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3 years ago

Given <1 and <2 are a linear pair, find the value of x if m<1 = 2x-5 and m<2 = 4x-7

Mathematics

1 answer:

Alecsey [184]3 years ago

5 0

Answer:

Step-by-step explanation:

Linear pair means they form a line, or add to 180°.

2x − 5 + 4x − 7 = 180

6x − 12 = 180

6x = 192

x = 32

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The equation for a circle is (x-2)2+(y+3)2=9, what is the center of the circle?

ki77a [65]

Answer:

(2, -3)

Step-by-step explanation:

Compare the given (x-2)2+(y+3)2=9 to the standard equation

(x - h)^2 + (y - k)^2 = r^2.

It becomes obvious that h = 2, k = -3 and r = 3.

The center of this circle is (h, k): (2, -3).

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3 years ago

Christina says the graph for the inequality r < -5 will be the same as the graph for the inequality -5 > r. Do you agree o

QveST [7]

Answer:

Agree

Step-by-step explanation:

Just copy and paste (without quotations): "I agree because r < -5 is just a flipped inequality of -5 > r. In other words, 'r is less than -5' is the same as '-5 is greater than r'."

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3 years ago

In a Match 6 Lotto, winning the jackpot requires that you select six different numbers from 1 to 49, and that the same six numbe

zimovet [89]

Answer:

$P=\frac{1}{13,983,816}=7.2\ x\ 10^{-8}$

Step-by-step explanation:

Consider the following characteristics of the problem:

The numbers that are selected are different between 1 and 49. This means that the same number is not repeated twice.

The order in which the selected numbers appear does not matter:

This means that (123) = (312)

With this in mind, we know that it is a problem of combinations without repetition. It is not calculated using permutations because in the permutations the order of selection is important, for example: (123) is not equal to (312)

The formula for calculating combinations without repetition is:

$nCr=\frac{n!}{r!(n-r)!}$

Where n is the number of "elements" you can choose and choose r from them

In this case:

n=49

r=6

So:

$49C6=\frac{49!}{6!(49-6)!}$

$49C6=13,983,816\ outcomes$

There are 13,983,816 possible results

This is the best method to calculate the number of possible outcomes.

<em><u>"Besides your method, is there another method to determine the number of outcomes?"</u></em>

Sure, make a list of the 13,983,816 different sets of 6 numbers.

To win it is necessary to obtain the 6 winning numbers in any order. The number of ways this can occur is calculated by combining 6 in 6

$6C6=\frac{6!}{6!(6-6)!}=1$

Finally the probability of winning is:

$P=\frac{1}{13,983,816}=7.2\ x\ 10^{-8}$

Note that the probability of winning is very close to 0. It is practically impossible to win the lottery, you will probably never win anything. Therefore it is better not to invest money in this

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