I will add you as BRAINLIEST if you can get it right! Someone Plz help!!!
Triangles ABC and DEF are similar.
Part 1: Find the lenght of segment DF (rounded to the nearest hundreth) _____ units.
Part 2: Find the lenght of segment EF (rounded to the nearest hundreth) _____units.
Find the ratio of the similar known sides:
1.34/2 = 0.67
The smaller triangle is 0.67 the size of the larger one.
Multiply the similar sides by the ratio:
DE = 4 x 0.67 = 2.68
FE = 3 x 0.67 = 2.01
Answer:
Find the ratio of the similar known sides:
1.34/2 = 0.67
The smaller triangle is 0.67 the size of the larger one.
Multiply the similar sides by the ratio:
DE = 4 x 0.67 = 2.68
FE = 3 x 0.67 = 2.01
Step-by-step explanation:
Jackson is working two summer jobs, landscaping and clearing tables. He must work
no less than 14 hours altogether between both jobs in a given week. Write an
inequality that would represent the possible values for the number of hours
landscaping, l, and the number of hours clearing tables, c, that Jackson can work in a
given week.
The inequality l + c ≥ 14 accurately represents the minimum total hours Jackson must work in both his jobs, landscaping and clearing tables, in a week.
Explanation:The subject of this question is Mathematics, more specifically it involves the topic of inequalities. The grade level of this question would be high school as it deals with algebraic concepts.
The inequality that represents the number of hours that Jackson can work in a given week in landscaping (l) and clearing tables (c) would be l + c ≥ 14. This inequality allows for the total number of hours worked to be equal to or more than 14, as stipulated in the conditions.
This represents the total amount of hours Jackson can work in both jobs simultaneously. This inequality is valid as long as he works at least 14 hours, in total, from both jobs.
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Which equation in slope-intercept form represents a line that is parallel to y=−4x−5 and passes through the point (0,0)?
y=4x−7
y=4x−9
y=−4x
y=−4x−7
y=−14x−5
Answer:
[tex]\displaystyle y = -4x[/tex]
Step-by-step explanation:
0 = 0 ± b
[tex]\displaystyle 0 = b \\ \\ y = -4x[/tex]
* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so −4 remains the way it is.
I am joyous to assist you anytime.
Heyo! ;D
The equation in slope-intercept form that represents a line that is parallel to y = -4x - 5 and passes through the point (0,0) would be Option C) y = -4x.
Hope this helps! If so, please lmk! Tysm!
The ratio of the side lengths of two squares is 2:5. What is the ratio of the areas of the same two squares?
Answer:
4 : 25
Step-by-step explanation:
Given the ratio of sides = a : b, then
ratio of areas = a² : b²
Thus
ratio of sides = 2 : 5, then
ratio of areas = 2² : 5² = 4 : 25
Writing an equation of the form A/x+B)C to solve a word probl...
Trey has a part-time job and gets pald the same amount each hour. For each hour he works, he puts $2 aside for his mom. Trey works 7 hours a day and the
total amount he keeps each day is $56. How much does he get paid each hour?
(a) Write an equation that could be used to answer the
question above. First, choose the appropriate form. Then,
fill in the blanks with the numbers 2, 7, and 56. Leth
represent the amount (in dollars) Trey gets paid each hour.
(b) Solve the equation in part (a) to find the amount (in
dollars) Trey gets paid each hour.
h =
Answer:
(a) The equation is [tex]7h-2=56[/tex].
(b) Trey gets approximately $8.29 for each hour of work.
Step-by-step explanation:
Given:
Number of hours Trey works = 7
Amount of money he put aside for mom = $2
Total Amount he keeps each day = $56
We need to find the amount he gets for each hour.
Let 'h' represent the amount (in dollars) Trey gets paid each hour.
Solving for part (a).
We need to write the equation to find the amount he gets paid for each hour.
Now we can say that;
Total Amount he keeps each day is equal to Number of hours Trey works multiplied by the amount he gets paid for each hour minus Amount of money he put aside for mom.
framing in equation form we get;
[tex]7h-2=56[/tex]
Hence the equation is [tex]7h-2=56[/tex].
Solving for part (b).
we need to solve the above equation to find the amount he gets paid for each hour.
