Answers
With f(1), we're being given an x-value of 1.
Since 1 < 3 (and not ≥3) we need to use the first formula that is used when x<3.
f(1) = 1 - 2 = -1
Related Questions
Ryan is building two gardens.
The flower garden is 6 feet long
and 4 feet wide. The vegetable
garden is the same length as the
flower garden. The area of the
flower garden is half the area of
the vegetable garden. What is the
width of the vegetable garden?
Answers
The width of the vegetable garden is 8 feet.
To determine the width of the vegetable garden.
Given information:
Flower garden length = 6 feet
Flower garden width = 4 feet
Vegetable garden length = Flower garden length
Area of the flower garden = half the area of the vegetable garden
To find the width of the vegetable garden, we need to find the area of both gardens.
Area of the flower garden = length × width
Area of the flower garden = 6 feet × 4 feet
Area of the flower garden = 24 square feet
Since the area of the flower garden is half the area of the vegetable garden, we can set up the following equation:
24 square feet = (1/2) × Area of the vegetable garden
To solve for the area of the vegetable garden, we multiply both sides of the equation by 2:
2 × 24 square feet = Area of the vegetable garden
48 square feet = Area of the vegetable garden
Now that we know the area of the vegetable garden is 48 square feet, we can find the width.
Area of the vegetable garden = length × width
48 square feet = 6 feet × width
To solve for the width of the vegetable garden, we divide both sides of the equation by 6:
48 square feet / 6 feet = width
8 feet = width
Therefore, the width of the vegetable garden is 8 feet.
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Essay Question.
You are purchasing a new car. In order to determine which car will provide maximum savings, you’ve researched miles per gallon (mpg) ratings of cars. If gas is $3.45 per gallon and you drive an average of 18,000 miles per year, the following rational equation is given:
Answers
a. You will find the gallons of gas consumed by the old car in one year when you divide [tex]\frac{18,000}{old\;miles\;per\;gallon}[/tex].
b. The amount of dollars you would save in the first year by switching to the 27 mpg car is $1,150.
c. The amount of dollars you would save after 5 years is $5,750.
d. Yes, the additional savings in gas be worth the extra $3000 over a 5 year loan.
e. The gas mileage your new car would have to be if you saved $800 per year over your 18 mpg current car is 23.4 mpg.
How to evaluate the rational equation?Based on the information provided about the car that would provide maximum savings, the following rational equation models the situation:
[tex]g(x)=3.45(\frac{18,000}{old\;miles\;per\;gallon})-3.45(\frac{18,000}{new\;miles\;per\;gallon})[/tex]
Note: "g(x) is used for calculating the amount of dollar savings for one year for driving a car that gets higher miles per gallon rate."
Part a.
Based on the rational equation, we can logically deduce that the expression [tex]\frac{18,000}{old\;miles\;per\;gallon}[/tex] would help to determine the gallons of gas consumed by the old car in one year.
Part b.
The amount of dollars you would save in the first year by switching to the 27 mpg car can be calculated as follows:
[tex]g(x)=3.45(\frac{18,000}{18})-3.45(\frac{18,000}{27})[/tex]
g(x) = 3,450 - 2,300
g(x) = $1,150.
Part c.
The amount of dollars you would save after five years can be calculated as follows:
f(5) = 5g(x)
f(5) = 5 × $1,150
f(5) = $5,750
Part d.
[tex]g(x)=3.45(\frac{18,000}{27})-3.45(\frac{18,000}{33})[/tex]
g(x) = 2,300 - 1,881.82
g(x) = $418.18.
f(5) = 5g(x)
f(5) = 5 × $418.18
f(5) = $2,090.9
Next, we would subtract the cost in 5 years as follows;
Difference = $5,750 - $2,090.9
Difference = $3,659.1.
Therefore, $3,659.1 is greater than $3,000, so an additional savings is worth it.
Part e.
