Answer:A vertex (or node) of a graph is one of the objects that are connected together. The connections between the vertices are called edges or links. A graph with 10 vertices (or nodes) and 11 edges (links).
Step-by-step explanation: (The vertex formula is derived from the completing-the-square process, just as is the Quadratic Formula. In each case, memorization is probably simpler than completing the square.) For a given quadratic y = ax2 + bx + c, the vertex (h, k) is found by computing h = –b/2a, and then evaluating y at h to find k.
The double implication "if and only if" is graphically represented by an arrow pointing in both direction, so the correct writing is
Answer:
Approximately 3 grams left.
Step-by-step explanation:
We will utilize the standard form of an exponential function, given by:
In the case of half-life, our rate <em>r</em> will be 1/2. This is because 1/2 or 50% will be left after <em>t </em>half-lives.
Our initial amount <em>a </em>is 185 grams.
So, by substitution, we have:
Where <em>f(t)</em> denotes the amount of grams left after <em>t</em> half-lives.
We want to find the amount left after 6 half-lives. Therefore, <em>t </em>= 6. Then using our function, we acquire:
Evaluate:
So, after six half-lives, there will be approximately 3 grams left.
Answer:
one solution
Step-by-step explanation:
* Lets start to solve the question
- The 1st equation x - y = -4
- The 2nd equation 3x + y = 8
- We will use the elimination method to solve this system of equation
∵ x - y = -4 ⇒ (1)
∵ 3x + y = 8 ⇒ (2)
- Add the two equation (1) and (2) to eliminate y
∴ x + 3x = -4 + 8
∴ 4x = 4
- Divide both sides by 4
∴ x = 1
- Substitute the value of x in equation (1) or equation (2) to find
the value of y
- We will use equation (1)
∴ 1 - y = -4
Subtract 1 from both sides
∴ -y = -5
- Divide both sides by -1
∴ y = 5
∴ The solution is (1 , 5)
* The system has one solution
Answer:
-27
Step-by-step explanation:
substitute x for 5
multiply -5 and 5
subtract 2 from -25
