Find two consecutive even integers whose product is 120

Mathematics

1 answer:

ipn [44]3 years ago

8 0

Answer:

10 and 12 are two even integers whose product =120

Step-by-step explanation:

10 and 12 are two even integers whose product =120

$10\times 12=120$

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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,

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

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

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

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

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

$15C_5 = 3003$

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Y=3x+13 2x=y-9 Solve for x and y points using addition method

GrogVix [38]

$y=3x+13 \\
2x=y-9 \ \ \ |-y-2x \\ \\
y=3x+13 \\
\underline{-y=-2x-9} \ \ \ \hbox{add the sides} \\
y-y=3x-2x+13-9 \\
0=x+4 \\
x=-4 \\ \\
y=3x+13=3 \times (-4)+13=-12+13=1 \\ \\
\boxed{(x,y)=(-4,1)}$