Lastly, we would determine the gas mileage your new car would have to be if you saved $800 per year over your 18 mpg current car;
[tex]800=3.45(\frac{18,000}{18})-3.45(\frac{18,000}{y})[/tex]
800 = 3,450 - 62,100/y
62,100/y = 3,450 - 800
62,100/y = 2,650
y = 62,100/2,650
y = 23.4 mpg.
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The figure below represents
marked central angle.
I
of a full circle. Find the measure of the
Answers
A full circle has [tex]360^{\circ}[/tex].
[tex]\dfrac{4}{9}\cdot 360^{\circ}=160^{\circ}[/tex]
The mark angle is [tex]160^{\circ}[/tex].
Thanks to social media, the happiest creature on earth, an always smiling Australian marsupial called a quokka, has become well known. Suppose that the weights of quokkas can be described by the Normal model N(12,2.9 ). Complete parts a through c. a) What percent of quokkas weigh over 16.8 pounds? b) What percent of quokkas weigh under 13.8 pounds? c) What percent of quokkas weigh between 13.8 and 16.8 pounds?
Answers
The percentages are given as follows:
a) Over 16.8 pounds: 4.85%.
b) Under 13.8 pounds: 73.24%.
c) Between 13.8 and 16.8 pounds: 21.91%.
How to obtain probabilities using the normal distribution?We first must use the z-score formula, as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which:
X is the measure.[tex]\mu[/tex] is the population mean.[tex]\sigma[/tex] is the population standard deviation.The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).
The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.
The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 12, \sigma = 2.9[/tex]
Item a:
The proportion is one subtracted by the p-value of Z when X = 16.8, hence:
Z = (16.8 - 12)/2.9
Z = 1.66.
Z = 1.66 has a p-value of 0.9515.
1 - 0.9515 = 0.0485, hence the percentage is of 4.85%.
Item b:
The proportion is the p-value of Z when X = 13.8, hence:
Z = (13.8 - 12)/2.9
Z = 0.62.
Z = 0.62 has a p-value of 0.7324.
Item c:
The proportion is the subtraction of the p-values, hence:
0.9515 - 0.7324 = 0.2191 = 21.91%.
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if a factor can produce 6.6 M of copper wire a minute how many meters of water can the factory producing 12-hour work day provided the factory stressed out for a half hour lunch
Answers
Using unit rate, the number of maters of copper wire produced in a 12 hour work day is 4554 m
What is unit rate?Unit rate is the rate at which a unit of a obect is done
if a factor can produce 6.6 M of copper wire a minute. To determine how many meters of copper can the factory produce in 12-hour work day provided the factory stressed out for a half hour lunch.
Now, we know that the factor produces 6.6 m of copper per minute. So, the unit rate is 6.6 m/min
Now since we have a 12 hour work day and and 1/2 hour lunch, the total time used to produce the copper wire is 12 h - 1/2 h = 12 h - 0.5 h = 11.5 h
We now convert this to minutes 11.5 h = 11.5 × 60 min
= 690 min
So, the number of meters of coppper wire produced in a 12 hour work day A = unit rate × time
= 6.6 m/min × 690 min
= 4554 m
So, the amount is 4554 m
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please help! maths hyperbolic functions
Answers
Answer:
See attachments.
Step-by-step explanation:
The quickest way to sketch the given functions, given that the coordinate plane is restricted to -5 ≤ x ≤ 5, is to substitute the values of x into the functions to find the points for the given interval. Plot these points on the given coordinate plane, and draw a continuous curve through the points.
