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3 years ago

Use the substitution method to solve the system of equations. Choose the correct ordered pair.

Mathematics

2 answers:

daser333 [38]3 years ago

6 0

Answer:

Ordered pair (x,y) is (6,2)

Step-by-step explanation:

Use the substitution method to solve the system of equations.

$2x + 2y = 16$ -----> first equation

$y=x-4$ -------> second equation

Divide the first equation by 2

$2x + 2y = 16$ -----> first equation

$x+y=8$

Now solve for y, subtract x from both sides

$y=-x+4$

Now plug in -x+8 for y in second equation

$y=x-4$ -------> second equation

$-x+8=x-4$

Subtract x from both sides

$-2x+8=-4$

Subtract 8 on both sides

$-2x=-12$

Divide both sides by -2

x=6

now we plug in 6 for x in second equation

$y=x-4$ -------> second equation

$y=6-4$

y=2

Ordered pair (x,y) is (6,2)

goldenfox [79]3 years ago

4 0

Correct one is A(6,2)

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Rudiy27

Looking at this problem in terms of geometry makes it easier than trying to think of it algebraically.

If you want the largest possible x+y, it's equivalent to finding a rectangle with width x and length y that has the largest perimeter.

If you want the smallest possible x+y, it's equivalent to finding the rectangle with the smallest perimeter.

However, the area x*y must be constant and = 100.

We know that a square has the smallest perimeter to area ratio. This means that the smallest perimeter rectangle with area 100 is a square with side length 10. For this square, x+y = 20.

We also know that the further the rectangle stretches, the larger its perimeter to area ratio becomes. This means that a rectangle with side lengths 100 and 1 with an area of 100 has the largest perimeter. For this rectangle, x+y = 101.

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4 years ago

Solve x^2 + 2 + 9 = 0

Serga [27]

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4 years ago

You know how to play 21 songs on your guitar. (a) If you want to choose 8 of the songs to make a setlist to play for a small gat

UNO [17]

Answer:

(a) 8,204,716,800

(b) 5,985

Step-by-step explanation:

Combinations and Permutations

Combinatorics is the part of the discrete mathematics that studies the enumeration of groups or sorting of a determined number of elements. The concept of combinations is tied to the different forms to group elements where the order of their arrangements is not important or does not differentiate from the very same set of elements picked in a different order.

The concept of combinations is tied to the differents forms to group elements where the order of their arrangements is not important or does not differentiate from the very same set of elements picked in different order.

On the other hand, permutations or variations are sets selected in a specific order and another set with the same element but in different order is considered a different set.

If we have n elements available to pick from in sets of m elements each, there can be C(n,m) different combinations, and it's given by

$\displaystyle C(n,m)=\frac{n!}{m!(n-m)!}$

Similarly the number of permutations is given by

$\displaystyle P(n,m)=\frac{n!}{(n-m)!}$

(a) I have n=21 songs to pick from and I want to choose m=8 of them where the order matters, so it's a permutation:

$\displaystyle P(21,8)=\frac{21!}{(13)!}=\frac{51,090,942,171,709,440,000}{6,227,020,800}=8,204,716,800$

I can make more than 8 billion different setlists

(b) To choose m=4 songs from n=21 songs where the order does not matter, we compute the combination

$\displaystyle C(21,4)=\frac{21!}{4!(17)!}=\frac{21\cdot 20\cdot 19\cdot 18\cdot 17!}{4\cdot 3\cdot 2\cdot 1(17)!}$

$\displaystyle C(21,4)=\frac{143,640}{24}=5,985$

I can make almost 6,000 sets of 4 songs

5 0

3 years ago