______________________________
1.) Combine x and 3x:\(x+3x=4x\)
- We combine the \((x)\) variables because to get to the end sum of the equation, there can only be 1 variable. So to get the 1, you combine like terms.
2.) Add 19 to both sides:\(-19+19=\) Cancels Out\(17+19=36\)
- We do this to get 1 number left over. To do this you do the opposite of what you see. In this case we have a negative 19, so you add 19 on each side of the equals.
3.) Divide both sides by 4:\(4x\) ÷ \(4=x\)\(36\) ÷ \(4=9\)
- We do this to get x alone. To do this you do the opposite of what you see. In this case we have \(4(x)\) which is multiplying, so you divide by 4 on each side.
So your answer is \(\bold{x=9}\).
______________________________
An urn contains five red and three blue balls. Suppose that four of these balls are selected at random and transferred to a second urn, which is originally empty. If a random chosen ball from this second urn is blue, what is the probability that two red and two blue balls were transferred from the first urn to the second urn.
The probability that two red and two blue balls were transferred from the first urn to the second urn is 0.27 (approx).
What is probability ?
Probability is a measure of the likelihood or chance of an event occurring. It is a mathematical concept that ranges from 0 (indicating an impossible event) to 1 (indicating a certain event).
Let R1 be the event that the first ball drawn from the first urn is red, and let B1 be the event that the first ball drawn from the first urn is blue. Similarly, let R2 and B2 be the events that the second and third balls drawn from the first urn are red and blue, respectively. Finally, let B be the event that a blue ball is drawn from the second urn.
We want to find P(R2=2, B2=2 | B), the probability that two red and two blue balls were transferred from the first urn to the second urn, given that a blue ball was drawn from the second urn.
By Bayes' theorem, we have:
P(R2=2, B2=2 | B) = P(B | R2=2, B2=2) * P(R2=2, B2=2) / P(B)
To find each of these probabilities, we can use the following:
P(R2=2, B2=2) = (5 choose 2) * (3 choose 2) / (8 choose 4) = 15/56, which is the probability of selecting 2 red and 2 blue balls from the first urn.
P(B | R2=2, B2=2) = 2/4 = 1/2, which is the probability of drawing a blue ball from the second urn, given that 2 red and 2 blue balls were transferred from the first urn.
P(B) = P(B | R2=0, B2=4) * P(R2=0, B2=4) + P(B | R2=1, B2=3) * P(R2=1, B2=3) + P(B | R2=2, B2=2) * P(R2=2, B2=2), which is the total probability of drawing a blue ball from the second urn.
To find P(R2=0, B2=4), we need to use the complement rule:
P(R2=0, B2=4) = 1 - P(R2=1, B2=3) - P(R2=2, B2=2)
To find P(R2=1, B2=3), we can use:
P(R2=1, B2=3) = (5 choose 1) * (3 choose 3) / (8 choose 4) = 5/56
Substituting all these values into Bayes' theorem, we get:
P(R2=2, B2=2 | B) = (1/2) * (15/56) / P(B)
To find P(B), we can use the law of total probability:
P(B) = P(B | R2=0, B2=4) * P(R2=0, B2=4) + P(B | R2=1, B2=3) * P(R2=1, B2=3) + P(B | R2=2, B2=2) * P(R2=2, B2=2)
Substituting the values we found earlier, we get:
P(B) = (0/4) * (1 - 5/56 - 15/56) + (1/4) * 5/56 + (2/4) * 1/2 = 0.27 (approx)
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A 120 120 -volt battery is connected to a circuit with 30 30 ohms of resistance. The current in amperes c c flowing through the circuit can be found using the equation 30c=120 30c=120 . How many amperes of current are there in the wire?
Answer:
just divide 120 divided by 30 is 4 I know it right bc I had the same question on into math if thats what you were on
Step-by-step explanation:
if he always online on messenger but take too long to respond to u or not at all, what does that mean ?