On solving the equation we get;
Adding both side by 2 we get
[tex]7h-2+2=56+2\\\\7h=58[/tex]
Now Dividing both side by 7 using Division Property we get;
[tex]\frac{7h}{7} = \frac{58}{7}\\\\h \approx \$8.29[/tex]
Hence Trey gets approximately $8.29 for each hour of work.
What is the cross-section of a cone that is perpendicular to the base? Rectangle that is perpendicular to the base? Cylinder that is parallel to the base? Triangular Prism that is parallel to the base? (urgent now please answer)
Answer:
1. Triangle or trapezoid.
2. A line
3. Circular
4. Triangular.
Step-by-step explanation:
1. The cross-section of a cone that is perpendicular to the base either of a shape of a triangle or a trapezoidal shape.
If we make the cross-section along the diameter of the base circle then the cross-section will be a triangle and otherwise, it will be of trapezoidal shape.
2. The cross-section of a rectangle that is perpendicular to the base is line only because a rectangle is a two-dimensional shape and if we cut it perpendicularly to the base it will give a line.
3. The cross-section of a cylinder that is parallel to the base is a circle only.
Because the shape of a cylinder is constantly circular along the vertical axis.
4. The cross-section of a triangular prism that is parallel to the base is a triangle only.
Because the shape of a triangular prism is constantly triangular along the vertical axis. (Answer)
12. The results of an election for mayor are shown
at the right. Which candidate received the
most votes and which received the least votes?
DATA
Candidate
Leonard Hansen
Margaret O'Connor
Jillian Garcia
Number of Votes
12,409
12,926
12,904
Answer:
Assuming the group of the candidates is ordered the same way as the votes they received, Margaret O'Conner received the MOST votes, at 12,926, while Leonard Hansen received the LEAST votes, at 12,409.
I can do this with Emma and Jacob or shopping in the store they notice to Cashiers are applying the discounts differently the cashier on the left is taking 20% off the total bill then subtracting $10 the cashier on the right is subtracting 10 first and then taking the 20% off the total who's getting the better deal
Answer: the person on the left
Step-by-step explanation:
by taking 20% off of the total cost first they are getting the better deal.
The customer gets a better deal from the cashier on the left. Explanation on determining the better deal between two cashiers based on how they apply discounts.
To determine who is getting the better deal, let's compare the total bill after discounts for both cashiers:
Cashier on the left: 20% off, then subtract $10
Cashier on the right: Subtract $10 first, then 20% off
Example Calculation:
If the total bill is $100:
Left cashier: $100 - 20%($100) = $80, then $80 - $10 = $70
Right cashier: $100 - $10 = $90, then 20%($90) = $18, so $90 - $18 = $72
In this scenario, the customer gets a better deal from the cashier on the left.
Mixed number equations that equal 10.
Please hurry.
Answer:
Mixed number equation equals to 10=[tex]9\frac{9}{9}[/tex]
Step-by-step explanation:
Here we have to find mixed number equation that equal 10,
Let, x=10 ------------(equation 1)
Now multiplying both side of equation 1 by 10 we get,
[tex]x\times 10=10\times 10[/tex]
[tex]10x=100[/tex] ------------------(equation 2)
Now by subtracting equation 1 from equation 2 we get,
[tex]10x-x=100-10[/tex]
[tex]9x=90[/tex]
[tex]\therefore\ x=\frac{90}{9}[/tex] ------------------(equation 3)
Equation 3 can be written as,
[tex]x=9\frac{9}{9}[/tex]
Since, [tex]9\frac{9}{9} [/tex]
[tex]= \frac{(9\times 9)+9}{9}[/tex]
[tex]=\frac{81+9}{9}[/tex]
[tex]=\frac{90}{9}[/tex][/tex]
[tex]\therefore 9\frac{9}{9}=\frac{90}{9}[/tex]
Therefore mixed number equation that equals 10=[tex]9\frac{9}{9}[/tex]
What is the period of the function?
Identify the period of a periodic function from its graph. π 2π 4π 8π
PLEASE HURRY
Answer:
4π
Step-by-step explanation:
Period is whenever a wave repeats itself. I highlighted the period.
The Period of the given function is 0 to 4π.
What is Period of Function?The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function.
Here, graph starts from 0 and goes down. After π our graph starts increasing and acheive maximum at 3π and then start coming down to y = 0 at 4π.
It means that from 0 to 4π graph complete its one cycle and in the same trend it start repeating again.
