In the figure, one exterior angle is drawn at each vertex of the triangle. Explain how to find the sum of the measures of these three exterior angles.
Answers
Explanation:
Here's one way:
At vertex A, draw the vertical angle to the given angle 4. That is, extend AC, rather than AB to show the exterior angle at that vertex.
Now, collapse triangle to one with zero area, so that vertices A, B, C lie on top of each other. You can do this using a dilation scale factor f such that f→0.
The result is that the exterior angles divide the circular space around point ABC into three parts that sum to 360°. Essentially, we have copied each of the exterior angles to the same vertex.
The sum of the measures of the exterior angles is 360°.
_____
Additional comment
This identical approach can be used to show the sum of exterior angles around any convex polygon is always 360°.
Related Questions
C. Because slope =
rise over run the slope of a "downhill" line must be
run
Answers
A machine takes 15 minutes to scan 1,125 pages. At this rate, how many pages can the machine in a hour?
Answers
Answer:
4500 pages
Step-by-step explanation:
an hour has 60 minutes. This means in 1 hour the machine will scan 60/15 more pages. 60/15 =4.
1125*4 =4500 pages/hour
In one hour the machine will scan 4500 pages.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a machine takes 15 minutes to scan 1,125 pages.
The machine takes 15 minutes to scan 1,125 pages.
Then, in 1 minute, it will scan (1125/15) = 75 pages.
So, in 1 hour, it will scan -
x = 75 x 60
x = 4500
Therefore, in one hour the machine will scan 4500 pages.
To solve more questions on algebraic expressions, visit the link below -
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#SPJ2
What is the L.C.M of 45 80 and 135
Answers
Answer:
LCM = 2160
Step-by-step explanation:
lcm of 45 80 and 125 is 2160 because LCM = 2160
Answer:
the answer is (that I found) is 2160
can anyone please help
Answers
Answer:
Adult tickets = $73.5
Child tickets = $20.5
Step-by-step explanation:
[tex]{ \rm{3x + 5y = 50 - - - \{eqn \: 1 \}}} \\ { \rm{x + 5y = 31 - - - \{eqn \: 2 \}}} \\ [/tex]
• Subtract eqn 2 from eqn 1:
[tex]{ \rm{2x = 21}} \\ { \rm{x = 10.5}}[/tex]
[tex]{ \rm{10.5 + 5y = 31}} \\ { \rm{5y = 20.5}} \\ { \rm{y = 4.1}}[/tex]
What are some possible solutions for the following?
Answers
Answer:
After solving the problem, the answer is x>1/2. However I do not see the answer choice provided so I do not know the answer to the question
Step-by-step explanation:
i need help with this like... now besties
if h(t) = 220 + 1.5x represents the height of a chair lift as a function of time where t is time (in seconds) and h is height (in feet). What would the ordered pair (12, 334) represent on the coordinate plane?
Answers
Step-by-step explanation:
it represents a point on the line defined by the function equation.
it means that after 12 seconds the chair lift will have reached a height of 334 ft (after a starting height of 220 ft).
The probability of event A is 0. 48, the probability of event A and B is 0. 21, and the probability of events A or B is 0. 89. What is the probability of event B? 0. 09 0. 20 0. 27 0. 62.
Answers
Probabilities are used to determine the chances of an event
The probability of event B is 0.62
The probabilities are given as:
[tex]\mathbf{P(A) = 0.48}[/tex]
[tex]\mathbf{P(A\ and\ B) = 0.21}[/tex]
[tex]\mathbf{P(A\ or\ B) = 0.89}[/tex]
To calculate the probability of event B, we make use of the following formula
[tex]\mathbf{P(A\ and\ B) = P(A) + P(B) - P(A\ or\ B)}[/tex]
So, we have:
[tex]\mathbf{0.21 = 0.48 + P(B) - 0.89}[/tex]
Collect like terms
[tex]\mathbf{P(B)= -0.48 +0.21 + 0.89}[/tex]
[tex]\mathbf{P(B)= 0.62}[/tex]
Hence, the probability of event B is 0.62
Read more about probabilities at:
https://brainly.com/question/11234923
A runing track is 400m long. Carrie runs wight laps. How far is this in kilometres.
Answers
Multiply length of track by number of times run:
8 x 400 = 3,200 meters
1 km = 1000 meters
3200 meters / 1000 = 3.2 kilometers
Answer: 3.2 kilometers
Solve for the variable 2y<14 A) y<12 B) y>-7 C) y>7 D) y<7
Answers
Answer:
D) y < 7
Step-by-step explanation:
So we have 2y < 14:
To solve, we will simply divide by 2 on both sides in order to isolate the y value. Now we have y < 7.