Part (a)Given function:
[tex]y=\dfrac{5}{x}-2, \quad x > 0[/tex]
Substitute the values of x = 1, x = 2, x = 3, x = 4 and x = 5 into the function:
[tex]\begin{aligned}x=1 \implies y&=\dfrac{5}{1}-2\\&=5-2\\&=3\end{aligned}[/tex]
[tex]\begin{aligned}x=2 \implies y&=\dfrac{5}{2}-2\\&=2.5-2\\&=0.5\end{aligned}[/tex]
[tex]\begin{aligned}x=3 \implies y&=\dfrac{5}{3}-2\\&=-0.333...\end{aligned}[/tex]
[tex]\begin{aligned}x=4 \implies y&=\dfrac{5}{4}-2\\&=1.25-2\\&=-0.75\end{aligned}[/tex]
[tex]\begin{aligned}x=5 \implies y&=\dfrac{5}{5}-2\\&=1-2\\&=-1\end{aligned}[/tex]
Plot the points (1, 3), (2, 0.5), (3, -0.333...), (4, -0.75) and (5, -1) on the given coordinate plane and draw a continuous curve through them.
End behaviour:
As x approaches 0 from the positive side, x tends to ∞.As x approaches ∞, y approaches -2.[tex]\hrulefill[/tex]
Part (b)Given function:
[tex]y=\dfrac{-2}{x+1}+3, \quad x < -1[/tex]
Substitute the values of x = -2, x = -3, x = -4 and x = -5 into the function:
[tex]\begin{aligned}x=-2 \implies y&=\dfrac{-2}{-2+1}+3\\&=2+3\\&=5\end{aligned}[/tex]
[tex]\begin{aligned}x=-3 \implies y&=\dfrac{-2}{-3+1}+3\\&=1+3\\&=4\end{aligned}[/tex]
[tex]\begin{aligned}x=-4 \implies y&=\dfrac{-2}{-4+1}+3\\&=0.666...+3\\&=3.666...\end{aligned}[/tex]
[tex]\begin{aligned}x=-5 \implies y&=\dfrac{-2}{-5+1}+3\\&=0.5+3\\&=3.5\end{aligned}[/tex]
Plot the points (-2, 5), (-3, 4), (-4, 3.666...) and (-5, 3.5) on the given coordinate plane and draw a continuous curve through them.
End behaviour:
As x approaches -1 from the negative side, x tends to ∞.As x approaches -∞, y approaches 3.if 30 is divided by .06 the result is ? what are the steps to solve it by hand
Answers
Answer:
30/.06 =500
Step-by-step explanation:
30÷6/100
==>
30*100/6
=500
1/8 of the cans in George‘s pantry are vegetables. 1/3 of the cans in George’s pantry are soup what fraction of the cans in George’s pantry are either soup or vegetables?
Answers
The fraction of the cans in George’s pantry which are either soup or vegetables is 11/24.
What fraction of the cans in George’s pantry are either soup or vegetables?Fraction of cans in George‘s pantry that are vegetables = 1/8
Fraction of cans in George‘s pantry that are soups = 1/3
Fraction of the cans in George’s pantry which are either soup or vegetables = 1/3 + 1/8
= (8+3) /24
= 11/24
Hence, 11/24 is the fraction of the cans in George’s pantry that are either soup or vegetables.
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The endpoints of segment XY are X(-2,3) and Y(7,4). The segment is translated along the vector <-3,1> and then rotated 90 degrees. What is the coordinate of X"?
Answers
The coordinate of point X" after translating segment XY along the vector <-3, 1> and then rotating it 90 degrees is X" (4, 5).
To find the coordinate of point X" after translating segment XY along the vector <-3, 1> and then rotating it 90 degrees, we need to follow these steps:
Translation: Add the components of the translation vector <-3, 1> to the coordinates of point X(-2, 3) to get the new coordinates of X'.
X' = (-2 + (-3), 3 + 1) = (-5, 4)
Now, we have the translated endpoint X'.
Rotation: To rotate the point X' by 90 degrees, we need to swap the x and y coordinates and negate the new x coordinate.
X" = (y-coordinate of X', -x-coordinate of X')
X" = (4, -(-5))
X" = (4, 5)
Therefore, the coordinate of point X" after translating segment XY along the vector <-3, 1> and then rotating it 90 degrees is X" (4, 5).