Thus, the Period of the given function is 0 to 4π.
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When Julia is writing a first draft, there is 0.7 probability that there will be no spelling mistakes on a page. One day, Julia writes a first draft that is 4 pages long. Assuming that Julia is equally likely to have a spelling mistake on each of the 4 pages, what is the probability that she will have no spelling mistakes on at least one of them?
Answer:
The required probability is given by, 0.9919.
Step-by-step explanation:
Let, X be the random variable denoting the no. of pages among those 4 pages which Julia writes where she makes no spelling mistake.
clearly,
X [tex]\sim[/tex] Binomial (4, 0.7)
So, P(X = x) = [tex]^4C_{x} \times (0.7)^{x} \times (0.3)^{(4 - x)}[/tex]
[when x = 0, 1, 2, 3, 4]
= 0 otherwise
According to the question, we are to find out P(X ≥ 1) .
Now, P(X ≥ 1)
= 1 - P(X = 0)
= [tex] 1 - (^4C_{0} \times (0.7)^{0} \times (0.3)^{4})[/tex]
= [tex] 1 - 0.0081[/tex]
= 0.9919
So, the required probability is given by, 0.9919
The probability that Julia will have no spelling mistakes on at least one of the pages is approximately 99.19%.
To determine the probability that Julia will have no spelling mistakes on at least one of the four pages she writes, we can first find the probability that she will make at least one spelling mistake on all four pages and then subtract this from 1.
The probability that there will be a spelling mistake on a page:
= 1 - 0.7 = 0.3.
Since the probability of a spelling mistake on each page is independent, we can multiply the probabilities for the four pages together.
The probability of at least one mistake on all four pages:
= 0.3 x 0.3 x 0.3 x 0.3 = 0.3⁴= 0.0081.
The probability that there will be no spelling mistakes on at least one page
= 1 - 0.0081 = 0.9919 or about 99.19%.
So, the probability is 99.19%.
Consider the net of a triangular prism where each unit on the coordinate plane represents four feet. If a sheet of plywood measures 4 ft x 8 ft, how many sheets of plywood will a carpenter need to build the prism?
A) 2
B) 3
C) 4
D) 5
Answer:
2 sheets of plywood will be needed.
Step-by-step explanation:
See the attached diagram.
Each three square plywood has area 1 units by 3 units = 4 feet by 12 feet = 48 feet square. {Since each unit on the coordinate plane represents four feet}
Now, the two triangular plywood has area half of a unit square area.
So, two triangular plywood has total area = 1 unit by 1 unit = 4 feet by 4 feet = 16 feet square.
Therefore, the total area of plywood required to make the triangular prism is (48 + 16) = 64 feet square.
Now, if a sheet of plywood measures 4 ft by 8 ft i.e. 32 feet square, then the carpenter will need [tex]\frac{64}{32} = 2[/tex] such sheets of plywood. (Answer)
Answer:A
Step-by-step explanation: HI
What is the reason for each step in the solution of the equation? -3(4-6x)
Answer:
-12+18x
Step-by-step explanation:
-3(4-6x)=-12+18x
Mr. Harris is packaging items to give to his students. He has 48 pencils and 30 notebooks. He wants each package to contain the same number of pencils and the same number of notebooks.
Answer:
The maximum number of packages that can be made with each package have same number of each item is = 6
Step-by-step explanation:
Given:
Mr. Harris has 48 pencils and 30 notebooks.
To find the number of packages he can make with each package have same number of each item.
Solution:
Number of pencils = 48
Number of notebooks = 30
In order to find the number of packages he can make with each package have same number of each item, we will find the greatest common factor of the given numbers.
To find the G.C.F., we will list down the prime factors of each.
[tex]48=2\times 2\times 2\times 2\times 3[/tex]
[tex]30=2\times 3\times 5[/tex]
We find that the G.C.F. = [tex]2\times 3[/tex] = 6
Thus, the maximum number of packages that can be made with each package have same number of each item is = 6
I have been asked this question and I substituted the value of x in f with g(x), and rearranged the equality but is incorrect.
