Area=LengthxWidth so 3/5=7/8xWidth. To get width by itself you must divide both sides by 7/8. When dividing fractions you can flip the fraction and multiply so multiply (3/5)(8/7). To do this just multiply the numerators and denominators to get 24/35 so width = 24/35
Y doesn't vary directly with x
[] signs mean that the number is included in the domain and () mean that the number is not included. Now,
1. [-1,5)
Because x is greater than or equal to -1 (included) but less than 5 (excluded
2. [-5,13)
When we plug in x = -1, we get the minimum value of -5, which is included because its x-value was included. The, we plug in x = 5 to find the range's maximum and this is excluded because its x-value was excluded.
3. 218
x = 6 lies in the domain of the first function so we will use it to evaluate the value of x = 6. We do this by simply substituting x into the function.
4. 12
x = 9 is included in the domain of the second function and the value of the second function at all points is 12.
5. 103
x = 10 is included in the domain of the second function so we will use it to evaluate the value of x = 10. This is done by substituting x into the equation.
The domain are all valid values for x (the independent variable) that can be used in an equation.
We have to look at any potential values of x which won't work. Easily put: in algebra, just look for values of x which cause either division by zero, or the square root of negative numbers.
A couple of examples:
y=2x+4
You can insert any negative or positive value, or zero, for x and get a valid equation. Therefore the domain is the set of all real numbers. Answers are usually written as:
x: {R}, or simply 'all real numbers'.
what about y=2/(x-1)
In this equation, x appears in the denominator. If x-1=0, then division by zero would occur.
Solve: x-1≠0
x≠1
In set notation:
x: (-∞,1)∪(1,∞)
Parentheses are next to the 1, as the domain comes up to 1, but does not include 1.
Read left to right, the domain is "negative infinity to 1, exclusive, in union with 1 to positive infinity"
