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3 years ago

A^2-b^2=(a+b)(a-b) label perfect square trinomial or difference two square

Mathematics

1 answer:

sleet_krkn [62]3 years ago

4 0

Answer:

difference of squares

Step-by-step explanation:

a^2 - b^2 = (a-b)(a+b)

This is the definition of the difference of squares

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How many solutions does the following system have? 2x+3y=1; -3x-2y=-1

zysi [14]

Answer:

x = 1/5 , y = 1/5

Step-by-step explanation:

Solve the following system:

{2 x + 3 y = 1 | (equation 1)

-3 x - 2 y = -1 | (equation 2)

Swap equation 1 with equation 2:

{-(3 x) - 2 y = -1 | (equation 1)

2 x + 3 y = 1 | (equation 2)

Add 2/3 × (equation 1) to equation 2:

{-(3 x) - 2 y = -1 | (equation 1)

0 x+(5 y)/3 = 1/3 | (equation 2)

Multiply equation 1 by -1:

{3 x + 2 y = 1 | (equation 1)

0 x+(5 y)/3 = 1/3 | (equation 2)

Multiply equation 2 by 3:

{3 x + 2 y = 1 | (equation 1)

0 x+5 y = 1 | (equation 2)

Divide equation 2 by 5:

{3 x + 2 y = 1 | (equation 1)

0 x+y = 1/5 | (equation 2)

Subtract 2 × (equation 2) from equation 1:

{3 x+0 y = 3/5 | (equation 1)

0 x+y = 1/5 | (equation 2)

Divide equation 1 by 3:

{x+0 y = 1/5 | (equation 1)

0 x+y = 1/5 | (equation 2)

Collect results:

Answer: {x = 1/5 , y = 1/5

8 0

3 years ago

40 POINTS, please help

Elis [28]

First, we must understand what standard form of a line is. Standard form of a line is written like such that A,B, and C are all integers, and A must be positive. First, we must calculate the slope of the line that passes through theses coordinates.

As a refresher, this is the equation to figure out the slope of two coordinates.Now, we just simplify the numerator and denominator.

The next step is to utilize point-slope form, which is where is a point on the line. Of course, we already know that (7,-3) and (4,-8) both lie of the line. Therefore, plug in one fot he coordinates. Once converted into point-slope, we must then convert into standard form. This is what is demonstrated in the next step.

Let's multiply all sides by 3 to get rid of the fraction early.Distribute the 5 to both terms in the parentheses.Subtract 9 from both sides.Subtract 5x on both sides.We aren't done yet! The coefficient of the x-term must be positive. Therefore, divide by -1 on both sides.This is standard form now, so we are done!

8 0

3 years ago

Five cards are drawn from a standard 52-card playing deck. A gambler has been dealt five cards—two aces, one king, one 3, and on

Nookie1986 [14]

Answer:

The probability that he ends up with a full house is 0.0083.

Step-by-step explanation:

We are given that a gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards.

We have to find the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind).

We know that gambler will end up with a full house in two different ways (knowing that he has given two more cards);

If he is given with two kings.
If he is given one king and one ace.

Only in these two situations, he will end up with a full house.

Now, there are three kings and two aces left which means at the time of drawing cards from the deck, the available cards will be 47.

So, the ways in which we can draw two kings from available three kings is given by = $\frac{^{3}C_2 }{^{47}C_2}$ {∵ one king is already there}

= $\frac{3!}{2! \times 1!}\times \frac{2! \times 45!}{47!}$ {∵ $^{n}C_r = \frac{n!}{r! \times (n-r)!}$ }

= $\frac{3}{1081}$ = 0.0028

Similarly, the ways in which one king and one ace can be drawn from available 3 kings and 2 aces is given by = $\frac{^{3}C_1 \times ^{2}C_1 }{^{47}C_2}$