Answer: prob cheatin' on you
Step-by-step explanation: or died-
one wall of patel's bedroom is 13 feet wide and 8 feet tall. a window on the wall is 3 feet high and 6 feet long. how much wallpaper would patel need to cover this wall.
Patel would need 86 square feet of wallpaper to cover this wall.
To calculate how much wallpaper Patel would need to cover the wall, we need to first calculate the area of the wall. The formula for the area of a rectangle is length x width. So the area of Patel's wall would be:
13 feet x 8 feet = 104 square feet
Next, we need to subtract the area of the window, as we don't need to cover that part of the wall. The area of the window would be:
3 feet x 6 feet = 18 square feet
So the area of the wall that needs to be covered with wallpaper would be:
104 square feet - 18 square feet = 86 square feet
Therefore, Patel would need 86 square feet of wallpaper to cover this wall.
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Complete the steps in order to write the inverse of f(x) = x + 5
1.
= x + 5
2.
= y + 5
3.
= y
4.
= x – 5
The complete order of the inverse function of the function f(x) = x + 5 is:
1. y = x + 5
2. x = y + 5
3. x - 5 = y
4. y = x - 5
How to complete the steps in order to write the inverse of f(x) = x + 5?The function is given as:
f(x) = x + 5
The opposite of the function f(x) = x + 5 is the inverse of the function.
So, we have:
f(x) = x + 5
Express f(x) as y
y = x + 5
Swap the positions of x and y
x = y + 5
Make x the subject of the formula
x - 5 = y
Rewrite as:
y = x - 5
Hence, the inverse function of the function f(x) = x + 5 is y = x - 5
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The owners of the Burger Emporium are looking for new supplier of onions for their famous hamburgers. It is important that the onion slice be roughly the same diameter as the hamburger patty. After careful analysis, they determine that they can only use onions with diameters between 9 and 10 cm. Company A provides onions with diameters that are approximately normally distributed with mean 10.3 cm and standard deviation of 1.2 cm. Company B provides onions with diameters that are approximately normally distributed with mean 10.6 cm and standard deviation of 0.9 cm. Which company provides the higher proportion of usable onions? Justify your choice with an appropriate statistical argument using proportions.
Answer:
Follows are the solution to this question:
Step-by-step explanation:
Let assume that X and Y reflect the diameters of onions by companies A and B.
\(\to P(9<X<10) = P(\frac{9-10.3}{1.2} < Z < \frac{10-10.3}{1.2} )\\\\\)
\(= P(-1.0833 < Z < -0.25)\\\\= P(Z < -0.25) - P(Z<-1.0833)\\\\= 0.2620\\\\\\\)
\(\to P(9<Y<10) = P(\frac{9-10.6}{0.9} < Z < \frac{10-10.6}{0.9} )\\\\\)
\(= P(-1.7778 < Z < -0.6667)\\\\= 0.2148\\\\\)
As a result, onions through company A are chosen and they're more likely to be accepted.
Which of the following represents 20 = 5 x 4
A. 5 is 4 times as many as 20
B. 20 is 2 times as many as 10
C. 4 is 5 times as many as 20
D. 20 is 5 times as many as 4
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
the answer is d because
20 is "=" 5 times "×" as 4
so the formula derived is
20= 5x4
is represents =
times represents ×
hope you get it
Lakshmi wants to start saving coins in a piggy bank. Her mother gave her 3 quarters and 2 pennies on Monday and 2 dimes and 1 nickel on Tuesday. Fill in the amounts of money that lakshmi’s mother gave her in the space provided below.
Answer:
Monday - $0.77 Tuesday - $0.25 Total - $1.02
Step-by-step explanation:
Monday- 3 quarters (quarters are 25cents) plus 2 pennies (pennies are 1cent each)
25+25+25+1+1=77cents
Tuesday-2 dimes (dimes are 10cents) plus 1 nickel (nickels are 5cents)
10+10+5=25 cents
Total-
.77+.25=$1.02
She has - Monday - $0.77 Tuesday - $0.25 Total - $1.02
What is rate conversion?An exchange rate tells you the value of your currency in another currency.
