Answer:
A general way of explaining this is
Suppose that we have a given property (or a pattern if we are working with a series of numbers):
Now, if that property is true, for example, for the numbers 1, 2, 3... etc. Then we can suppose that the property is also true for an unknown number N.
Now, if using the hypothesis that the property is true for N, we can prove that the property is also true for N + 1, then we actually proved that the property is true for all the set.
We actually can use any set, not only the natural numbers.
For example, we can use the set of the even numbers {2, 4, 6, 8....}, suppose that the property is true for a random number N, that is even, and then see if using that hypothesis we can prove that the property is also true for the next number in the set; N + 2.
Answer:
b
Step-by-step explanation:
The number of adults is 42.
The number of children is 196.
<u>Step-by-step explanation</u>:
- Adult admission = $13
- Child admission = $4
- Total people = 238
- The total bill amount = $1330
Let 'x' be the number of adults.
Let 'y' be the number of children.
The equations are,
x+y = 238 --------(1)
13x + 4y = 1330 ---------(2)
Multiply eq(1) by 4 and subtract eq(2) from eq(1)
4x+4y = 952
-(<u>13x+4y = 1330</u>)
<u>-9x = -378</u>
x = 378/9
x = 42
∴ The number of adults = 42
Substitute x=42 in eq(1)
42+y = 238
y = 238-42
y = 196
∴ The number of children = 196
The quadratic formula used to solve a quadratic of the form ax^2+bx+c is:
x=(-b±√(b^2-4ac))/(2a) so in this case:
x=(3±√(9+8))/4
x=(3±√17)/4