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Talja [164]
3 years ago
10

Of 20 possible​ books, you plan to take 6 with you on vacation. How many different collections of 6 books can you​ take?

Mathematics
1 answer:
Anon25 [30]3 years ago
6 0
3 collections. 20 / 6 = 3.33
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The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral
Iteru [2.4K]

The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.

To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.

Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...

A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1

translated, that's CD║BC and CD⊥BC - contradictory; second half right

B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1

CD ║ AB and CD ⊥ AB - only the parallelogram half is right

C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1

CD║AB and CD⊥BC - that's TRUE

D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1

CD║AC and CD⊥AB - nope

Answer: C

The way I'd get the proper expression is with the dot product.

A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.

Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have y_4 - y_3 so one side is CD. The other side must be BC or AD; AD would give y_4 - y_1 terms which don't appear among the answer, so let's go with BC.

The direction vectors are

D-C = (x_4 - x_3, y_4 - y_3)

C-B = (x_3 - x_2, y_3 - y_2)

For perpendicularity we need a zero dot product:

0 = (D-C)\cdot(C-B) = (x_4 - x_3)(x_3 - x_2) + (y_4 - y_3)(y_3 - y_2)

- (x_4 - x_3)(x_3 - x_2) = (y_4 - y_3)(y_3 - y_2)

That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.

8 0
2 years ago
I NEED help with this ASAP
boyakko [2]

Answer:

This triangle is a scalene triangle.

Step-by-step explanation:

A scalene triangle means that all of the sides are different.

Hope this helps!

3 0
2 years ago
Write an expression that will have a product less than both factors.
anzhelika [568]
-2 * 3 = -6


-6 \ \textless \  -2 \ \textless \  3
6 0
3 years ago
Read 2 more answers
Can someone help me pls!!!
Cerrena [4.2K]

Answer:

First one: Function

Second one: not a function (a function cannot have two outputs)

Third one: Function

Last one: Not a function (doesn't pass vertical line test)

Step-by-step explanation:

Hope it helps!

6 0
2 years ago
Read 2 more answers
P is a polynomial of degree 4 with three zeros: -1 and 2 are zeros of multiplicity one, and 3 is a zero with multiplicity two. I
tatyana61 [14]

Answer:

P(x) = (x+1)(x-2)(x-3)^2 + 108

Step-by-step explanation:

let me know if you want an explanation

3 0
2 years ago
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