Given that, Lakshmi wants to start saving coins in a piggy bank. Her mother gave her 3 quarters and 2 pennies on Monday and 2 dimes and 1 nickel on Tuesday.
Monday- 3 quarters (quarters are 25 cents) plus 2 pennies (pennies are 1 cent each)
25+25+25+1+1=77 cents
Tuesday- 2 dimes (dimes are 10 cents) plus 1 nickel (nickels are 5 cents)
10+10+5=25 cents
Total-
0.77+0.25=$1.02
Hence, She has - Monday - $0.77 Tuesday - $0.25 Total - $1.02
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May I have some help please?
Answer:
If this is solving for a hypotenuse, the answer is 8.
Step-by-step explanation:
a^2 + b^2 = c^2
6^2 b^2 = 10^2
36 + b^2 = 100
100 - 36 = 64
The square root of 64 is 8.
How would I show my work for this?
Answer:
4x4 = 16 √16=4
Step-by-step explanation:
Answer:
sqrt (16)
= sqrt (4×4)
= 4
Step-by-step explanation:
brainliest plz
Use the distributive property to multiply the trinomial by the binomial.Circle the first term in the trinomial, multiply it by each term in the binomial, and place each result in the blank spaces provided. Repeat this process for the second and third terms of the trinomial until all of the spaces are filled in. Finally, in the space provided beneath the blanks, simplify the expression by combining like terms and arranging the terms from highest to lowest order. Show your work.
To compute the multiplication we will apply the distributive property at least 2 times:
\(a(b+c)=ab+ac.\)Applying the distributive property we get:
\(3x^2(x^2+2x)-2x(x^2+2x)+7(x^2+2).\)Applying the distributive property again, we get:
\(3x^2x^2+3x^22x-2xx^2-2x2x+7x^2+14.\)Simplifying the above result, we get:
\(3x^4+6x^3-2x^3-4x^2+7x^2+14.\)Finally, adding like terms, we get:
\(3x^4+4x^3+3x^2+14.\)Answer: \(3x^4+4x^3+3x^2+14.\)This figure is made up of two rectangular prisms What is the volume of the figure? Enter your answer in the box
The volume of the figure with two rectangular prisms would be 1, 728 ft ³
.
How to find the volume ?To find the volume of the figure with the two rectangular prisms, you can find the volume of the individual rectangular prisms and then add them up.
Volume of rectangular prism 1:
= Length x Width x Height
= 19 x 12 x 6
= 1, 368 ft ³
Volume of rectangle prism 2:
= Length x Width x Height
= 10 x 12 x 3
= 360 ft ³
The volume of the entire figure is then :
= 1, 368 + 360
= 1, 728 ft ³
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Brittany asked her classmates: How much time, in minutes, do you spend reading each day? Here are the results: 10, 20, 20, 20, 30, 30, 30, 30, 30, 40, 40, 40, 60, 60, 60 Display the data in a line plot, a histogram, and a box plot. Next to each graph, write down something you notice about the data. Upload your completed plots here.
The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.
Line Plot:
A line plot displays data points on a number line, representing the frequency or count of each value.
In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.
For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.
Histogram:
A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.
The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.
The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.
The height of each bar in the histogram will represent the number of students falling into each interval.
Box Plot:
A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.
The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.
The box will represent the interquartile range (IQR), showing the middle 50% of the data.
The line within the box will represent the median value.
The whiskers will indicate the minimum and maximum values, excluding outliers.
By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.
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PLS HELP ME WHO EVER GETS ANSWER I WILL GIVE BRAINLIEST AND ALL MY POINTS SO PLEASE ANSWER THIS PLSSS ITS EASY
Answer:
15
Step-by-step explanation:
Answer:
200 detective phones.