In summary, we first translate point X(-2, 3) along the vector <-3, 1> to get X' (-5, 4). Then, we rotate X' by 90 degrees to obtain X" (4, 5).
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Find the indicated angle.
?
6
6
9
A.) 9
B.)4
C.)28
D.)3
Answers
Prompt:
A researcher wants to answer 2 research questions related to Americans level of trust
The researcher is using the General Social Survey which has the following questions:
Generally speaking, would you say that people can be trusted or that you can't be too careful in dealing with people? The response options for this variable are (Always trusted, Usually trusted, Usual not trusted, Always not trusted)
This trust variable is coded in the dataset with the name “cantrust”
In addition, in its demographic questions the GSS asks respondents to state their highest education degree achieved. The response options for this variable are: high school or less- college or higher. This educational attainment variable is coded “college” in the dataset.
Research question #1: What percentage of Americans believe strangers can always be trusted?
Create a frequency distribution table for the variable “cantrust”. Make sure you filter out all nonvalid responses (i.e. responses coded “IAP” or “NA” or are “Blank”).
Create and show a (relative) frequency distribution table
Create and show a pie chart with the distribution of responses
State what percentage of respondents say strangers can be “always trusted”?
Calculate and interpret the 95% confidence margin of error for the proportion of Americans that answer strangers can “always be trusted”
Calculate and interpret the 95% confidence interval and make a statement of what proportion of Americans say strangers can “always be trusted”
Explain why we go through the trouble of calculating margin of errors and confidence intervals.
Answers
The solution to all parts is shown below.
First, let's filter out all non-valid responses, such as "IAP" (Inapplicable), "NA" (Not Applicable), or "Blank."
Frequency distribution table for the variable "can trust":
| Response | Frequency |
| Always trusted | x |
| Usually trusted | y |
| Usually not trusted | z |
| Always not trusted | w |
Relative frequency distribution table for the variable "cantrust":
| Response | Relative Frequency |
| Always trusted | x/n |
| Usually trusted | y/n |
| Usually not trusted | z/n |
| Always not trusted | w/n |
Pie chart with the distribution of responses:
To find the percentage of respondents who say strangers can be "always trusted," we calculate the relative frequency or proportion for the "Always trusted" category.
Percentage of respondents who say strangers can be "always trusted"
= (x/n) x 100%
Now, let's calculate the 95% confidence margin of error for the proportion of Americans who answer strangers can "always be trusted":
Margin of error = (z-score) (standard error)
The z-score depends on the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.
The standard error can be calculated as:
Standard error = √[(p (1 - p)) / n]
Once we have the margin of error, we can calculate the 95% confidence interval as follows:
Confidence interval = p ± margin of error
The confidence interval provides a range within which the true proportion of Americans who say strangers can be "always trusted" is likely to fall.
By interpreting margin of errors and confidence intervals is essential because survey data is collected from a sample rather than the entire population.
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50 students are asked whether they like English, History or Geography.3 students like none of them,25 like English,25 like History and 11 like Geography,2 like English and history only,2 like Geography and history only.No student like English and geography. (A) represent the information in a venn diagram (B) use the ven diagram to calculate how many students like all three
Answers
Answer:
history Is a good subject
Please help me please only answer if correct
Answers
The surface area of the sphere is 50.3 yard².
The volume of the rectangular prism is 245 inches³.
The volume of the pyramid is 149.3 m³.
