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sattari [20]
3 years ago
10

Quadrilateral EFGH is inscribed inside a circle as shown below. Write a proof showing that angles H and F are supplementary.

Mathematics
2 answers:
puteri [66]3 years ago
8 0
That is called a cyclic quadrilateral. Angles E and G add up to 180 degrees and angles H and F add up to 180 degrees.
yarga [219]3 years ago
3 0

Answer:

Step-by-step explanation:

Given is a quadrilateral EFGH inscribed in a circle with centre J.

Consider angle E, which is subtended by minor arc FGH.

Hence angle E = half of angle FGH (by subtended angles theorems for circles)

Similarly G is the angle subtended by major arc FGH

angle G = half of angle subtended by major arc FEH

Since total angle around J is 360 degrees we have

angle subended by minor and major arc add to 360

Consequently, angle E + angle G = 1/2 (360) = 180

Hence E and G are supplementary

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Find the distance between the points (-10,-7) and (2,9).
soldier1979 [14.2K]
20 (units)

Distance formula is:

Sqrt of (x-x1)^2+(y-y1)^2

So define which coordinate is (x,y) and what (x1,y1)

I’m going to define (-10,-7) as (x,y) and (2,9) as (x1,y1)

So plug in your variables!

Sqrt(-10-2)^2+(-7-9)^2

Sqrt-12^2+-16^2

Sqrt144+256

Sqrt400

So sqrt of 400 is 20! :))

3 0
3 years ago
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility
pashok25 [27]

Answer: a) D = √148

                 m = (-5,4)

b) D = √241

m = (1, 7.5)

c) D = √20

m = (0,-4)

Step-by-step explanation:

Distance and Midpoint Formulas

distance = D = √[(x₂-x₁)² + (y₂-y₁)²]

Midpoint: m = ((x₂+x₁)/2 , (y₂+y₁)/2)

(−4, 10) and (−6, −2)

D = √[(-6-(-4))² + (-2-10)²] = √[(-6+4))² + (-2-10)²] = √[(-2))² + (-12)²] =

√[4 + 144] = √148

m = ((-6+(-4))/2 ; (-2+10)/2

m = (-10/2 ; 8/2)

m = (-5,4)

(−1, 15) and (3, 0)

D = √[(3-(-1))² + (0-15)²] = √[(3+1))² + (0-15)²] = √[(4)² + (-15)²] =

√[16 + 225] = √241

m = ((3+(-1))/2 ; (0+15)/2

m = (2/2 ; 15/2)

m = (1,7.5)

(2, −3) and (−2, −5)

D = √[(-2-2)² + ((-5)-(-3)²] = √[(-4))² + (-5+3)²] = √[(-4)² + (-2)²] =

√[16 + 4] = √20

m = (-2+2))/2 ; (-5+(-3))/2

m = (0/2 ; -8/2)

m = (0,-4)

3 0
3 years ago
Find the surface area of the above solid
vazorg [7]

Answer:did u ever find the answer i need it

Step-by-step explanation:

6 0
3 years ago
Identify any extraneous solution. See above pic
Sav [38]

Answer:

There are no extraneous solutions

Reasoning:

An extraneous solution is a solution that isn't valid, it might be imaginary like the square root of a negative number.

first we want to isolate z:

1+sqrt(z)=sqrt(z+5)

^2 all      ^2 all

(1+sqrt(z))(1+sqrt(z))=z+5

expand

1+2sqrt(z)+z=z+5

-1              -z  -z -1

2sqrt(z)=4

/2           /2

sqrt(z)=2

^2 all    ^2 all

z=4

Since there is one solution and it is a real number, there are no extraneous solutions.

4 0
3 years ago
Read 2 more answers
What is pi squared as a fraction?
ivolga24 [154]
Π=3.14
Let's start with two digits:

3.14 = 3 14/100

= 3 7/50

= 157/50

would be the approximation for that. Let's add a few more digits:

3.1415 = 3 1415/10000

= 3 283/2000

= 6283/2000
3 0
4 years ago
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