the scale of a map is 1 cm : 72km. What is the actual distance between two towns that are 4 cm apart on the map

You are graphing Square ABCDABCDA, B, C, D in the coordinate plane. The following are three of the vertices of the square: A(4,

Vsevolod [243]

Answer:

D(4,-3)

Step-by-step explanation:

Given three of the vertices of the square: A(4, -7), B(8, -7),C(8, -3)

Let the coordinate of the fourth vertex be D(x,y).

We know that diagonals of a square are perpendicular bisector. So, the midpoint of both diagonals is the same.

The diagonals are BD and AC

Midpoint of BD = Midpoint of AC

$\left(\dfrac{8+x}{2},\dfrac{-7+y}{2}\right) =\left(\dfrac{4+8}{2},\dfrac{-7+(-3)}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(\dfrac{12}{2},\dfrac{-10}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(6,-5\right)\\$Therefore$:\\\dfrac{8+x}{2}=6\\8+x=12\\x=12-8\\x=4\\$Similarly$\\\dfrac{y-7}{2}=-5\\y-7=-5*2\\y-7=-10\\y=-10+7=-3$

The coordinates of the fourth vertex is D(4,-3)

8 0

3 years ago

Ishaan is 222 times as old as Christopher. 353535 years ago, Ishaan was 777 times as old as Christopher.

klemol [59]

<h3><u>Question:</u></h3>

Ishaan is 2 times as old as Christopher. 35 years ago, Ishaan was 7 times as old as Christopher. How old is Christoper now?

<h3><u>Answer:</u></h3>

The present age of Christoper is 42 years old

<h3><u>Solution:</u></h3>

Given that Ishaan is 2 times as old as Christoper

Let the present age of Christoper be "x"

Then, Present age of Ishaan = 2 times as old as Christoper

present age of Ishaan = 2x

<em><u>35 years ago, Ishaan was 7 times as old as Christopher</u></em>

Age of Ishaan 35 years ago = Present age of Ishaan - 35

Age of Ishaan 35 years ago = 2x - 35

Similarly,

Age of christoper 35 years ago = Present age of christoper - 35

Age of christoper 35 years ago = x - 35

From given statement, 35 years ago, Ishaan was 7 times as old as Christopher

Age of Ishaan 35 years ago = 7 times the age of Christoper 35 years ago

(2x - 35) = 7(x - 35)

<em><u>Solve the above equation for "x"</u></em>

2x - 35 = 7x - 245

2x - 7x = -245 + 35

-5x = -210

Thus present age of Christoper is 42 years old

5 0

3 years ago

Luis set up an A-frame ladder so that the angle formed between each side of the ladder and the ground is 125 degrees. What is th

Firlakuza [10]

Answer:

70°

found by considering A-frame ladder as a triangle

Step-by-step explanation:

Given that,

angle form on either side of A-frame ladder with the ground = 125°(exterior)

As it is a A-frame ladder so its a triangle, we will find the angle at the top of ladder by using different properties of triangle

1) find interior angle form by A-frame ladder with the ground

125 + x = 180 sum of angles on a straight line

x = 180 - 125

x = 55°

2) find the angle on top of ladder

55 + 55 + y = 180 sum of angle of a triangle

110 + y = 180

y = 180 - 110

y = 70°

3 0

3 years ago

If F(x) and G(x) are two functions such that F(G(x)) = x then F(x) and G(x) are ..?

lana [24]

They are inverse functions though to be completely thorough your teacher should have also put g(f(x)) = x as well. Though I can see what your teacher is aiming for at least.

The idea is that whatever the output of g(x) is, it's plugged into f(x) and the initial input is the result. So g(x) takes a step forward and f(x) takes a step back undoing everything g(x) did. Which is exactly what an inverse operation does.

4 0

3 years ago

Read 2 more answers

Abigail bought 6/8 of a pound of turkey at the deli She used 2/4 of it to make sandwiches for lunch how much of the turkey did A

pogonyaev

Answer:

2/8

Step-by-step explanation:

I think this is subtraction (if not just tell me i'll edit)

6/8 - 2/4 = 6/8 - 4/8 = 2/8

7 0

3 years ago

Read 2 more answers