How to find the volume of a shape?The volume and surface area of the figures can be found as follows:
surface area of the sphere = 4πr²
where
r = radiusTherefore,
surface area of the sphere = 4 × 3.14 × 2²
surface area of the sphere = 50.3 yard²
Volume of the rectangular prism = lwh
where
l = lengthw = widthh = heightTherefore,
Volume of the rectangular prism = 7 × 7 × 5
Volume of the rectangular prism = 245 inches³
Volume of the pyramid = 1 / 3 Bh
where
B = base areah= height of the pyramidTherefore,
B = 8² = 64 m²
h = 7 m
Therefore,
Volume of the pyramid = 1 / 3 × 64 × 7
Volume of the pyramid = 149.3 m³
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find inverse of function y=x2 x>=0
Answers
Answer:
The inverse function is:
f(x)=√x−2
Step-by-step explanation:
To find the inverse function of y=f(x) you have to transform the formula to calculate x in terms of y.
y=x2+2
x2=y−2
x=√y−2
Now we can change the letters to follow the convention that x is the independent variable and y is the function's value:
y=√x−2
You have to calculate the domain of the result function.
Here you have the expression under square root sign, so the domain is the set where x−2≥0
x−2≥0⇒x≥2
Please Refer to the Images
Answers
For the expression [tex]x^2^/^4x^3^/^6[/tex] the value of exponent of x is 1.
8ab²√5a is the simplified form of the expression 4√20a³b⁴ .
The given expression is [tex]x^2^/^4x^3^/^6[/tex]
x is the variable in the expression.
We know that when bases are same in the product then the powers will be added.
[tex]x^1^/^2^+^1^/^2[/tex]
When 1/2 and 1/2 are added we get 1.
So the value of r is 1.
Now 4√20a³b⁴ is the expression.
4√4×5a².a.b².b²
4.2.ab²√5a
8ab²√5a is the simplified form of the expression.
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A person needs to fill 14 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes. How long to finish filling the remaining jugs?
Answers
Answer:
The remaining Jugs will take us 18 minutes to fill.
Explenation:
14 -2 =
12 jugs remain
2 = 3min /2
1 = 1.5min
12 x 1.5= 18min
The two triangles are similar.
What is the value of x?
Enter your answer in the box.
x =
Answers
The value of x from the given similar triangles is 10 units.
The given triangles are similar.
Here, 3x/(4x+2) = 20/28
3x/(4x+2) = 5/7
7×3x = 5(4x+2)
21x=20x+10
21x-20x=10
x=10 units
Therefore, the value of x from the given similar triangles is 10 units.
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The difference of the same side interior angles of two parallel lines is 50 degrees. Find all angles
Answers
If the difference between the same side interior angles of two parallel lines is 50 degrees, we know that those angles must sum up to 180 degrees (because they are opposite each other).are supplementary angles. As a result, each of the four angles is 65 degrees, 115 degrees, 65 degrees, and 115 degrees..
Let's call one of the angles "x". Then, the other angle must be (x+50).
Now, let's look at the angles formed by a transversal intersecting those two parallel lines. There are eight angles in total, but we only need to find four of them since the other four are congruent (due to alternate interior angles being congruent).
The angles we need to find are:
1. x (one of the same side interior angles)
2. (x+50) (the other same side interior angle)
3. the corresponding angle to x (opposite x, on the other side of the transversal)
4. the corresponding angle to (x+50) (opposite (x+50), on the other side of the transversal)
Since corresponding angles are congruent when two parallel lines are intersected by a transversal, we know that angles 3 and 4 are equal to angles 1 and 2, respectively.
To determine all four angles, we just solve for x:
x + (x+50) = 180
2x + 50 = 180
2x = 130
x = 65
Therefore, our four angles are:
1. x = 65 degrees
2. (x+50) = 115 degrees
3. the angle corresponding to x = 65 degrees
4. the corresponding angle to (x+50) = 115 degrees
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Find the values of x and y that make the equation true.
4 X
3x - 4
+
3 4y
y 8
7 25
- 2 4
The value of x that makes the equation true is
(Simplify your answer)
Answers
Answer:
x = -3y = 7Step-by-step explanation:
You want to solve the system of equations ...
x +4y = 253x +y = -2SolutionWe can eliminate y by subtracting the first equation from 4 times the second:
4(3x +y) -(x +4y) = 4(-2) -(25)
11x = -33
x = -3
Using the second equation, we have ...
y = -2 -3x = -2 -3(-3) = 7
The values of x and y that make the equation true are ...
x = -3y = 7__
Additional comment
The sum of matrices is the sum of corresponding terms. The constant terms on the diagonals are irrelevant to the values of x and y. The off-diagonal sums give the two equations solved here.
