Answer:
- none
- none
- x ≥ 4
Step-by-step explanation:
The restrictions placed on the independent variable in a function are those necessary to ensure that the function is defined for all allowed values of that variable.
In the graphs of problems 1) and 2), we see that the functions are defined for all values of x, so there are no restrictions.
__
3. For the function ...
the value under the radical cannot be negative. The square root function is not defined for negative values, so the restriction is ...
x -4 ≥ 0
x ≥ 4 . . . . . . . add 4 to both sides of the inequality
Answer:
2x - 3
x - 9
Step-by-step explanation:
The root of a problem is the x value that makes the equation equal to zero.
If the factored form of the equation is (2x-3)(x-9) that means if either 2x - 3 or x - 9 is equal to zero, the entire equation will equal zero, because zero times any number is equal to zero.
Therefore you must solve for (2x-3)=0 and (x-9)=0
Answer:
Altitude
Step-by-step explanation:
An altitude of the triangle is the line segment from a vertex to the opposite side and perpendicular to the opposite side. The orthocenter will not always be inside the triangle. This is why the orthocenter is the point of concurrency of the lines containing the altitudes rather than just the altitudes.
Answer:
∠A = ∠B = 80°
Step-by-step explanation:
The angles are corresponding angles where a transversal crosses parallel lines, so are congruent. That means ...
∠A = ∠B
8x -8° = 5x +25° . . . . . substitute the given expressions
3x = 33° . . . . . . . . . . . . add 8°-5x
x = 11° . . . . . . . . . . . . . . divide by 3
Then the angles are ...
8·11° -8° = 80°