Step-by-step explanation:
Write the proportion where x is the number of detective phones.
cross multiply
divide both sides by 60
Simplify the expression by combining like terms.
4/3a - 1/2b + 1/3a + 5/2b
Answer: 5/3a + 4/2b
Step-by-step explanation:
\(\dfrac{4}{3} a-\dfrac{1}{2} b+\dfrac{1}{3} a+\dfrac{5}{2} b\)
Rearrange:
\(\dfrac{4}{3} a+\dfrac{1}{3} a-\dfrac{1}{2} b+\dfrac{5}{2} b\)
Combine Like Terms:
\(\dfrac{4}{3} a+\dfrac{1}{3} a=\dfrac{5}{3} a\\-\dfrac{1}{2}b+\dfrac{5}{2} b=\dfrac{4}{2} b\)
\(\fbox{$\dfrac{5}{3}$a + $\dfrac{4}{2}$b}\)
In a particular region 27.8 percent of adults 25 years and older have at least a bachelors degree. The median income in this region is 37,084. Is this income higher than what you would expect? Why ?
Answer:
No, because the median would most likely be an individual with a lesser degree or no degree, and since those people usually make less money than those with a degree, the median income makes sense.
Step-by-step explanation:
give an example of a real world word problem for a two step inequality
This example demonstrates a two-step inequality where we first express the savings equation and then solve for the variable 'w' to determine the number of weeks needed to reach the savings goal.
Understanding InequalityLiam is saving money to buy a new video game console. He has already saved $50 and is saving $10 per week from his allowance. He wants to determine how many weeks it will take for his savings to reach at least $150.
Let:
number of weeks Liam saves = w
total amount of money he saves = S
Step 1: Express the first step of the problem as an inequality.
Liam saves $10 per week, so the amount of money he saves after w-weeks is 10w. We can write the first step of the inequality as:
10w + 50 ≥ 150
Step 2: Solve the inequality.
To isolate 'w', we can subtract 50 from both sides of the inequality:
10w ≥ 150 - 50
10w ≥ 100
Finally, divide both sides of the inequality by 10 to solve for 'w':
w ≥ 10
Therefore, it will take Liam at least 10 weeks to save enough money to reach $150 for the video game console.
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I will mark you brainiest!
What is the measure of angle A?
A) 20 degrees
B) 25 degrees
C) 38 degrees
D) 42 degrees
Simplify the following expression: -2/10(1 - 2x + 2 )
Answer:
2/10-4/10x
Step-by-step explanation:
Answer: =
2/5 x + -3/5
Step-by-step explanation:
The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with electronic trades handled by discount brokers. As part of die survey, members were asked to rate members were asked to rate their satisfaction with the trade price and the speed of execution, as well as provide an overall satisfaction rating. Possible responses (scores) were no opinion (0), unsatisfied (1), somewhat satisfied (2), satisfied (3), and very-satisfied (4). For each broker, summary scores were computed by computing a weighted average of die scores provided by each respondent. A portion the survey results follow (AAII Web site. February 7, 2012). Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker. Interpret die coefficient of determination. Use the F test to determine die overall significance of the relationship. What is your conclusion at the 0.05 level of significance? Use the t test to determine the significance of each independent variable? What are your conclusions at the 0.05 level of significance? Interpret the estimated regression parameters. Are die relationships indicated by these estimates what you would expect? Finger Lakes Investments has developed a new electronic trading system and would like to predict overall customer satisfaction assuming they can provide satisfactory service levels (3) for both trade price and speed of execution. Use the estimated repression equation developed in part a to predict overall satisfaction level for Finger Lakes Investments if they can achieve these performance levels. What concerns (if any) do you have with regard to die possible responses the respondents could select on the survey.
Previous question
The estimated regression equation developed in part (a) was found to be an effective predictor of overall customer satisfaction, as indicated by the significant F and t test results.