Hope this helps you :)
Given that a [] b = b2 + a. Evaluate 2 [] (6[] - 5).
Answers
Answer:
963
Step-by-step explanation:
Evaluate 6 | - 5 , then the outside part, that is
6 | - 5 ( with a = 6 and b = - 5 )
= (- 5)² + 6 = 25 + 6 = 31
Now evaluate 2 | 31 ( with a = 2 and b = 31 )
= 31² + 2 = 961 + 2 = 963
The function f(x)is graphed on the coordinate plane.
What is f(−2)?
Enter your answer in the box.
f(−2) =
Answers
Answer:
f(-2) = -2
Step-by-step explanation:
f(-2) means find the y value when x = -2
The y value when x = -2 is-2
f(-2) = -2
Solve for u. (u + 6)(u − 6) = 0
Answers
Answer:
u= 6, -6
Step-by-step explanation:
simplify the equation. Isolate the variable.
Hey there!
(u + 6)(u − 6) = 0
DISTRIBUTE “u” WITHIN the PARENTHESES
u(u) + (-6) + 6(u) + 6(-6) = 0
u^2 - 6u + 6u - 36 = 0
COMBINE the LIKE TERMS
u^2 - 36 = 0
ADD 36 to BOTH SIDES
u^2 - 36 + 36 = 0 + 36
CANCEL out: -36 + 36 because it gives you 0
KEEP: 0 + 36 because it helps solve for the u-value
NEW EQUATION: u^2 = 0 + 36
SIMPLIFY IT!
0 + 36 = 36
NEW EQUATION: u^2 = 36
TAKE the SQUARE ROOT
u = ± √36
u = -6 or u = 6
Therefore, your answer is: u = 6 or u = -6
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Please help me on question two
Answers
Answer:
The following are the answers of questions asked above :-
a) 40
b) 4
c) 4000
PLEASE HELP ME I BEG IMMA FAILLLLLLLLLLLLLLLL
A 10 cm cube is built from small cubes, each 1 cm on an edge. Write a ratio that compares the edge lengths of the large and small cubes.
2:1
3:1
11:1
10:1
Answers
Answer:
10:1
Step-by-step explanation:
This ratio is N to n for all answers. (N = Larger than n, n = Smaller than N)
Look at the Larger number. (10)
Look at the Smaller number. (1)
Turn 10 and 1 into a ratio. (10:1)
Complete the tables of values. X 4â’x â’1 4 0 a 2 b 4 c a = b = c = x ( 2 3 ) x â’1 3 2 0 d 2 e 4 f d = e = f =.
Answers
The corresponding values of d, e ad f are 1, 1/16, and 1/256 respectively
Find the table of values attached. From the given table the function of the output is expressed as [tex]g(x) = 4^{-x}[/tex]
If x = 0, then;
[tex]g(0) = 4^{-0}\\g(0) = 1/4^0\\g(0)=1/1 = 1\\[/tex]
If x = 2
[tex]g(2) = 4^{-2}\\g(2) = 1/4^2\\g(2)=1/16[/tex]
If x = 4;
[tex]g(4) = 4^{-4}\\g(4) = 1/4^4\\g(4)=1/256[/tex]
Therefore the corresponding values of d, e ad f are 1, 1/16 and 1/256 respectively
Learn more on table of functions here: https://brainly.com/question/3632175
Answer:
a = ⇒ 1
b = ⇒ 1/16
c = ⇒ 1/256
d = ⇒ 1
e = ⇒ 4/9
f = ⇒ 16/81
What is the value of q in the equation 49 - 2 = 39+8?
q
=
10
0 -
7
10
7
06
0 10
Answers
Answer:
The is no "q" in the equation provided. If there is supposed to be, please add it. Otherwise, q is undefined. It can have any value. I choose 0.
Step-by-step explanation:
There are 120 people in a sport centre.
78 people use the gym.
46 people use the swimming pool.
45 people use the track.
21 people use the gym and the pool.
16 people use the pool and the track.
24 people use the gym and the track.
9 people use all three facilities.
Given that a randomly selected person uses the gym and the track, what is the probability they do not use the swimming pool? PLEASE HELP THE CORRECT ANSWER WILL GET BRAINLIEST ANSWER
Answers
Answer:
71/120
Step-by-step explanation:
I need help with this question
Answers
Answer:
The time may be calculated by making the equations equal each other:
2w +7 = .5w + 10
1.5w = 3
weeks = 2
Step-by-step explanation:
Find the slope-intercept equation of the line
that passes through (5, -3) and has a
slope of -1/2
Answers
Answer:
y = -1/2x - 1/2
Step-by-step explanation:
lmk if you want an explanation
please help me :(
NO LINKS PLEASE
Answers
Answer:
Option A
Step-by-step explanation:
Given equation is:
[tex]x^2+1=2x-3[/tex]
Setting it up as a quadratic equation.
[tex]x^2+1-2x+3=0\\\\x^2-2x+4=0[/tex]
Comparing it with quadratic equation [tex]ax^2+bx+c=0[/tex], we get:
a = 1 , b = -2 , c = 4
Putting the values in quadratic equation:
[tex]\displaystyle x = \frac{-b +-\sqrt{b^2-4ac} }{2a} \\\\x = \frac{-(-2)+-\sqrt{(-2)^2-4(1)(4)} }{2(1)}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Answer:
A
Step-by-step explanation:
a = 1, b = -2, and c =4
d = -b +- sqrt (b^2 - 4*a*b)
= - (-2) +- sqrt ((-2)^2 - 4*1*4)
The table shows the average temperatures of different cities on a particular day. On a number line, which city's temperature will be between the temperatures of Manning and Stanville?
Answers
Answer:
chicken tender
Step-by-step explanation:
rgerr
Answer:
Step-by-step explanation:
I NEED HELP!!!
solve x^3 - 6x^2 - 7x + 60 by factoring. show all work
(using the method in the picture below)
Answers
Answer: x = -3, 5, 4
Step-by-step explanation:
Don't have time for it
Find e and d
3e+d=8
2e+d=8
Answers
Answer:
Step-by-step explanation:
2e+d=8
Multiply the second equation by -1
You get
-3e-d=-8
Use eliminating methods
-3e-d=-8
2e+d=8
We get
-e=0
So e=0
Find e by substitute it in one of the equation
2*0+d=8
D
d=8
The instructions for a fruit drink say to mix one part blackcurrant juice with four parts water. I
want to make one litre of this fruit drink. How much blackcurrant juice should I use? Give your
answer in millilitres.
ml
Answers
Answer:
you should use minimum 8 black cur
Find the missing base.
Write your answer as a whole number.
?^2=36
Answers
Answer:
6
Step-by-step explanation:
6^2 = 36
hope this helps! :D
have a miraculous day!! <3
20) A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test
Answers
Answer:
50-50 chance I suppose (1/2 or 5/10) or 40% to 60% percent chance
Step-by-step explanation:
He can guess all of the questions and get all of them right, and it is a possibility that he can also get all of them wrong. So I say, 50-50. I can't lie, I'm having trouble with probability as we speak.
8. A 20 point test was given to two classes. Each class had results shown in the box plots below. Which of the
two classes has the greater interquartile range?
Answers
Multiply (5.6 x 10") (6.1 x 10* )and write the
answer in scientific notation.
Answers
Answer:
3.416 x 10^(" + * + 1)
Step-by-step explanation:
The exponents of (5.6 x 10") (6.1 x 10* ) seem incorrect. Whatever they are, do the following:
1) multiply 5.6 times 6.1. Result = 34.16
Add the two exponents: (" + *)
The result is 34.16 x 10^(" + *)
Then move the decimal point one to the left and add 1 to the 10 exponent:
3.416 x 10^(" + * + 1)
Pleaseeeeee help! I don’t understand and I just wanna go to sleep but this is due in 35 minutes
Answers
Answer:
69
Step-by-step explanation:
it is 69 becuase 4x-7+11x-8 equals 69
We have: 2.(4x - 7)° + 2(11x - 8)° = 360°
So: 8x - 14 + 22x - 16 = 360°
<=> 30x - 30 = 360°
<=> 30(x - 1) = 360°
<=> x - 1 = 12
<=> x = 13°
We know: ∠G = ∠F = (11x - 8)° = ( 11.13-8)° = 135°
The answer: ∠G = 135°
Ok done. Thank to me :>
A car travels 15 km in 13 minutes. What is its average speed in km/h?
Answers
Answer:
69.45 km/hStep-by-step explanation:
Speed = Distance/Time=> Speed = 15 km ÷ 13/60 => Speed = 15 km ÷ 0.216=> Speed = 15 km/0.216=> Speed = 15 x 4.63/0.216 x 4.63=> Speed = 69.45 km/1 h (Approximate)Conclusion:
Therefore, the speed is 69.45 km/h (Approximate)Hoped this helped.
