Show that the sum of the measures of the external angles of any polygon is 360°. [ HINT:- Draw three different polygons like a triangle, quadrilateral, pentagon. Extend each side, then measure the exterior angles from there. Finally, find the sum of measures of all exterior angles of each polygon.]

Answer:

∅=6

Step-by-step explanation:

let ∅=x

[tex]\csc(3x+15)=\frac{1}{\sin(3x+15)}\\\sin(5x+3)*(\frac{1}{\sin(3x+15)})\\\frac{\sin(5x+3)}{\sin(3x+15)}=1\\\sin(5x+3)=\sin(3x+15)\\5x+3=3x+15\\2x=12\\x=6[/tex]

Given : GH bisects ∠FGI

It means : ∠FGH and ∠HGI are equal

Given :

∠FGH = (5x - 8)°

∠HGI = (6x - 15)°

⇒  5x - 8 = 6x - 15

⇒  6x - 5x = 15 - 8

⇒  x = 7°

Substituting the value of x, We get :

∠FGH = 5(7) - 8 = (35 - 8) = 27°

∠HGI = 6(7) - 15 = (42 - 15) = 27°

∠FGI = ∠FGH + ∠HGI = (27 + 27) = 54°

Answer:

D. 5 /12 + 1 /12 + 4/ 12 + 2 /12 + 5 /12

Step-by-step explanation:

Ive friends each knit one part of a scarf that is 1 5/ 12 yards long.

Hencfy, the fractions of the scarf each friend could have knit is calculated by comparing the options

A. 1 /12 + 2 /12 + 3 /12 + 8 /12 + 4 /12

Lowest Common Denominator = 12

Hence = 18/12 = 1 6/12 = 1 1/2

Option A is wrong

B. 1 /12 + 6/ 12 + 3 /12 + 2 /12 + 4 /12

Lowest Common Denominator = 12

Hence = 16/12 = 1 4/12 = 1 1/3

Option B is wrong

C. 2/12 + 3/ 12 + 3/ 12 + 2/ 12 + 5/ 12

Lowest Common Denominator = 12

Hence = 15/12 = 1 3/12 = 1 1/4

Option C is wrong

D. 5 /12 + 1 /12 + 4/ 12 + 2 /12 + 5 /12

Lowest Common Denominator = 12

Hence = 17/12 = 1 5/12

Option D is correct

Therefore, the fractions of the scarf each friend could have knit is Option D

Answer:

he would have to change 19 and 25 because they dont match the rest of the numbers because they are odd numbers.

Answer:

23.6 units

Step-by-step explanation:

If we have a circle of radius R, the perimeter of the arc is given by:

P = 2*pi*R

Now, if we only want to find the length of an arc defined by an angle "a", it will be:

L = (a/2*pi)*2*pi*R = a*R

In this case, we know that DA = 10, so we can think that this is a circle of radius R = 10 units

And for the arc DE, we have the angle:

a = 2.36 rad

replacing these two in the formula, we get:

L = 2.36*10 units = 23.6 units

Answer:

false negatives - 2%

false positives - 3%

Step-by-step explanation:

Here is the complete question :

A test to detect an infection gives a positive result 98% of the time when an infection is present. It is 97% accurate when an infection is not present.

% of results will be false negatives, and % of results will be false positives.

False negative means a negative result which in actuality it is positive

False negative = 100% - percent of positive result

100% - 98% = 2%

False positive result means a positive result which in actuality is negative

False positive = 100% - percent of false positive

100 - 97 = 3%

Answer:

10 quarts

thank you

i think

Answer:

6x-3

Step-by-step explanation:

that is the procedure above

Step-by-step explanation:

5+4X+2x-8

=6x-3

answer is third option

Answer:

41 square units

Step-by-step explanation:

this polygon can be split into several sub-shapes, for which we can calculate their areas much easier. and then we simply add all the sub-results for the total result.

for me this split would be

1. square CDEF, with F being an additional point at (6,5) : 4 units to the right of C.

2. a right-angled triangle ABF (the same F as for 1.).

the area of a square is the square of a side length.

the side length in 1. is 4.

so, its area is 4×4 = 16 square units.

the area of a right-angled triangle is

a×b/2

with a and b being the sides enclosing the 90 degree angle.

in our case here a = BF = 10, b = FA = 5

so the area of the triangle is 10×5/2 = 25 square units.

so, the total area is 16 + 25 = 41 square units.

Answer:

x ≈ 2.8

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan26° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{CD}{DE}[/tex] = [tex]\frac{x}{5.7}[/tex] ( multiply both sides by 5.7 )

5.7 × tan26° = x , then

x ≈ 2.8 ( to the nearest tenth )

Answer:

2.8

Step-by-step explanation:

1. c = a · sin(C) / sin(A)  

This is the equation to find x. Let's see what we have.

c = x

a = 5.7

C = 26

A = ?

Let's find A. We know B is 90 and C is 26.  Triangle Sum Theorem time!

2. 180 = 90 + 26 + A

180 = 116 + A

64 = A

A = 64

We found A. Let's see what we have now!

c = x

a = 5.7

C = 26

A = 64

Let's solve the equation now.

3. x = 5.7 · sin26 / sin64

Let's use a calcalator to find the answer.