Answer:
if fg(x)=6x+q
then f(gx) =6x+q
3(px+4)+p =6x+q
3px+12+p = 6x+q
3px+p = 6x+q-12
make p the subject
p( 3x+1) = 6x+q-12
p= (6x + q -12 )/ 3x +1
Answer:
p = 2 and q = 14
Step-by-step explanation:
f(g(x)) = 3(px + 4) + p
f(g(x)) = 3px + 12 + p
6x + q = 3px + 12 + p
The trick here is to equate the coefficients.
6 = 3p and q = 12 + p
p = 2 and q = 14
Mike wants a job as car salesmen. He receives two job offers.
• Hudson cars dealership offers Mike a salary of $2500 per month, plus a commission of
$200 on every car he sells.
• Kennedy used cars dealership offers Mike a salary of $2000 per month, plus a
commission of $250 on every car he sells.
Let T represent the total monthly earning, in dollars, and let n represent the number of cars sold in a
month. For each company, write an equation that represents the relationship between T and n.
Hudson: T = 200n + 2500
Kennedy: T = 250n + 2000
im no math teacher but i do a ton of questions like these, hope this helps
The equation for Mike job which represents the relationship between T and n for Hudson cars is $2500+$200n and for Kennedy used cars is $2000+$250n.
What is linear equation?A linear equation is the equation in which the highest power of the unknown variable is one.
Mike wants a job as car salesmen. He receives two job offers.Let T represent the total monthly earning, in dollars, and let n represent the number of cars sold in a month.
Hudson's cars dealership offers Mike a salary of $2500 per month, plus a commission of $200 on every car he sells. Then the equation for this company is,
[tex]T=2500+200n[/tex]
Kennedy used cars dealership offers Mike a salary of $2000 per month, plus a commission of $250 on every car he sells. Thus, he equation for this company is,
[tex]T=2000+250n[/tex]
Hence, the equation for Mike job which represents the relationship between T and n for Hudson cars is $2500+$200n and for Kennedy used cars is $2000+$250n.
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Round the fraction to the nearest one-half. Start Fraction 14 over 27 End Fraction A. 0 B. one-half C. 1
To round the fraction 14/27 to the nearest one-half, the answer would be 0 (choice A).
Explanation:To round the fraction to the nearest one-half, we need to determine if the fraction is closer to zero, one-half, or one. Start by identifying which two one-half intervals the fraction falls between: 13/27 (closer to zero) and 15/27 (closer to one-half). As 14/27 is closer to 13/27, the answer is A. 0.
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For the function ƒ(x) = x2 – 4, find the value of ƒ(x) when x = 6.
Answer:8
Step-by-step explanation:They said f(x)=x2–4 and they said find the value of f(x) when x=6
When x=6 you equate the value of x into the question
F(6)=6*2–4=8
Therefore the value of f(x) is 8
Can anyone help me solve this.I need proper equation..Thanks
Answer:
y = 9[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex]
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9}{y}[/tex]
Multiply both sides by y
y × sin45° = 9, that is
y × [tex]\frac{1}{\sqrt{2} }[/tex] = 9
Multiply both sides by [tex]\sqrt{2}[/tex]
y = 9[tex]\sqrt{2}[/tex]
Answer: ?=9
√2
Step-by-step explanation:
x=9 =a side of squre
y=diagonal
use equation :
y=a√2
y=9√2
y=12.69
Mindy and Troy combined ate 9 pieces of cake. Mindy ate 3 pieces of cake and Troy at 1/4 of the whole cake. Find C, the total pieces of cake. Also include the equation
Answer:
The total pieces of cake are 24
Step-by-step explanation:
Linear equations
It's a relation between one or more variables and or numbers, connected with the equal sign. An example is 4x-5=7, or 2(x+y)=7-(x-y)
This problem can be easily solved without the use of equations, but we are required to.
We know Mindy and Troy combined ate 9 pieces of cake, we also know that Mindy ate 3 pieces of cake. It leaves 6 pieces to Troy. Since Troy ate 1/4 of the whole cake, then
[tex]\displaystyle \frac{1}{4}X=6[/tex]
Where X is the number of pieces of cake
Solving for X
[tex]X=(4)(6)=24\ pieces[/tex]
Jane evaluates x squared minus 3 x + 5 for x = negative 2 below.
Step 1: (negative 2) squared minus 3 (negative 2) + 5
Step 2: Equals negative 4 + 6 + 5
Step 3: Equals 7
What, if any, was Jane’s mistake?
Jane made no mistakes.
