Answer:
Only option B is correct, i.e. all real values of x except x = 2.
Step-by-step explanation:
Given the functions are C(x) = 5/(x-2) and D(x) = (x+3)
Finding (C·D)(x) :-
(C·D)(x) = C(x) * D(x)
(C·D)(x) = 5/(x-2) * (x+3)
(C·D)(x) = 5(x+3) / (x-2)
(C·D)(x) = (5x+15) / (x-2)
Let y(x) = (C·D)(x) = (5x+15) / (x-2)
According to definition of functions, the rational functions are defined for all Real values except the one at which denominator is zero.
It means domain will be all Real values except (x-2)≠0 or x≠2.
Hence, only option B is correct, i.e. all real values of x except x = 2.
He should boil 12.5 gallons of water for 5 cups of oats.
4. To determine if a triangle is a right triangle, given that you know the length of its sides, you have to check if its lengths follow the Pythagorean theorem.
This theorem states that the square of the hypothenuse (c) is equal to the sum of the squares of the legs of the triangle (a and b), following the expression:

The triangle is:
We have to check that a²+ b² is equal to c².
The square of the hypothenuse is:

The sum of the squares of the legs of the triangle is:

As you can see, the sum of the squares of the legs of the triangle is 100, which is the same as the square of the hypothenuse. The triangle follows the Pythagorean theorem and can be considered a right triangle.
Both triangle are isosceles, which means their base angles are congruent.
54 + 2y = 180
2y = 126
y = 63
The measure of the base angles of the triangle on the left is 63 degrees.
180 - 63 = 117
117 + 2x = 180
2x = 63
x = 31.5
Answer:
x = 31.5
Hope this helps.