^(n+3)/2^(n-1)
base is same so powers will subtract since there is division sign
2^(n+3-(n-1))
2^(n+3-n+1)
2^(3+1)
2^4= 16 thousands of bacteria in each group
