If x=1 and y=2, what is the value of the expression 2x^2-3xy

How many 5-member chess teams can be chosen from 15 interested players? Consider only the members selected, not their board posi

ryzh [129]

Answer:

3003 number of 5-member chess teams can be chosen from 15 interested players.

Step-by-step explanation:

Given:

Number of the interested players = 15

To Find:

Number of 5-member chess teams that can be chosen = ?

Solution:

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula $nCr = \frac{n!}{r!(n - r)!}$

where

n represents the total number of items,

r represents the number of items being chosen at a time.

Now we have n = 15 and r = 5

Substituting the values,

$15C_5 = \frac{15!}{5!(15- 5)!}$

$15C_5 = \frac{15!}{5!(10)!}$

$15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 }{5 \times 4 \times 3 \times 2 \times 1(10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)}$

$15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11}{(5 \times 4 \times 3 \times 2 \times 1)}$

$15C_5 = \frac{360360}{120}$

$15C_5 = 3003$

7 0

3 years ago

Evaluate :11/3 + -3/7 + -4/9

solmaris [256]

Answer:

3.67+(-0.43)+(-0.44)

3.67-0.43-0.44

3.24-0.44

2.8 Ans

8 0

2 years ago

Four friends are planning to play 18 holes of golf. two of them need to rent clubs at $5 per set. total cart rental is $10. the

natka813 [3]

B how much did the friends pay in green fees

4 0

3 years ago

2. Factor f(x) = x4 + 10x3 + 35x2 + 50x + 24 completely showing all work and steps with synthetic division. Then sketch the grap

Ira Lisetskai [31]

Solution: The factor form of the given polynomial is $f(x)=(x+4)(x+3)(x+2)(x+1)$ .

Explanation:

To find the factor form of the given polynomial fisrt find the random value of x for which the vlaue of f(x) is 0.

The value of the function f(x) is 0 for $x=-1$ , therefore $(x+1)$ is a factor of given function.

Use synthetic method to divide the given polynomial for by $(x+1)$ . Write coefficients of polynomial in top line and -1 on left side of the line. Write first element in bottom line then multiply it by -1 and write it in second line below the element second element and the add. The division by synthetic method is given in figure 1.

The bottom line shows the coefficients of the quotient polynomial.

So $f(x)=(x+1)(x^3+9x^2+26x+24)$

Similarly $(x+2)$ is the factor of given polynomial because for x=-2 the value of parenthesis polynomial is 0.

Use synthetic method to divide the parenthesis polynomial for by $(x+2)$ . it is shown in figure 2.

So

$f(x)=(x+1)(x+2)(x^2+7x+12)\\f(x)=(x+1)(x+2)(x^2+3x+4x+12)\\f(x)=(x+1)(x+2)(x(x+3)+4(x+3))\\f(x)=(x+1)(x+2)(x+3)(x+4)$

Hence the factor form of the given polynomial is $f(x)=(x+4)(x+3)(x+2)(x+1)$ . The graph of the given function is given in figure 3.

4 0

3 years ago

Write a quadratic equation with the solutions x=-5+sqrt 13/2 , -5-sqrt 13 /2 HELP please

QveST [7]

Answer:

If we used the quadratic formula to solve the equation we can say:

-b = -5

b² - 4ac = 13

2a = 2

Solving the first and last equations we get b = 5 and a = 1. Substituting these values into the second equation we get:

25 - 4c = 13

Solving this we get c = 3 so the answer is x² + 5x + 3.

4 0

3 years ago