<95141404393)
Section 1 Mathematics Multiple-C 6 Isla can run 800 metres in 10 minutes. At this rate, how many kilometres can she run in 50 minutes?
Answers
We know that Isla can run 800 meters in 10 minutes. Let's set up a proportion to find the distance she can run in 50 minutes:
Distance in meters / Time in minutes = Distance in meters / Time in minutes
800 meters / 10 minutes = x kilometers / 50 minutes
To solve for x, we cross-multiply and then divide:
(800 meters) * (50 minutes) = (10 minutes) * x kilometers
40,000 meters = 10x kilometers
Dividing both sides by 10:
40,000 meters / 10 = x kilometers
4,000 meters = x kilometers
Therefore, Isla can run 4,000 meters (or 4 kilometers) in 50 minutes.
I hope this helps! :)
800/10 = 80
Isla runs 80m in 1 minute
80 x 50 = 4000
Isla runs 4000m in 50 minutes
4000m = 4km
I NEED SELP ASAP PLEASEEEE 50 POINTS
Answers
Answer:
(x - 0)² + (y - 9)² = (√87.25)²
Step-by-step explanation:
equation of circle is (x - a)² + (y - b)² = r², where a and b are centre of the circle and r is the circle's radius.
(x - 0)² + (y - 9)² = r²
x² + (y² - 18y + 81) = r²
x² + y² - 18y + 81 = r²
at the point (7.5, 5):
(7.5)² + (5)² - 18(5) + 81
= 87.25
so r² = 87.25.
in standard form:
(x - 0)² + (y - 9)² = (√87.25)²
Enter the number that belongs in the green box
Answers
Answer:
28.21°
Step-by-step explanation:
use the Cosine rule (Cos A = (b² + c² - a²) / 2bc)
let's call our angle A.
then Cos A = (12² + 20² - 11²) / (2 X 12 X 20)
= 141/160.
A = Cos^-1 (141/160)
= 28.21° to nearest hundredth
The event coordinator asks you to determine how many students participated in th track and field day.the total number of students in 7th and eighth grade grade combined is 584; of the are seventh graders , and of them are eighth graders. If of the seventh graders participated in track and field day, and of the eighth graders participated? Describe the process you used to find your answer.
Answers
The total students participated in in track-and-field day is 485.
How to find total students participated?A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.
We have:
Total number of students combined = 584
5/8 of are seventh graders and 3/8 of are eighth graders
If 4/5 if the seventh graders participated in track-and-field day. Thus, the of number seventh graders participated in track-and-field day will be:
5/8 * 4/5 * 584 = 294
If 7/8 of the eighth graders participated. Thus, the of number eighth graders that participated will be:
3/8 * 7/8 * 584 = 191
total students participated = 294 + 191 = 485
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Complete Question
The event coordinator asks you to determine how many students participated in the track-and-field day. The total number of students in seventh and eighth grade combined is 584. 5/8 of them are seventh graders and 3/8 of them are eighth graders. If 4/5 if the seventh graders participated in tack-and-field day and 7/8 of the eight graders participated, about how many total students participated? Describe the process you used.
NO LINKS!! URGENT HELP PLEASE!!
1. Find the area of a regular octagon. Each side is 12 m.
2. The perimeter of a regular polygon is 72 feet. An exterior angle of the polygon measures 40°. Find the length of each side.
3. If the perimeter of a regular pentagon is 50 in. Find the area. Show a drawing and work please.
Answers
Answer:
1) 695.3 m²
2) 8 ft
3) 172.0 in²
Step-by-step explanation:
Question 1To find the area of a regular polygon, we can use the following formula:
[tex]\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}[/tex]
Given the polygon is an octagon, n = 8.
