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3 years ago

State the postulate or theorem that proves that x is parallel to y

Mathematics

1 answer:

Schach [20]3 years ago

3 0

Converse of the alternate interior angles theorem states the postulate or theorem that proves that x is parallel to y.

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Exercise 2.4.2: Proving statements about rational numbers with direct proofs. About Prove each of the following statements using

IgorLugansk [536]

Answer:

See Explanation

Step-by-step explanation:

(a) Proof: Product of two rational numbers

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The product:

$A * B = \frac{1}{2} * \frac{2}{3}$

$A * B = \frac{1}{1} * \frac{1}{3}$

$A * B = 1 * \frac{1}{3}$

$A * B = \frac{1}{3}$

Proved, because 1/3 is rational

(b) Proof: Quotient of a rational number and a non-zero rational number

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The quotient:

$A / B = \frac{1}{2} / \frac{2}{3}$

Express as product

$A / B = \frac{1}{2} / \frac{3}{2}$

$A / B = \frac{1*3}{2*2}$

$A / B = \frac{3}{4}$

Proved, because 3/4 is rational

(c) x + y is rational (missing from the question)

Using direct proofs.

Let x and y be

Such that:

$x = \frac{1}{2}$

$y = \frac{2}{3}$

The sum:

$x + y = \frac{1}{2} + \frac{2}{3}$

Take LCM

$x + y = \frac{3+4}{6}$

$x + y = \frac{7}{6}$

Proved, because 7/6 is rational

The above proof works for all values of A, B, x and y; as long as they are rational values

8 0

3 years ago

It is a 375-mile drive from San Francisco to Los Angeles. A map scale shows 2 centimeters equaling 10 actual miles. How long is

Arte-miy333 [17]

18.75 centimeters because it’s 37.5 divided by 2

6 0

3 years ago

Two numbers multiply to be -7 and add to be -6. What are the numbers? Example; 2,3

rewona [7]

Given:

Let the two numbers be x and y.

Two numbers multiply to be -7 and add to be -6.

This can be written in equation as,

$xy=-7$ and

$x+y=-6$

Value of the two numbers:

Let us determine the value of the two numbers using substitution method.

Substituting $y=-6-x$ in the equation $xy=-7$ , we get;

$x(-6-x)=-7$

Simplifying, we get;

$-6x-x^2=-7$

$x^2+6x-7=0$

$(x+7)(x-1)=0$

$x=-7, 1$

Thus, the values of x are x = 1,-7

When x = 1 , the equation $x+y=-6$ becomes $y=-7$

When x = -7, the equation $x+y=-6$ becomes $y=1$

Therefore, the two numbers are 1 and -7

3 0

3 years ago

Two ways to write a algebraic expression of n-5

deff fn [24]

-5 + n is another way to write the expression.

5 0

3 years ago

Read 2 more answers

A human body that is performing light work generates about 650 BTUs of body heat per hour. If a storage room that is 20 ft × 25

Damm [24]

in case your wodering its 2.1 BTUs/ft^3

6 0

3 years ago