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Archy [21]
3 years ago
9

Why is the product of two rational numbers always rational? select from the drop-down menus to correctly complete the proof?

Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
6 0

Getting the product of two rationals is like multiplying two fractions, which will have another fraction of this alike form as the result because integers are sealed under multiplication. All rational number can be signified as q/r, with q and r are both integers. Another explanation is the product of two rational numbers is q/r * s/t, with q, r, s, and t are integers. Nonetheless, this is just (qs)/(rt), and qs and rt are both results of integers and hence integers themselves. The product of two rational numbers can be characterized as the quotient of two integers and is itself rational. Therefore, multiplying two rational numbers yields another rational number.

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Alborosie
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3 years ago
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Which is not an equation of the line going through (3, -6) and (1, 2)?
777dan777 [17]

Answer:

B, C

Step-by-step explanation:

The equation of a line can be given by y -y₁= m(x -x₁), where m is the slope. This is also known as the point-slope form.

\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }

Slope of the line

=  \frac{2 - ( - 6)}{1 - 3}

=  \frac{2 + 6}{ - 2}

= \frac{8}{ - 2}

= -4

<em>Substitute m= -4 into the equation:</em>

y -y₁= -4(x -x₁)

<em>Substitute a pair of coordinates into (x₁, y₁):</em>

Let's start by substituting (1, 2).

y -2= -4(x -1)

This gives us the same equation as D, making D an incorrect option. Note that the question asks for which is not the correct equation.

Let's change the above into the slope-intercept form, where by y is the subject of formula.

<em>Start by expanding the right-hand side:</em>

y -2= -4x +1

<em>+</em><em>2</em><em> on both sides:</em>

y= -4x +3

This equation is not the same as C. C is thus the correct option.

Let's check for options A and B.

The equation in option B is not the correct equation either as they have substituted (2, 1) instead of (1, 2) into (x₁, y₁). Thus, option B is also correct.

y -y₁= -4(x -x₁)

Substitute (3, -6) into (x₁, y₁):

y -(-6)= -4(x -3)

y +6= -4(x -3)

This is the same as option A, making option A incorrect too.

4 0
2 years ago
PLEASE HELP GUYS !!!
crimeas [40]

Answer:

y = -3/2x + 3

y = x + 1

y = 5/4x - 2

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