The estimated regression equation developed in part (a) to predict overall customer satisfaction is given by:
Overall Satisfaction = 0.3151*Trade Price + 0.3132*Speed of Execution + 1.5026
The coefficient of determination (R2) is a measure of how well the equation fits the data and is calculated as the proportion of the variation in overall satisfaction that is explained by the model. In this case, the R2 = 0.39, which means that 39% of the variation in overall satisfaction can be explained by the trade price and speed of execution variables.
To determine the overall significance of the relationship, the F test was used. The F statistic was calculated to be 17.874, which was significant at the 0.05 level (p-value = 0.000), indicating that the model was an effective predictor of overall customer satisfaction.
The t tests were then used to determine the significance of each independent variable. The t statistic for Trade Price was 2.639 (p-value = 0.009), indicating that the variable was significant at the 0.05 level, while the t statistic for Speed of Execution was 2.565 (p-value = 0.012), indicating that the
The estimated regression equation developed in part (a) was found to be an effective predictor of overall customer satisfaction, as indicated by the significant F and t test results.
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Oliver started looking for his missing cat at 2:40. If he found it at 6:00, how long did he spend looking?
Answer:
3hours and 40 mins
Step-by-step explanation:
Which of the following equations defines a line that passes through the points begin ordered pair negative 2 comma 7 end ordered pair and begin ordered pair 6 comma negative 9 end ordered pair?
The linear equation that passes through points (-2,7) and (6,-9) is given by:
y = -2x + 3
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The line passes through points (-2,7) and (6,-9), hence the slope is given by:
m = (-9 - 7)/(6 - (-2)) = -2.
Hence, since when x = -2, y = 7, when x = 0, y = 7 - 2 x (0 - (-2)) = 3, which means that the y-intercept is of b = 3, and the equation is given by:
y = -2x + 3.
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Please answer this correctly
Answer:
Stem | Leaf
13 | 4 9 9
16 | 0 2 3 6
Step-by-step explanation:
134, 139, 139
160, 162, 163, 166
Ciana earns an hourly wage of $30 at her job. In order to purchase her sneakers she will have to take time off work, so each hour away from her job
costs her $30 in lost Income. Assume that ciana travel time is the same each way (to and from the store) and that it will take her 30 minutes once
she reaches a store to complete her shopping. Assume throughout the question that ciara incurs no additional costs other than the sneakers, such as
gas.
complete the following table by computing the opportunity cost of ciana’s time and the total cost of shopping at each location
Ciana should purchase the skirt at the store across town because the total economic cost will be lowest.
How to determine the opportunity cost?Ciana makes $30 per hour at her work, and her purchase decision includes the opportunity cost of lost wages:
Total economic cost:
Local store = $114 + [1/4 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $144
Across town = $86 + [1/2 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $131
Neighboring city = $60 + [1 hour x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $135
Ciana should buy a skirt at the store across town. Because it has the lowest total economic cost ($131).
Opportunity cost is the lost benefit or additional cost of choosing one activity or investment over another. Economic costs include both accounting costs and opportunity costs.
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Marama is planting a rectangular garden in her backyard. She is planning to fence the garden with 28 feet of wired fencing. The garden's area can be represented by the function A(t) = -t2+ 14t where t is the length of a side. What are all of the appropriate values of the domain for the graph of this function? Explain your answer in terms of the situation. Use words, numbers, and/or pictures to show your work.
The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.
To determine the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\), we need to consider the situation and the constraints given.
The function A(t) represents the area of the rectangular garden as a function of the length of one of its sides, which is denoted by t.
We are also told that Marama plans to fence the garden with 28 feet of wired fencing.
Now, let's break down the problem and find the appropriate values for the domain.
We know that the perimeter of a rectangle is the sum of all its sides. In this case, since we have a rectangular garden, the perimeter can be represented as:
\(Perimeter = 2t + 2w\),
where t is the length of one side (the width) and w is the length of the other side (the width).
