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enot [183]
3 years ago
14

In this diagram, which equation could you prove to be true in order to conclude that the lines are parallel?

Mathematics
2 answers:
yan [13]3 years ago
7 0

Answer: Hey, so the answer is the second choice, b/a=c/d. I just took the quiz, it's correct.

Y_Kistochka [10]3 years ago
6 0
<span>b/a=c/d Two lines are parallel to each other if they have the same slope. So let's look at the options and see which one matches that statement. b/aâ‹…c/d=â’1 * This is checking to see if the two lines are perpendicular to each other. Almost the exact opposite of parallel. So this is the wrong answer. b/a=c/d * b/a is a legitimate slope. c/d is also a good slope. And they're being checked to see if they're equal to each other. So this is the correct answer. But let's see if the next two options will give us a chuckle or two. b/a=d/c * b/a is OK. d/c almost looks ok, check the figure. And d/c is NOT a slope. The slope is delta Y over delta X. And d/c is delta X over delta Y. The inverse of the slope. So comparing those two values is meaningless. So it's a wrong answer. b/aâ‹…d/c=â’1 * And they're trying the inverse of the slope trick again. WRONG. And they're checking if it's perpendicular. Also wrong. So definitely not a good choice.</span>
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given examples of relations that have the following properties 1) relexive in some set A and symmetric but not transitive 2) equ
rodikova [14]

Answer: 1) R = {(a, a), (а,b), (b, a), (b, b), (с, с), (b, с), (с, b)}.

It is clearly not transitive since (a, b) ∈ R and (b, c) ∈ R whilst (a, c) ¢ R. On the other hand, it is reflexive since (x, x) ∈ R for all cases of x: x = a, x = b, and x = c. Likewise, it is symmetric since (а, b) ∈ R and (b, а) ∈ R and (b, с) ∈ R and (c, b) ∈ R.

2) Let S=Z and define R = {(x,y) |x and y have the same parity}

i.e., x and y are either both even or both odd.

The parity relation is an equivalence relation.

a. For any x ∈ Z, x has the same parity as itself, so (x,x) ∈ R.

b. If (x,y) ∈ R, x and y have the same parity, so (y,x) ∈ R.

c. If (x.y) ∈ R, and (y,z) ∈ R, then x and z have the same parity as y, so they have the same parity as each other (if y is odd, both x and z are odd; if y is even, both x and z are even), thus (x,z)∈ R.

3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial but not transitive, so the relation provided in (1) satisfies this condition.

Step-by-step explanation:

1) By definition,

a) R, a relation in a set X, is reflexive if and only if ∀x∈X, xRx ---> xRx.

That is, x works at the same place of x.

b) R is symmetric if and only if ∀x,y ∈ X, xRy ---> yRx

That is if x works at the same place y, then y works at the same place for x.

c) R is transitive if and only if ∀x,y,z ∈ X, xRy∧yRz ---> xRz

That is, if x works at the same place for y and y works at the same place for z, then x works at the same place for z.

2) An equivalence relation on a set S, is a relation on S which is reflexive, symmetric and transitive.

3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial and not transitive.

QED!

6 0
3 years ago
0.5 (2x + 2) = -4<br><br> Solve for x.
Ivanshal [37]

0.5(2x+2)=-4

Multiply by 2 on both sides

2x+2=-8

Subtract 2 on both sides

2x=-10

Divide by 2 on both sides

x=-5

3 0
2 years ago
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9(v+2)
When you factor you are essentially dividing by 9 when you take it out and add parenthesis
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2 years ago
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Graph points A(-1, -1), B(-1, 3) and C(3, 2) on the coordinate plane. What is the area of triangle ABC? A) 7 square units B) 8 s
Ray Of Light [21]

Answer:

8 square units is the answer

6 0
3 years ago
Which function below is the inverse of f(x) = The quantity of four x minus three, over two.?
Genrish500 [490]
y = \frac{4x-3}{2}  \\ 2y=4x-3 \\ 4x=2y+3 \\ x= \frac{2y+3}{4}  \\  f^{-1} (x)=\frac{2x+3}{4}
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