Three vertices of square PQRS are P(–3, –2), Q(–1, 3), and R(4, 1). What are the coordinates of the fourth vertex?

Answers

Answer 1

Answer:
I made a quick sketch of these three points on a scratch paper, and
I think this is the way to solve the problem. Even though it seems
long and complicated, it's just doing things that you know how to do,
several times.

On paper, sketch and mark the three points.

You'll see that there are two sides of the square missing:
-- the side from 'P' to the missing point,
-- the side from 'R' to the missing point.

==> Find the slope of the side between 'Q' and 'R'.
Q=(-1, 3) . . . R=(4, 1)
Slope = (1-3) / (4 - -1) = -2/5
The side from 'P' to the missing point has the same slope,
and it goes through the point 'P' (-3, -2), so you can find its equation.
y = -2/5x + b
-2 = -2/5(-3) + b
-2 = 6/5 + b
-2 - 6/5 = b = -10/5 - 6/5 = -16/5
y = -2/5x - 16/5

==> Find the slope of the side between 'P' and 'Q'.
The side from 'R' to the missing point has the same slope,
and it goes through the point 'R', so you can find its equation.

Maybe a bit shorter, you could say that this line is perpendicular to
the line between 'Q' and 'R' that you just found, so its slope is the
negative reciprocal of that one ... 5/2 instead of -2/5s .

y = 5/2 x + b
This line goes through point 'R' (4, 1), so
1 = 5/2(4) + b
1 = 20/2 + b
1 = 10 + b
-9 = b
y = 5/2x - 9

Now you have the equations for the two lines that go through the
missing point. When you solve this system of two equations, you'll
have the 'x'; and 'y' coordinates of the missing point, because that's
where they intersect.

y = -2/5x - 16/5 , and
y = 5/2x - 9

   -2/5 x - 16/5 = 5/2 x - 9
Multiply each side by 10 : -4 x - 32 = 25 x - 90
Add 4x to each side :    - 32 = 29 x - 90
Add 90 to each side:     58 = 29 x
Divide each side by 29 : x = 2

y = 5/2 x - 9 = 5/2(2) - 9 = 5 - 9 = -4

The missing corner is the point (2, -4) .

Like I said ... It seems long and complicated, but it's just a matter of
doing things that you know how to do, several times. And trying to
not make any mistakes along the way (like I did about four times.)

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Mia has a piece of ribbon that is 30.5 yards long. The length is just enough ribbon to make 5 bows that are the same size. How long is the ribbon that she uses for each bow?

Answers

30.5/5= 6.1 yards per ribbon

Just divide 30.5 and 5 together to get answer hope I help

What is 1/5 of £3.00 please

Answers

3.00 /5 = 0.6 pound :))
i hope this be helpful

3.00 pounds* (1/5)= 0.6 pound.

1/5 of 3.00 pounds is 0.6 pound~

Which expression correctly represents “ten times the difference of a number and six”

Answers

Answer:

Expression will be 10(x - 6).

Step-by-step explanation:

Let the given number is x.

Difference of this number and 6 will be represented by

(x - 6)

Then ten times the difference of this number and 6 will be represented by

10(x - 6)

Therefore, the statement " ten times the difference of a number and six " will be represented by the expression 10(x - 6)

Answer:

10 * (m * 6)

Step-by-step explanation:

hope thats alright!

Number sequence 1. 2, 11, 4, 13, __, __.

2. 4, 12, 36, 108, __, __.

3. 8, 13, 18, 23, __, __.

4. 5, 10, 8, 13, 11, __, __.

Answers

Answer:

1. 6, 15

2. 324,972

3. 28, 31

4. 16, 14

Step-by-step explanation:

Answer:

1. 6, 15

2. 324,972

3. 28, 31

4. 16, 14

Step-by-step explanation:

Emmanuel wants to tile his rectangular floor. he has two kinds of tiles to choose from, one of which is larger than the other. emmanuel hired your services to help him decide which tile to use.a.what area will be covered by 7"x7" tile? 21"x21" tilwe
b.if the rectangular floor has dimension of 420" by 630"
c.how many big square tiles are needed to cove rthe rectangular floor?
d.if each small tile costs P15.00 and each big tile costs P60.00which which tile should emmanuel use to econimize in tiling his floor? why?

Answers

a).
The 8" by 7" tile covers 49 square inches.
The 21" by 21" tile covers 441 square inches.

b).
The area of the floor is (420" x 630") = 264,600 square inches.

c).
It would take (264,600) / (441) = 600 large tiles to cover the floor.

d).
Emmanuel should use the big tiles to cover his floor.
-- A big tile costs 4 times as much as a small tile, but it has 9 times
as much area as a little tile has, so it is a better buy.
-- Plus, he would have to pay the floorman a lot more to glue down 5,400 tiles
than he will have to pay to glue down only 600 tiles.
-- Since he has hired my services to advise him, I will charge him only 15%
of the difference if he takes my advice, so he will still be money ahead.

Calculate the area of the following parallelogram: