Prove that the measures of the exterior angles of a triangle have a sum of 360°.
Given: <1, <2, and <3 are exterior angles.
Prove: m<1 +m<+m<3 = 360
Answers
Sum of Exterior Angles of Triangle is 360°.
Define Exterior Angle
The angle between any side of a shape and a line that extends from the next side is known as the exterior angle.
Let's Prove: ∠1 + ∠2 + ∠3 = 360°
The angle that is created between one of a triangle's sides and its adjacent extended side is known as the external angle. A triangle has three external angles. Let's learn about the equation for adding a triangle's exterior angles.
From the figure, we can observe that ∠1, ∠2, and ∠3 are the exterior angles of triangle ABC. We know that the sum of all the exterior angles of any polygon is equal to 360°.
Thus, sum of all the exterior angles of a triangle = 360°
Therefore, In triangle ABC the sum of exterior angles,
∠1 + ∠2 + ∠3 = 360°
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Related Questions
Calculate the height of a tree whose shadow is 20m shorter when the angle of elevation of the sun is 60 than when the angle of elevation is 30
Answers
The height of a tree whose shadow is 20m shorter when the angle of elevation of the sun is 60 is 17.3 meters.
What is elevation?The elevation is the distance above sea level. They are usually measured in meters or feet.
Let t be the height of the tree, then the length of the shadow will be:
Shadow length = t/tan(α)
where α is the angle of elevation. The difference in shadow lengths is:
20 m = t/tan(30°) -t/tan(60°) = t(√3 -1/√3)
= (20 m)/(2/√3) = 10√3 m
= 17.3 m
The height is 17.3 meters.
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a certain type of aluminum screen 2 feet in width has, on the average, three flaws in a 100-foot roll. we assume flaws occur randomly so the number of flaws follow some poisson distribution. what is the probability that the first 40 feet in a roll contain no flaws?
Answers
The probability of that the first 40 feet in a roll contain no flaws is ≈ .3012
What is probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
CalculationΘ = μ = [tex]\frac{100 foot}{3 flaws}[/tex]
a ) We assume that the length until the first flaw follows an exponential distribution.
Probability density function of exponential distribution:
f(x) = [tex]\frac{1}{Θ} e^{\frac{-x}{Θ} } = \frac{1}{100/3}e^{-x/(100/3)} = \frac{3}{100}e^{-3x/100}[/tex]
The first 40 feet in a roll of 100 feet contain no flaws if the first flaw occurs after 40 feet.
The probability is the integral over the corresponding interval:
the further calculation has been shown in fig. attached
since equation was not possible to write here
b) We assume that the length until the first flaw follows an exponential distribution.
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A table is made using the following two patterns.
Pattern x: Starting number: 3, Rule: add 3
Pattern y: Starting number: 6, Rule: add 6
Complete the table for the given patterns.
And then it asks to graph the points from 3 points
Answers
The rules of the patterns are 3 + 3x and 6 + 6y
How to complete the pattern?The patterns are given as:
Pattern x: Starting number: 3, Rule: add 3Pattern y: Starting number: 6, Rule: add 6For pattern x, we have the following highlights:
Start = 3
Rule = Add 3
This means that the nth term of pattern x is:
Pattern x = 3 + 3x
For pattern y, we have the following highlights:
Start = 6
Rule = Add 6
This means that the nth term of pattern y is:
Pattern y = 6 + 6y
The complete tableFor pattern x, set x = 0, 1, 2 and 3
So, we have
3 + 3x = 3 + 3(0) = 3
3 + 3x = 3 + 3(1) = 6
3 + 3x = 3 + 3(2) = 9
3 + 3x = 3 + 3(3) = 12
For pattern y, set y = 0, 1, 2 and 3
So, we have
6 + 6x = 6 + 6(0) = 6
6 + 6x = 6 + 6(1) = 12
6 + 6x = 6 + 6(2) = 18
6 + 6x = 6 + 6(3) = 24
Next, we plot the graphs of both patterns (see attachment) where the blue line represents pattern 1, and the other represents the second pattern
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what is the Riemann Hypothesis??
Answers
Answer:
lie on a certain vertical straight line
Step-by-step explanation:
In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics.
Garcia's bike rentals, it cost $38 to rent a bike for 9 hours. How many hours of bike use does the customer get per dollar. If necessary, round the answer to the nearest hundredth
Answers
From the question, we were told that Garcia's bike rentals cost $38 to rent bike for 9 hours.
We are to find how many hours will a customer use the bike per dollar.
This can also be likened to calculating miles per gallon.
if i can drive 300 miles on 10 gallons of gas then my miles per gallon is 300/10 = 30 mpg.
So, hours per dollar is also a division problem too.
(9 hours)/($38)
= 9/38
= 0.2368
= 0.24 hours per dollar (to the nearest hundredth)
Find the volume of the cylinder (rounded to the nearest tenth).9 in.3 in.
Answers
We have the next formula to calculate the volume of the cylinder
[tex]V=\pi r^2h[/tex]where
r is the radius
h is the height
in our problem
r=3in
h=9in
we substitute the values
[tex]V=\pi(3)^2(9)=254.46in^3[/tex]the volume round to the nearest tenth is V=254.5 in ^3
the denominator of a fraction is two more than the numerator. if both numerator and denominator are increased by ten, the simplified is 9/10. find the original fraction. (Do not simplify).
Answers
Give to each part of the fraction a variable (a letter)
Numerator: n
Denominator: d
the denominator of a fraction is two more than the numerator:
[tex]d=n+2[/tex][tex]\frac{n}{d}=\frac{n}{n+2}[/tex]both numerator and denominator are increased by ten, the simplified is 9/10:
[tex]\frac{n+10}{n+2+10}=\frac{9}{10}[/tex]Use the equation above to find the value of n:
[tex]\begin{gathered} 10(n+10)=9(n+12) \\ 10n+100=9n+108 \\ 10n-9n=108-100 \\ n=8 \end{gathered}[/tex]As n is equal to 8 find the value of d:
[tex]\begin{gathered} d=n+2 \\ d=8+2 \\ d=10 \end{gathered}[/tex]The original fraction is:
[tex]\frac{8}{10}[/tex]2-3x + 4 + x = -2x + 1
Answers
Answer:
No solution
Step-by-step explanation:
2- 3x + 4 + x = -2x + 1
2 -3x + 4 + x = -2x + 1
6 -3x + x = -2x + 1
6 -3x + x = -2x + 1
6 -2x = -2x + 1
6 -2x = -2x + 1
move -2x to the right by adding 2x on both sides
6 -2x = -2x + 1
+2x +2x
6 = + 1
is 6 equal to 1?
No, so No solution
Solve the system of linear equations using the substitution method.
2d + 8y = 20 and y = 2
A. (1, 1)
B. 4, 4
C. (1, 2)
D. (2, 2)
Answers
Answer:
D
Step-by-step explanation:
2d + 8y = 20
y = 2
substitute y = 2 into the other equation
2d + 8(2) = 20
2d + 16 = 20 ( subtract 16 from both sides )
2d = 4 ( divide both sides by 2 )
d = 2
solution is (2, 2 )
answer-> D. (2,2)
Given,
2d + 8y = 20 .............................................(Equation i)
y = 2 .............................................................(Equation ii)
substituting y = 2 in equation i, we get
2d + 8(2) = 20
2d + 16 = 20
2d = 20 - 16
2d = 4
d = 2
Hence the correct answer would be option D. (2,2)
We have used the substitution method to solve the given system of linear equations.
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The length of a rectangle is eight more than twice it's width. If the length is less than 34,then what is the width?
Answers
Answer:
width < 13
Step-by-step explanation:
let width of the rectangle = x
length = 8 + 2x
according to the question,
8+2x < 34
2x < 34-8
2x < 26
x < 13
Find the values of x and y.
Answers
Answer:
x=71 y=109
Step-by-step explanation:
-9^2 x 3
evaluate the experssion!!
Answers
Answer:
243
Step-by-step explanation:
-9^2 = -9 * -9 = 81
81 * 3 = 243
Wasif spent 1/3 of his income on housing and 2/5 on daily expenditure and save the rest if he save 24600 what was his income altogether
Answers
Answer:
61500
Step-by-step explanation:
1/3 = 3/15
2/5 = 6/15
1 - 3/15 - 6/15 = 6/15
6/15 = 24600
24600 ÷ 6 × 15 = 61500
Answer:
92250
Step-by-step explanation:
Forming algebraic equation and solving:
Let the income = x
Amount spent on housing = (1/3) of the income
[tex]\sf = \dfrac{1}{3}x[/tex]
Amount spent of daily expenditure = (2/5) of the income
[tex]\sf =\dfrac{2}{5}x[/tex]
Income = Savings + housing expenditure + daily expenditure
Income - housing expenditure - daily expenditure = savings
[tex]\sf x - \dfrac{1}{3}x-\dfrac{2}{5}x=24600\\\\\\\dfrac{x*15}{1*15}-\dfrac{1*5}{3*5}x-\dfrac{2*3}{5*3}x = 24600\\\\\\[/tex]
[tex]\sf \dfrac{15}{15}x-\dfrac{5}{15}x-\dfrac{6}{15}x = 24600\\\\\\\dfrac{(15 -5 - 6)}{15}x = 24600[/tex]
[tex]\sf \dfrac{4}{15}x = 24600[/tex]
[tex]\sf x = 24600 *\dfrac{15}{4}\\\\ x = 6150*15[/tex]
Income = 92250
A vacant lot is being converted into a community garden. The garden and a walkway around its perimeter have an area of 238 square feet. Find the width of the walkway if the garden measures 12 feet wide by 15 feet long.
Answers
Considering the area of the rectangular lot, the width of the walkway is of 3.9 feet.
What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that the area and the perimeter are given as follows:
The area is given by A = lw.The perimeter is given by P = 2(l + w).In the context of this problem, for the garden and the walkway, the dimensions are given as follows:
Length of 15 feet.Width of 12 + w, in which w is the width of the walkway.Considering that the area is of 238 square feet, we can solve for the width of the walkway as follows:
15(12 + w) = 238
12 + w = 238/15
12 + w = 15.9.
w = 15.9 - 12
w = 3.9 feet, which is the width of the walkway.
Since the area is in square feet, the length and the width are in feet.
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in Oak Grove, Erik bought a mattress that was marked down 70% from an original price of $500. If the sales tax in Oak Grove is 8%, what was the total cost of the mattress?
Answers
The mattress has a total cost of $24.28
How to determine the total cost for the mattress?From the question, the given parameters are:
Cost of a mattress = $74.95
Markdown = 70%
Sales tax in oak grove = 8%
Using the sales tax and the markdown, the total cost for the mattress is calculated using
Total cost of mattress = Cost of a mattress * (1 + Sales tax) * (1 - Markdown )
Substitute the known values in the above equation
So, we have the following equation
Total cost of mattress = 74.95 * (1 + 8%) * (1 - 70%)
Evaluate the products
Total cost of mattress = 24.28
Hence, the total cost of the mattress is $24.28
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a couple has four children. neither the father nor the mother is bald; one of the two sons is bald, but neither of the daughters is bald. (a) if one of the daughters marries a nonbald man and they have a son, what is the chance that the son will become bald as an adult? (b) if the couple has a daughter, what is the chance that she will become bald as an adult?
Answers
If one of the daughters marries a non-bald man and they have a son, the chance that the son will become bald as an adult is 0%
If the couple has a daughter, the chance that she will become bald as an adult is 0%
In the question, we have been given that the neither the father nor the mother is bald, and out of the four children only one son is bald, but the other son and the two daughters are not bald, now we solve the following:
Part a
A chance that the son will become bald as an adult:
If the daughter has no bald gene (XX), and she marries a non bald man then there is 0% chance that the son will become bald as an adult because neither the mom nor the dad has the baldness gene
Part b
The chance that she will become bald as an adult:
If the daughter having a bald gene ([tex]X^{b} X[/tex]) marries a non bald (XY)man then also there is a 0% chance that the daughter will be bald as an adult. As the baldness is a recessive trait, for the daughter to be bald she needs to have two baldness gene( one from father and one from mother). And since this is not the case the daughter might have baldness gene but the phenotype will be non-bald.
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WILL AWARD BRAINLIEST
Answers
I NEED HELP ASAP
What is the slope-intercept equation for the linear function represented by the
table?
A. y = -x +4
B. y =
-x-4
C. y = x-4
OD. y=x+4
0
x
2 4 6 8
y -4 -1 258
Answers
Answer: C : y = 3/2 - 4
Step-by-step explanation:
Find the Slope (Slope Formula)
(4,2) (6,5)
m = (5-2)/(6-4)
m = 3/2
Find "b"
y = mx + b (Slope intercept form)
2 = 3/2(4) + b
2 = 6 + b
-4 = b
need help again with a question
Answers
Answer: x = 58
Step-by-step explanation:
The angles are alternating interior angles. This means that the angles are equal.
So x = 58
2. Ryan is running in a 5-kilometer race. How many feet will he run in the race? Use the conversion rates 5, 280ft = 1mi and 1m i approx 1.61 km. Round to the nearest hundred feet
Answers
Answer:
16,400 ft
Step-by-step explanation:
You want to know the number of feet in a 5 km race, rounded to the nearest hundred. You are given conversion factors 5280 ft = 1 mi = 1.61 km.
Unit conversionUnit conversion can be done by multiplying by a conversion factor whose numerator is equal to its denominator, and that cancels unwanted units, replacing them with units you want.
[tex]5\text{ km}=5\text{ km}\times\dfrac{5280\text{ ft}}{1.61\text{ km}}\approx16397.5\text{ ft}\approx\boxed{16,\!400\text{ ft}}[/tex]
__
Additional comment
Both of the given conversions are equal to 1 mile, so their ratio is 1. We put feet on top of the fraction, because that is the unit we want. The km value is in the denominator so the km units in numerator and denominator cancel.
The conversion for km is 1 mi = 1.609344 km (exactly). The actual conversion to ft will give 16,404 76/381 ft. This has a very long repeating decimal fraction.
Please i really need help
Answers
Answer:
2:4 ratio (1:2)
2cups carrot + 4cups apple = 6cups (ratio 1:2)
Therefore 4cups carrot + 8 cups apple = 12 cups (ratio 1:2)
Hope that helps
solve each linear equation 7+2x=4x-3
Answers
Answer:
Simplifying
7 + 2x = 4x + -3
Reorder the terms:
7 + 2x = -3 + 4x
Solving
7 + 2x = -3 + 4x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4x' to each side of the equation.
7 + 2x + -4x = -3 + 4x + -4x
Combine like terms: 2x + -4x = -2x
7 + -2x = -3 + 4x + -4x
Combine like terms: 4x + -4x = 0
7 + -2x = -3 + 0
7 + -2x = -3
Add '-7' to each side of the equation.
7 + -7 + -2x = -3 + -7
Combine like terms: 7 + -7 = 0
0 + -2x = -3 + -7
-2x = -3 + -7
Combine like terms: -3 + -7 = -10
-2x = -10
Divide each side by '-2'.
x = 5
Simplifying
x = 5
If I stated 2 * - 3 OR -10/-5 what steps would you follow to find the factor/quotient and its sign? You may use these examples to explain.
Answers
If I stated 2 * - 3 OR -10/-5 then the factor/quotient and its sign is given by -6 and 2
What is a quotient in math?
The number that is being divided (in this case, 15) is called the dividend, and the number that it is being divided by (in this case, 3) is called the divisor. The result of the division is the quotient
What is quotient formula?
The quotient formula is given as follows: Dividend ÷ Divisor = Quotient (if the remainder is zero) The general formula for any division problem is given by: Dividend ÷ Divisor = Quotient + Remainder.
2 * -3 = -6 or -10/-5= 2
Thus the quotient is -6 and 2
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scores on the wechsler adult intelligence scale for the 20 to 34 age group are approximately normally distributed with mean 110 and standard deviation 15. how high must a person score to be in the top 5% of all scores? enter your answer as a whole number.
Answers
The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.
What is defined as the normal distribution?A normal distribution is a data set arrangement in which the majority of values cluster inside the center of the range and the remainder taper off symmetrically toward any extreme.A histogram inside a normal distribution curve is sometimes used to design the curve.The formula for the normal distribution is;
z = (x - μ)/σ
where,
z = z- score, taken fro tableMean μ = 110Standard deviation σ = 15Sample mean x.If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.
In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.
z = 1.7
Put the value in formula ad find x.
1. 7 = (x - 110)/15
x = 25.5 + 110
x = 135.5
x = 136 (whole number)
Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.
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Can you simplify 6:4 ?
Answers
yes, it is the same than 3:2. And we can not simplify it more
hello..as fast a possible I need the ans pls
Answers
Answer:
I think it's because the triangle sides are isometrics so that's why the sides are equal
when an integer is subtracted from 8 times the next consecutive integer, the difference is 71. Find the vale of the greater integer.
Answers
First, define variables for the integer and the next consecutive integer. Then set up an equation that represents the problem. Solve for x. Since x+1 is greater than x, insert your value into the expression and evaluate.
See details:
The value of the greater integer will be 10.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The algebraic expression is,
'' An integer is subtracted from 8 times the next consecutive integer, the difference is 71.''
Now,
Let a number = x
Then, Its consecutive number = (x + 1)
So, We can formulate;
⇒ 8 (x + 1) - x = 71
Solve for x as;
⇒ 8x + 8 - x = 71
⇒ 7x + 8 = 71
⇒ 7x = 71 - 8
⇒ 7x = 63
⇒ x = 9
Thus, The value of greater number = x + 1
= 9 + 1
= 10
Therefore, The value of the greater integer will be 10.
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-5 < 3x -8 / means greater than or equal to
Answers
Answer:
Equation: -5 <3× -8
+8. +8
3 <3x
_ _
3. 3
Answer: 1 = X
Step-by-step explanation:
Equation: -5 <3× -8
First Step: You must add 8 to -8 and move it to both sides. The reason why we do this is because on the left side we have 1 number and on the right side we have 2 numbers. We see that the right side has more numbers than the left, so we must move the -8 turning it to a positive 8 (8-8 cancels each other making 0) and adding the +8 in -8 to -5 as well, since we're adding to both sides.
Second Step: Since we added 8 to -5, it equals 3 now 8-5=3. Changing the equation to 3 <3x. Now we have to divide 3 to both sides as well, because we want the x to be by itself. So, 3 ÷ 3 = 1 and 3x ÷ 3 = x
Results: After our extraordinary calculations we recieve
the answer 1=x
Pleaseeeeeeeee helpppp
Answers
Answer:n= -129/t
im not sure if thats the answer ur looking for
antonio is comparing the crowdedness at three different sports events. which 222 ways could antonio find the least crowded event? choose 2 answers: choose 2 answers: (choice a) a find the least people per square meter. (choice b) b find the most people per square meter. (choice c) c find the least square meters per person. (choice d) d find the most square meters per person
Answers
The best possible ways to compare least crowded place are options A and D
Given that,
Antonio is comparing the crowdedness at three different sports events. Our aim to find the least crowded sporting event. Here we use square meter as measurement for population. So it is pretty obvious that a place is less crowded when people in that region are less in number. So the option A is correct which is less people per square meter. Similarly, option D is also correct because if a person have more square meters then it is clear that the region is less populated .
Therefore, the options A and D are the go-to ways to compare the least crowdedness in the sporting events.
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Answer:
The things that you need to pick are option A and option D. Trust me on this, I did the exact same question and I got is correct. Also please please please pick me as Brainliest... or y'know don't... and then feel bad.