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3 years ago

Use the Pythagorean theorem to find the distance between the two points ANB round your answer to the nearest hundredth

Mathematics

1 answer:

jek_recluse [69]3 years ago

6 0

Answer:

5.39 units

Step-by-step explanation:

Pythagorean theorem: $a^{2} + b^{2} = c^{2}$

Let point (-2,1) be C

Line segment AC would be 2 units long.

Line segment BC would be 5 units long.

Insert the length of the line segments in to the Pythagorean theorem

$2^{2} + 5^{2}$

4 + 25 = 29

$\sqrt{29}$ ≅ 5.385

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Carter draws one side of equilateral △PQR on the coordinate plane at points P(-3,2) and Q(5,2). Which ordered pair is a possible

Law Incorporation [45]

Step-by-step explanation:

Hey, there!!!

Let me simply explain you about it.

We generally use the distance formula to get the points.

let the point R be (x,y)

As it an equilateral triangle it must have equal distance.

now,

let's find the distance of PQ,

we have, distance formulae is;

$pq = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} }$

$or \: \sqrt{( {5 + 3)}^{2} + ( {2 - 2)}^{2} }$

By simplifying it we get,

$8$

Now,

again finding the distance between PR,

$pr = \sqrt{( {x2 - x1}^{2} + ( {y2 - y1)}^{2} }$

or,

$\sqrt{( {x + 3)}^{2} + ( {y - 2)}^{2} }$

By simplifying it we get,

$= \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 }$

now, finding the distance of QR,

$qr = \sqrt{( {x - 5)}^{2} + ( {y - 2)}^{2} }$

or, by simplification we get,

$\sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 }$

now, equating PR and QR,

$\sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13} = \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 }$

we cancelled the root ,

${x}^{2} + {y}^{2} + 6x - 4y + 13 = {x}^{2} + {y}^{2} -10x - 4y + 29$

or, cancelling all like terms, we get,

6x+13= -10x+29

16x=16

x=16/16

Therefore, x= 1.

now,

equating, PR and PQ,

$\sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } = 8}$

cancel the roots,

${x}^{2} + {y}^{2} + 6x - 4y + 13 = 8$

now,

(1)^2+ y^2+6×1-4y+13=8

or, 1+y^2+6-4y+13=8

y^2-4y+13+6+1=8

or, y(y-4)+20=8

or, y(y-4)= -12

either, or,

y= -12 y=8

Therefore, y= (8,-12)

by rounding off both values, we get,

x= 1

y=(8,-12)

So, i think it's (1,8) is your answer..

Hope it helps...

3 0

3 years ago

Find the value of x. Round your answer to the nearest tenth

Sergio039 [100]

Answer:

Your answer would be 24 but then if you round it to the nearest tenth the you would have 20

Step-by-step explanation:

i hope this helps

4 0

2 years ago

Give an example of a rule for a pattern. List a set of numbers that fit the pattern.

Jlenok [28]

In this pattern , the numbers are doubling..
2,4,6,8,10...

7 0

3 years ago

The circumference of a circular hot tub at a hotel is 56.5 yards. What is the diameter of the hot tub?

Scorpion4ik [409]

$c = 2\pi \times r \\ 56.5 \div 2 = \pi \times r \\ 28.25 \div \pi = r \\ 9 = r \: then \: \times 2 = d \: \\ diameter \: is \: 18$

7 0

3 years ago

Choose the TWO factored binominals for the expression: x2+6x – 27 Question 6 options: A) (x - 3) B) (x - 9) C) (x + 6) D) (x + 9

Vera_Pavlovna [14]

Answer:

A) x-3 and D) x+9

Step-by-step explanation:

x^2 + 6x - 27

You need to find two numbers that multiply to -27 and add up to 6

Those two numbers are -3 and 9, because 9 * -3 = -27 and 9+ -3 = 6

So you add those to x and those are your two factored binomials

(x-3) and (x+9)

4 0

3 years ago