4. 2.78008 =  5.7 · sin26 / sin64

5.7 · sin26 / sin64 =  2.78008

We should round this to the nearest tenth. 7 is in the tenth place. Though 8 is behind 7. 8 is greater than 4 which means 7 must be rounded up.

5. 2.8 is the answer.

Hope this help!!!

Have a nice day!!!

Answer:

that gy is rong dount do it

Step-by-step explanation:

Answer:

There isnt a diagram

Step-by-step explanation:

Answer:

First you convert the mixed numbers into improper fraction

[tex]8\frac{3}{8} = \frac{67}{8} \\\\6 \frac{3}{4} = \frac{27}{4}[/tex]

Solution

[tex]A=\frac{\frac{27}{4} + \frac{67}{8} }{2}[/tex]

[tex]A=\frac{\frac{54 + 67}{8} }{2}[/tex]

[tex]A\frac{\frac{121}{8} }{2}[/tex]

[tex]A=\frac{121}{8}[/tex] * [tex]\frac{1}{2}[/tex]

[tex]A= \frac{121}{16}[/tex]

[tex]A= 7 \frac{9}{16}[/tex]

Step-by-step explanation:

Answer:

-2/7

Step-by-step explanation:

We have two points so we can use the slope formula

m = (y2-y1)/(x2-x1)

m = (8-0)/(-14-14)

   = 8/-28

   = -2/7

Answer:

263

Step-by-step explanation:

424+339=764

1000-764=236

Answer:

It is -4 :)

Step-by-step explanation:

I just did this lol

Answer:

The slope of the line is [tex]m = \frac{3}{5}[/tex] and the equation of the line is [tex]y = \frac{3}{5}\cdot x[/tex].

Step-by-step explanation:

From table we understand that slope of the line is constant, that is, for each change of [tex]x[/tex] there is one and only change in [tex]y[/tex], fulfilling the main characteristic of a line and we can determine the slope for every point of the line by means of the following expression:

[tex]m = \frac{y_{f}-y_{o}}{x_{f}-x_{o}}[/tex] (1)

Where:

[tex]x_{o}, x_{f}[/tex] - Initial and final x-coordinates of the line.

[tex]y_{o}, y_{f}[/tex] - Initial and final y-coordinates of the line.

If we know that [tex](x_{o}, y_{o}) = (0,0)[/tex] and [tex](x_{f},y_{f}) = (8,4.8)[/tex], then the slope of the line is:

[tex]m = \frac{4.8-0}{8-0}[/tex]

[tex]m = \frac{3}{5}[/tex]

From graph we conclude that x-intercept of the line is [tex]b = 0[/tex]. Hence, the equation of the line is [tex]y = \frac{3}{5}\cdot x[/tex] and we proceed to plot the expression with the help of a graphing tool.

Answer:

The duration of the flight is 1 hour

Step-by-step explanation:

Since average speed = distance traveled / time

Let the duration of the flight be in z hours

So, (600km/z hours) - (600km/ z hours + (1/2)) = 200km/hr

Note: 1/2 is used as a result of 30 minutes increased in time which is half an hour.

200 = (600/z ) - (600/z + (1/2))

Multiply 2 through on (600/z + (1/2))

200 = (600/z ) - (1200 / (2z + 1))

Divide through by 200

= z(2z + 1) = 3

convert to quadratic equation

2z² + z = 3

2z² + z - 3 = 0

(2z + 3) ( z-1) = 0

z-1 = 0

z = 1 hour

Answer:

c

Step-by-step explanation:

This is a parabola, so it is a quadratic parent function.

Answer:

Its just a slide 2 up and 3 to the right it seems. It can be a mirror because in never changes the shape. as of rules i dont understand want you need please comment and ill let you know

Step-by-step explanation:

It is not a rotation, a mirror a flip or anything like that i think its only slides.

I didnt se this before every slide counts as 2 so its 4 up and 6 to the right

Answer:

142.5

Step-by-step explanation:

150/x=100/95

95*150/100=

142.5

Answer:

Sr i dont know

Step-by-step explanation:

Answer:

[tex]\text{C. }g(x)=(x-5)^2[/tex]

Step-by-step explanation:

The function [tex]y=(x-c)^2[/tex] has a phase shift of [tex]c[/tex] to the parent function [tex]y=x^2[/tex]. Since [tex]g(x)[/tex] has moved to the right 5 units from the parent function [tex]f(x)=x^2[/tex], we're looking for a value of [tex]c=5[/tex].

Therefore, we have:

[tex]g(x)=\boxed{(x-5)^2}[/tex]

Answer:

[tex]Area~of~quarter:-[/tex]

[tex]=\frac{\pi *8*8}{4}[/tex]

[tex]=16\pi[/tex]

If an event occurs 0 times (out of 4, in this case) then it does not occur at least once. So we can find the probability of it not occurring and then subtract that value from 1.

So, what are the chances of it not occurring in 1 trip?

1−.37=.63

What about not occurring in 2 trips?

(1−.37)⋅(1−.37)=.63⋅.63=.3969

Now what about not occurring in 4 trips?

.63^4 = 0.15752961

We must subtract this value from 1

(recall that what we just calculated is the probability of it not occurring, so the probability of it occurring at least once is:

1−0.15752961 = .84247039

TLDR - In 4 trips the chance of a guest catching a cutthroat once in under 4 trips in 0.84.