Jane incorrectly evaluated (negative 2) squared in step 2.
Jane incorrectly added the terms in step 3.
Jane incorrectly substituted in x = negative 2 in step 1.
Answer:
B On 2020 edge
Step-by-step explanation:
Karli and her friend can paint 6/7 of a picture in 3/14 of an hour. How many pictures can they paint in a full hour?
Answer:
4 pictures
Step-by-step explanation:
(6/7)/(3/14)=x/1
cross product
3/14*x=6/7*1
3/14x=6/7
x=(6/7)/(3/14)
x=(6/7)(14/3)
x=(6/1)(2/3)
x=12/3
x=4
The number of pictures which Karli and her friend can paint in a full hour is equal to 4 pictures.
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.
It is given that Karli and her friend can paint 6/7 of a picture in 3/14 of an hour.
Let's assume they can paint x number of pictures in a full hour.
So , the fraction by dividing 6/7 by 3/14 can be written equal to x .
i.e.,
[tex]\frac{6/7}{3/14}[/tex] = x
We need to do the cross product here :
[tex]\frac{3}{14}[/tex] × x = [tex]\frac{6}{7}[/tex]
or
x = ([tex]\frac{6}{7}[/tex]) ÷ ([tex]\frac{3}{14}[/tex])
We know that when dividing two fractions we need to change the division sign to multiplication sign by inverse the fraction value right to the division sign i.e.,
x = ([tex]\frac{6}{7}[/tex]) × ([tex]\frac{14}{3}[/tex])
x = 84 / 21
x = 4
Therefore , the number of pictures which Karli and her friend can paint in a full hour is equal to 4 pictures.
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the greatest of four consecutive even integers is 14 less than twice the smallest integer. what are the integers
The four consecutive even integers are 20, 22, 24, 26
Solution:
Let the four consecutive even integers are a , a + 2, a + 4, a + 6
Let "a" be the smallest integer and "a + 6" be the largest integer
To find: the four consecutive even integers
Given that the greatest of four consecutive even integers is 14 less than twice the smallest integer
largest integer = twice the smallest integer - 14
a + 6 = 2(a) - 14
a + 6 = 2a - 14
a - 2a = -14 - 6
-a = -20
a = 20
Thus the four consecutive even integers are:
a = 20
a + 2 = 20 + 2 = 22
a + 4 = 20 + 4 = 24
a + 6 = 20 + 6 = 26
Thus the four consecutive even integers are 20, 22, 24, 26
(-8)-(6+30i) Express your answer in the form (a+bi)
Answer:
-14 - 30 i
Step-by-step explanation:
We recall that when combining complex numbers, we need to combine the real parts among themselves to get the new real part, and the imaginary parts among themselves to get the imaginary part of the new complex that results from the operation.
In our case the firs complex number is "-8" which consists of strictly real part (with zero imaginary part). The second complex number is (6+30 i) which has real part = 6 and imaginary part = 30 i.
now we operate separately on the real parts and on the imaginary parts performing the requested subtraction:
Real part: -8 - 6 = -14
Imaginary part: 0 i - 30 i = -30 i
Therefore the final complex number that results from this subtraction is: "-14 - 30 i"
Fatima conducted an experiment where she asked people to estimate the temperature of glasses of water. She recorded how far the estimates were from the actual temperatures, using positive values for guesses that were too high and negative values for guesses that were too low. Her results are in the table below.
Answer:3/4
Step-by-step explanation
Person A: -3 +(-1) + 0
+ =-2
And you divide by 12 and get
9/12=3/4
Answer: 3/4
Step-by-step explanation:
Which is the same as 7/3?
Which is the same as 73?
CLEAR CHECK
7÷13
3÷7
17 of 3
7 divided by 3
Answer:
D) 7 divided by 3
Step-by-step explanation:
Answer:
7 divided 3
Step-by-step explanation:i got it correct
OUTCOME 4: There is a 70% Chance that a student will pass a statistics course if I randomly choose a group of five students find the probability that exactly two will pass the course and explain how you derived your solutions
Answer:
The required probability is [tex]\frac{1323}{10000}[/tex]Step-by-step explanation:
It is given that The chance, that a student will pass the statistic course is [tex]\frac{70}{100}[/tex]
Hence, The chance that a student will fail in the statistic course is [tex]\frac{100 - 30}{100} = \frac{30}{100}[/tex]
Any 2 students from the total of 5 students can be choosen in [tex]^{5}C_2 = \frac{5!}{3! \times2!} = 10[/tex] ways.
