Answer:
A complete graph is a graph in which each pair of graph vertices is connected by an edge. The complete graph with graph vertices is denoted and has (the triangular numbers) undirected edges, where is a binomial coefficient. In older literature, complete graphs are sometimes called universal graphs.
Step-by-step explanation:
Answer:
1.Solve the system of equations.
y = 2x^2 - 3
y = 3x - 1
a. no solution
b. (-1/2, 5), (2, -5/2)
c. (-1/2, -5/2), (2,5)
d. (1/2, 5/2), (2, 5)
2.how many real number solutions does the equation have 0 = -3x^2 + x - 4
a. 0
b. 1
c. 2
d. 3
3. solve the equation by completing the square. If necessary round to the nearest hundredth.
x^2 - 18x = 19
a. 1; 19
b. -1; 19
c. 3; 6
d. -3; 1
4. solve. x^2 - 81 = 0
a. 0
b. -9
c. -9, 9
d. 9
5. which model is most appropriate for the data shown in the graph below? (need wedsite to know the problem)
a. quadratic
Answer:
Step-by-step explanation:
Given,
Cost price of three thermos flask = 1080
Selling price of each thermos flask = 400
<u>Finding </u><u>the </u><u>selling </u><u>price </u><u>of </u><u>three </u><u>thermos </u><u>flask</u>
Since, the cost of 3 thermos flask is more than that of 1 thermos flask. So, the cost of 1 thermos flask is multiplied by 3 ( i.e 400 × 3 = 1200 )
Here, the selling price is greater than cost price.
So, there is profit.
And we know that,
⇒
⇒
Profit amount = 120
<u>Finding </u><u>the </u><u>profit </u><u>percentage</u>
⇒
⇒
Hope I helped!
Best regards!!
Answer:
Step-by-step explanation:
This is a third degree polynomial because we are given three roots to multiply together to get it. Even though we only see "2 + i" the conjugate rule tells us that 2 - i MUST also be a root. Thus, the 3 roots are x = -4, x = 2 + i, x = 2 - i.
Setting those up as factors looks like this (keep in mind that the standard form for the imaginary unit in factor form is ALWAYS "x -"):
If x = -4, then the factor is (x + 4)
If x = 2 + i, then the factor is (x - (2 + i)) which simplifies to (x - 2 - i)
If x = 2 - i, then the factor is (x - (2 - i)) which simplifies to (x - 2 + i)
Now we can FOIL all three of those together, starting with the 2 imaginary factors first (it's just easier that way!):
(x - 2 - i)(x - 2 + i) =
Combining like terms and canceling out the things that cancel out leaves us with:
Remembr that , so we can rewrite that as
and
That's the product of the 2 imaginary factors. Now we need to FOIL in the real factor:
That product is
which simplifies down to
And there you go!
Question:
Which statement is true about the polynomial
–3x4y3 + 8xy5 – 3 + 18x3y4 – 3xy5 after it has been fully simplified?
It has 3 terms and a degree of 5.
It has 3 terms and a degree of 7.
It has 4 terms and a degree of 5.
It has 4 terms and a degree of 7.
Answer:
Option D: It has 4 terms and a degree of 7.
Explanation:
The given polynomial is
We need to simplify the polynomial to determine the number of terms and the degree of the polynomial.
Hence, the simplified polynomial is given by
Term of a polynomial:
The term of a polynomial consists of a number multiplied by a variable or it may be a constant.
Thus, the simplified polynomial has 4 terms.
Degree of a polynomial:
The degree of a polynomial is the sum of exponents of the variables in a term.
Thus, the simplified polynomial has a degree of 7.
Hence, the polynomial has 4 terms and a degree of 7.
Therefore, Option D is the correct answer.