1. Integers numbers are defined as the set of numbers that is formed by Positive numbers, which are also called "Natural numbers"; Negative numbers (They are less than zero) and zero (This has no sign). This set is represented with the letter "Z". Therefore: Z={...-2, -1, 0, 1, 2 ...}.
2. So, if 12 is added to the square of a positive integer, you can write the following the expression:
12+x²=133
3. You can obtain the value of the positive integer "x", by clearing it. Then, you have:
12+x²=133
x²=133-12
x=√(133-12)
x=√121
x=11
Therefore, the positive integer is: 11
Distributive property
12-3x-13 = 0
Combine like terms
-1-3x = 0
-3x = 1
Divide by -3
x = -1/3
<span>Let's use the quadratic formula:
2w² -</span><span><span> 20w </span>+ 50 = 0</span>
a = 2 b = -20 c = 50
x = -b +-sq root(b^2 - 4*a*c) / 2*a
x = --20 +-sq root(400 -4*2*50) / 4
x = 20 +-sq root(400 -4*2*50) / 4
x = 20 +-sq root( 0) / 4
x = 20 / 4 =5
I'd say it has one rational solution.
It does NOT have 2 solutions because the "plus / minus" section = 0.
<h3>Answer: 8 people</h3>
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Work Shown:
x = number of people
y = cost per person
The cost per person varies inversely with the number of people, so y = k/x for some fixed number k.
"It costs $90 each for five people", meaning that x = 5 and y = 90 pair up. Plug these values in and solve for k.
y = k/x
90 = k/5
90*5 = k
450 = k
k = 450
Therefore the equation updates to y = 450/x
Now we want to know how many passengers there are (x) when the cost per person is y = 56.25
Let's find out:
y = 450/x
56.25 = 450/x ... replace y with 56.25
56.25x = 450
x = 450/56.25
x = 8
If you have 8 people, then it costs $56.25 per person.
side note: the total cost is $450 which is the value of k we found earlier. Divide 450 over 8 and you should get 56.25 exactly. Optionally you can turn y = k/x into x*y = k form. So the equation y = 450/x is the same as x*y = 450.