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2 years ago

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]2 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]2 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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A square is constructed on side AD of quadrilateral ABCD such that FA lies on AB, as shown in the figure.

Elza [17]

Answer: The co-ordinates of F are (4.4, -4.6) and the co-ordinates of D are (4.4, -1.4).

Step-by-step explanation: Given that a square is constructed on side AD of quadrilateral ABCD such that FA lies on AB as shown in the figure. The co-ordinates of A are (6, -3) and the co-ordinates of B are (10, 1).

Also, AD : AB = 2 : 5 and the co-ordinates of the point E are (2.8, -3).

We are to select the correct co-ordinates of the points F and D.

Let, (a, b) are the co-ordinates of F and (c, d) are the co-ordinates of D.

Since ADEF is a square, so we have

AD = DE = EF = FA.

Given that

AD : AB = 2 : 5, so FA : AB = 2 : 5.

That is, \left(\dfrac{c+4.4}{2},\dfrac{d-4.6}{2}\right)=\left(\dfrac{2.8+6}{2},\dfrac{-3-3}{2}\right)

We have, after applying the internal division formula that

$\left(\dfrac{2\times 10+5\times a}{2+5},\dfrac{2\times 1+5\times b}{2+5}\right)=(6,-3)\\\\\\\Rightarrow \left(\dfrac{20+5a}{7},\dfrac{2+5b}{7}\right)=(6,-3)\\\\\\\Rightarrow \dfrac{20+5a}{7}=6,~~~~~\dfrac{2+5b}{7}=-3\\\\\\\Rightarrow 20+5a=42,~~~~\Rightarrow 2+5b=-21\\\\\\\Rightarrow 5a=22,~~~~~~~~~~\Rightarrow 5b=-23\\\\\\\Rightarrow a=4.4,~~~~~~~~~~~\Rightarrow b=-4.6.$

So, the co-ordinates of F are (4.4, -4.6).

Now, since ADEF is a square, and the diagonals of a square bisect each other.

So, the mid-points of both the diagonals are same.

That is,

$\textup{mid-point of DF}=\textup{mid-point of AE}\\\\\\\Rightarrow \left(\dfrac{c+4.4}{2},\dfrac{d-4.6}{2}\right)=\left(\dfrac{2.8+6}{2},\dfrac{-3-3}{2}\right)\\\\\\\Rightarrow \left(\dfrac{c+4.4}{2},\dfrac{d-4.6}{2}\right)=\left(\dfrac{8.8}{2},\dfrac{-6}{2}\right)\\\\\\\Rightarrow \dfrac{c+4.4}{2}=\dfrac{8.8}{2},~~~~~~\dfrac{d-4.6}{2}=-\dfrac{6}{2}\\\\\\\Rightarrow c+4.4=8.8,~~~~~\Rightarrow d-4.6=-6\\\\\Rightarrow c=4.4,~~~~~~~~~~~~\Rightarrow d=-1.4.$

So, the co-ordinates of D are (4.4, -1.4).

Thus, the co-ordinates of F are (4.4, -4.6) and the co-ordinates of D are (4.4, -1.4).

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2 years ago

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A pie was a radius of 4.25 inches

s2008m [1.1K]

Do you want to find the area for this or circumference. If you want to find the area, the answer will be about 56.7 square inches. Finally, if you want to find the circumference, the answer will be about 26.69 inches. Hope you get it!

8 0

2 years ago

Helga [31]

There both types of numbers but a whole number is a number with no exponents or decimals, but decimals are like a broken un half whole number

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2 years ago

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In some languages, every consonant must be followed by a vowel. How many seven-letter ‟words” can be made from the Hawaiian word

emmasim [6.3K]

Answer:

One. Kamala.

Step-by-step explanation:

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1 year ago

A gallon of Moo Milk costs \$5.12$5.12dollar sign, 5, point, 12. What is the price, in dollars, of an 888 ounce glass of Moo Mil

Sladkaya [172]

The correct statement is:
A gallon of Moo Milk costs $5.12 What is the price, in dollars, of an 8 ounce glass of Moo Milk? There are 128 ounces in 1 gallon.

Solution:
Cost of 1 gallon of Moo Milk = $ 5.12

1 gallon = 128 ounces, so we can write:

Cost of 128 ounces of Moo Milk = $ 5.12

Cost of 1 ounce of Moo Milk = $ 5.12/128 = $ 0.04

Cost of 8 ounces of Moo Milk = $ 0.04 x 8 = $ 0.32

Thus, 8 ounces of Moo Milk will cost $ 0.32

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2 years ago

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