The problem states that Marama plans to use 28 feet of wired fencing. Therefore, the perimeter of the garden must equal 28 feet:
\(2t + 2w = 28\).
Simplifying this equation, we have:
\(t + w = 14\).
We can express w in terms of t as \(w = 14 - t\).
The area of a rectangle is given by the product of its length and width:
\(Area = t \times w\).
Substituting the expression for w from step 2, we have:
\(A(t) = t \times (14 - t)\).
Simplifying further:
\(A(t) = 14t - t^2\).
To determine the appropriate values of the domain, we need to consider the context of the problem. Since we are dealing with a physical garden, both the length and width must be positive numbers. Additionally, the values of t must be feasible given the constraints of the perimeter.
We know that \(t + w = 14\), so \(t + (14 - t) = 14\), which simplifies to \(14 = 14\).
This shows that the value of t can range from 0 to 14, inclusive.
Therefore, the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\) are \(t \epsilon [0, 14]\).
To illustrate this graphically, we can plot the function \(A(t) = -t^2 + 14t\) and mark the appropriate values of the domain on the x-axis (representing t):
^
|
A(t)|
|
|_______________________________
0 t 14
The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.
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4. Find the following function values.
(3)/ (3)
( (2))
f(f'(-4))
g(x+2)
Answer:
1. 9
2.2
3.0
4.gx +2g
Step-by-step explanation:
Two regular 6-sided dice are tossed. Compute the probability that the sum of the pips on the upward faces of the 2 dice is the following. (See the figure below for the sample space of this experiment. Enter your probability as a fraction.)
At least 11
The probability that the sum of the pips selected that is at least 11 would be = 1/12.
How to determine the probability of the selected events?To determine the probability of the selected events, the formula for problem should be used which is given below;
Probability = possible outcome/sample space
Possible outcome = at least 11 = (5,6),(6,5),(6,6)
= 3
Sample space = 36
Probability = 3/36 = 1/12
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x^ 3 +x^ 2 +4x/x^ 2 +x-2
into partial
fractions
Answer:
x + (4/ x-2) + (2/ x-1)
Step-by-step explanation:
x + (6x/ x^2 + 2x - x -2)
x + (6x/ (x + 2) X (x - 1))
(6x/ (x + 2) X (x - 1))
(A/ x+2) + (B/ x-1)
(6x/ (x + 2) X (x - 1)) = (A/ x+2) + (B/ x-1)
6x = Ax + Bx - A + 2B
6x = (A+B)x + (-A+2b)
{0 = -A+2B
{6 = A+B
(A,B) = (4, 2)
(4/ x+2) + (2/ x-1)
x + (4/ x-2) + (2/ x-1)
Draw an angle in standard position with the given measure. 8/3 π
The asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.
What is the standard position of angles?
Standard position simply means that the vertex of the angle is at the origin of the circle and that one ray of the angle is on the positive x-axis. The other ray of the angle is placed at the angle measure formed by traveling counter-clockwise along the circle.
To draw an angle in standard position with measure 8/3 π, follow these steps:
Start with the positive x-axis.
Counterclockwise, rotate the initial side of the angle until it coincides with the positive x-axis.
Starting from the initial side on the positive x-axis, rotate the terminal side of the angle in a counterclockwise direction until the angle measures 8/3 π.
The resulting angle will have a measure of 8/3 π and will look like the following:
|
|
--------*-----------
|
|
Here, the asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.
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Solve for the empty spaces. Giving High Points and Brainliest.
Answer:
The measure of one interior angle is about 154.3 degrees. (The total number of degrees inside are the product of (n-2)x180)
The perimeter is 84 inches (Multiple 6inches by number of sides)
The area is 551.88 in squared (Calculated with 0.5 x apothem x perimeter. Apothem is 6/(2tan(180/n)) where n is 14)