Hence, the probability will be [tex]10\times [\frac{70}{100}] ^{2} \times[\frac{30}{100} ]^{3} = \frac{49\times27}{10000} = \frac{1323}{10000}[/tex]
Final answer:
The probability that exactly two students will pass the statistics course is approximately 30.87%.
Explanation:
To find the probability that exactly two students will pass the statistics course, we can use the binomial probability formula. The formula is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
In this case, n = 5 (number of students), k = 2 (number of students passing), and p = 0.7 (probability of passing).
Plugging in these values, we get:
P(X = 2) = C(5, 2) * 0.7^2 * (1 - 0.7)^(5 - 2)
Calculating, we find that P(X = 2) ≈ 0.3087, or approximately 30.87%.
in a game of tug of war your team changes -1 3/10 feet in position every 10 seconds. What is your change in position after 30 seconds?
To calculate the change in position after 30 seconds, multiply the rate of change per 10 seconds, which is -1 3/10 feet, by the number of 10-second intervals in 30 seconds, resulting in a total change of -3 9/10 feet or -3.9 feet.
If your team changes its position by -1 3/10 feet every 10 seconds in a tug of war game, we need to find out the change in position after 30 seconds.
Since the change in position is consistent over time, we can calculate the total change by multiplying the rate of change per 10 seconds by the number of 10-second intervals in 30 seconds.
The number of 10-second intervals in 30 seconds is:
30 seconds / 10 seconds per interval = 3 intervals.
The total change in position is then:
-1 3/10 feet/change × 3 changes = (-1 × 3)+(3/10 × 3)
= -3 9/10 feet or -3.9 feet.
Your team's change in position after 30 seconds is -3 9/10 feet or -3.9 feet.
You and your friend are selling magazine subscriptions. You sell 8 fewer magazine subscriptions than your friend. Together you sell 42 magazine subscriptions
The question is incomplete, here is the complete question:
You and your friend are selling magazine subscriptions. You sell 8 fewer magazine subscriptions than your friend. Together you sell 42 magazine subscriptions. Write a system of linear equations that represents this situation.
The system of linear equations that represents this situation is:
x + y = 42
x - y = 8
Step-by-step explanation:
To solve the problem assume that
x represent the number of magazine subscriptions that your friend selly represents the number of magazine subscriptions that you sell∵ Your friend sells x magazine subscriptions
∵ You sell y magazine subscriptions
∵ Together you sell 42 magazine subscriptions
∴ x + y = 42 ⇒ (1)
∵ You sell 8 fewer magazine subscriptions than your friend
∵ Your friend sells x magazine subscriptions
∵ You sell y magazine subscriptions
- That means y = x - 8
∴ y = x - 8
- Add 8 for both sides
∴ 8 + y = x
- Subtract y from both sides
∴ 8 = x - y
- Switch the two sides
∴ x - y = 8 ⇒ (2)
The system of linear equations that represents this situation is:
x + y = 42
x - y = 8
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Find the length of an arc
made by an 80° central
angle in a circle with a
10 ft. radius.
I'm not an expert at this but the answer should be 13.9 or 14
Final answer:
The length of the arc made by an 80° central angle in a circle with a 10 ft. radius is approximately 13.96 ft.
Explanation:
In order to find the length of an arc made by an 80° central angle in a circle with a 10 ft. radius, we need to use the formula for the circumference of a circle. The formula for the circumference is C = 2πr, where C is the circumference and r is the radius. In this case, the angle is 80°, so we need to find the fraction of a full circle that the angle represents. Since a full circle is 360°, the fraction is 80/360 = 2/9. Therefore, the length of the arc is 2/9 times the circumference of the circle with a 10 ft. radius.
To find the circumference of a circle with radius 10 ft., we can use the formula C = 2πr. Plugging in the value of the radius, we get C = 2π(10) = 20π ft. Since the length of the arc is 2/9 times the circumference, the length of the arc is (2/9)(20π) ft. Simplifying, we get (40/9)π ft. This is approximately 13.96 ft. Therefore, the length of the arc made by an 80° central angle in a circle with a 10 ft. radius is approximately 13.96 ft.