A number
, where
are distinct prime numbers, has
divisors.
We know that
has 7 divisors. 7 is a prime number, so among the numbers
there is only one that is equal to 7.
So,
That means
where
is a prime number.
, therefore the
has
divisors.
Answer:
(4,4)
Step-by-step explanation:
There are two ways that you can solve this. You can solve it with the help of technology or you can solve it traditionally. I will show how to do it in both ways so you can pick which way you want to solve it.
<em>Traditional Method:</em>
5x - 2y = 12
6x + 2y = 32
Look at the variables and numbers in both equations. One of them has to be the same value but have to have opposite signs. The 2y in both equations are the same value but have different signs. That's what we want. We can add everything in the equation now. (5x + 6x), (-2y + 2y), and (12 + 32).
11x = 44
To get x alone, Divide each side by 11. Then we will get the value of x.
11/11x = 44/11
x = 4
Horray! We got x, but what about y? Pick one of the equations. I will go with 5x - 2y = 12. Substitute the x value inside the equation.
5(4) - 2y = 12
20 - 2y = 12
-2y = -8
y = 4
Good! We figured out y. Now we know the solution! The solution is (4,4).
<em>Technology Method:</em>
Grab a graphing calculator. Enter the equations. You will see two lines. Look at where they intersect. The point where they intersect is the solution. That line is (4,4). You could also do this on a piece of paper by graphing the equations.
I hope this helps! Let me know if you need any more help or if I got anything wrong.
Answer:
a) 6 gigabytes
b) $100
Step-by-step explanation:
Let c represent the total cost in dollars and d represent the amount of data used in gigabytes.
For the first smartphone
One smartphone plan costs $52 per month for talk and messaging and $8 per gigabyte of data used each month.
Equation =
c = 52 + 8d
For the Second smartphone
A second smartphone plan costs $82 per month for talk and messaging and $3 per gigabyte of data used each month.
Equation =>
c = 82 + 3d
How many gigabytes would have to be used for the plans to cost the same?
We would equate both cost to each other
52 + 8d = 82 + 3d
Collect like terms
8d - 3d = 82 - 52
5d = 30
d = 30/5
d = 6
Therefore,
a) The number of gigabytes for the cost of both Smartphone data plans to be the same = 6 gigabytes.
b) The cost of both plans if 6 gigabytes is used =>
c = 52 + 8d
c = 52 + 8 × 6
c = $100
<span>Two sides of a triangle have lengths a = 10 and b = 15
c < a+b and c > |a - b|
</span><span>A) less than 25 </span>
Answer:
The domain of exponential functions is all real numbers. The range is all real numbers greater than zero. The line y = 0 is a horizontal asymptote for all exponential functions. When a > 1: as x increases, the exponential function increases, and as x decreases, the function decreases.