Given each side measures 12 m, s = 12.
Substitute the values of n and s into the formula for area and solve for A:
[tex]\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}[/tex]
[tex]\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}[/tex]
[tex]\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}[/tex]
[tex]\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}[/tex]
[tex]\implies A=695.29350...[/tex]
Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.
[tex]\hrulefill[/tex]
Question 2The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.
If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.
To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:
[tex]\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}[/tex]
Therefore:
[tex]\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}[/tex]
[tex]\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}[/tex]
[tex]\implies 40^{\circ}n=360^{\circ}[/tex]
[tex]\implies n=\dfrac{360^{\circ}}{40^{\circ}}[/tex]
[tex]\implies n=9[/tex]
Therefore, the regular polygon has 9 sides.
To determine the length of each side, divide the given perimeter by the number of sides:
[tex]\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}[/tex]
[tex]\implies \sf Side \;length=\dfrac{72}{9}[/tex]
[tex]\implies \sf Side \;length=8\;ft[/tex]
Therefore, the length of each side of the regular polygon is 8 ft.
[tex]\hrulefill[/tex]
Question 3The area of a regular polygon can be calculated using the following formula:
[tex]\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}[/tex]
A regular pentagon has 5 sides, so n = 5.
If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.
Substitute the values of s and n into the formula and solve for A:
[tex]\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}[/tex]
[tex]\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}[/tex]
[tex]\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}[/tex]
[tex]\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}[/tex]
[tex]\implies A=172.047740...[/tex]
Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.
Answer:
1.695.29 m^2
2.8 feet
3. 172.0477 in^2
Step-by-step explanation:
1. The area of a regular octagon can be found using the formula:
[tex]\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}[/tex]
where a is the length of one side of the octagon.
In this case, a = 12 m, so the area is:
[tex]\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}[/tex]
Therefore, the Area of a regular octagon is 695.29 m^2
2.
The formula for the exterior angle of a regular polygon is:
[tex]\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}[/tex]
where n is the number of sides in the polygon.
In this case, the exterior angle is 40°, so we can set up the following equation:
[tex]\bold{40^o=\frac{ 360^0 }{n}}[/tex]
[tex]n=\frac{360}{40}=9[/tex]
Therefore, the polygon has n=9 sides.
Perimeter=72ft.
We have
[tex]\boxed{\bold{Perimeter = n*s}}[/tex]
where n is the number of sides in the polygon and s is the length of one side.
Substituting Value.
72 feet = 9*s
[tex]\bold{s =\frac{ 72 \:feet }{ 9}}[/tex]
s = 8 feet
Therefore, the length of each side of the polygon is 8 feet.
3.
Solution:
A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = [tex]\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}[/tex]
The area of a regular pentagon can be found using the following formula:
[tex]\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}[/tex]
where s is the length of one side of the Pentagon.
In this case, s = 10 in, so the area is:
[tex]\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}[/tex]
Drawing: Attachment
For the function y = 9x2 + 9x +3, at the point x = 7, find the following.
(a) the slope of the tangent to the curve
0
(b) the instantaneous rate of change of the function
Answers
a) The slope of the tangent to the curve is,
⇒ dy/dx = 18x + 9
b) the instantaneous rate of change of the function at point x = 7 is
⇒ dy/dx = 135
We have to given that;
Function is,
⇒ y = 9x² + 9x + 3
Now, We know that;
The slope of function is defined by derivative of function with respect to x.
Here, Function is,
⇒ y = 9x² + 9x + 3
Hence, the slope of the tangent to the curve is,
⇒ dy/dx = 18x + 9
And, the instantaneous rate of change of the function at point x = 7 is
⇒ dy/dx = 18x + 9
⇒ dy/dx = 18 x 7 + 9
⇒ dy/dx = 126 + 9
⇒ dy/dx = 135
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SP - Rs 325 profit percent - 25% find Cp
Answers
Step-by-step explanation:
Cost price = 260
given , SP =325
. Profit%- 25%
CP= SP*100 / 100+ PROFIT%
=325*100/ 100+25
= 32500/ 125
=260
. Cp= SP * 101 ^
enter the number that belongs in the green box 11 12 20
Answers
The number that belongs in the green box is 57.8 degrees.
We are given that;
The triangle sides 11 12 20
Now,
The interior angles of a triangle always add up to 180 degrees. To find the interior angles of a triangle whose sides are 11 cm, 12 cm and 20 cm, we can use the law of cosines1.
Let’s call the angle opposite the side of length 11 cm as A, the angle opposite the side of length 12 cm as B, and the angle opposite the side of length 20 cm as C. Using the law of cosines, we can find that:
[tex]cos(A) = (b^2 + c^2 - a^2) / (2bc) = (12^2 + 20^2 - 11^2) / (2 * 12 * 20) = 0.55cos(B) = (a^2 + c^2 - b^2) / (2ac) = (11^2 + 20^2 - 12^2) / (2 * 11 * 20) = 0.6cos© = (a^2 + b^2 - c^2) / (2ab) = (11^2 + 12^2 - 20^2) / (2 * 11 * 12) = -0.45[/tex]
We can then use inverse cosine function to find the angles:
[tex]A = cos^-1(0.55) ≈ 57.8 degreesB = cos^-1(0.6) ≈ 53.1 degreesC = cos^-1(-0.45) ≈ 129.1 degrees[/tex]
The interior angles of this triangle are approximately 57.8 degrees, 53.1 degrees, and 129.1 degrees.
Therefore, by the angle answer will be 57.8 degrees.
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Simplify (−4b)(−19b).
Answers
Answer:
76b^2
Step-by-step explanation:
Basically you just multiply 4x19 which gives you 76, and the two b's equal b^2 (I'm not great at explaining i know)
write the expression 3a2b + 4ab2 as an equivalent algebraic expression
Answers
Answer:
ab(3a + 4b)
Step-by-step explanation:
Here are the steps on how to write the expression
3a^2 b + 4ab^2 as an equivalent algebraic expression:
1. Factor out the greatest common factor, which is ab.
2. The expression becomes ab(3a + 4b).
3. This is an equivalent algebraic expression to 3a^2 b + 4ab^2.
steps:
Original expression: 3a^2 b + 4ab^2Greatest common factor: abFactored expression: ab(3a + 4b)Equivalent expression: ab(3a + 4b)I hope this helps! Let me know if you have any other questions.
Answer:
Step-by-step explanation:
To simplify the expression 3a^2b + 4ab^2, [ we can factor out the common factor of ab from both terms: Step 1: Take out the common factor of ab. 3a^2b + 4ab^2 = ab(3a + 4b) Now the expression is in its factored form.
12 4 8 16 3'9' 27' 81' 243 a. yes, b. yes. 2 233 119 C. d. yes. 6 not geometric
Answers
Option A is correct, the sequence is a geometric and common ratio is 2/3.
To determine whether the given sequence is geometric, we need to check if there is a common ratio between consecutive terms.
Let's examine the given sequence:
1/3, 2/9, 4/27, 8/81, 16/243...
To find the ratio between consecutive terms, we can divide each term by its preceding term:
(2/9)/(1/3) = 2/9 × 3/1 = 2/3
(4/27)/(2/9) = 4/27 × 9/2 = 4/6 = 2/3
(8/81)/(4/27) = 8/81 × 27/4 = 2/3
(16/243)/(8/81) = 16/243 × 81/8 = 2/3
As we can see, there is a common ratio of 2/3 between consecutive terms.
Therefore, the given sequence is indeed geometric.
Hence, the sequence is a geometric and common ration is 2/3, Option A is correct.
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