Solve the equation without using a calculator
[tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-1)[/tex]
^{10}+99x^{10}=10x^9(x^2-1)[/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/qhfopGYDnQI4QtsYHWuMBfGjOIc3Q47s.png)
Answers
Answer:
x = 5 ± √26-------------------------
Convert the given equation as below:
[tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-1)[/tex][tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-9x-1)+10x^9(9x)[/tex][tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-9x-1)+90x^{10}[/tex][tex](x^2-9x-1)^{10}+9x^{10}=10x^9(x^2-9x-1)[/tex][tex](x^2-9x-1)^{10}-9x^9(x^2-9x-1)=x^9(x^2-9x-1)-9x^9x[/tex]Let's substitute x² - 9x - 1 = t, then the equation is:
[tex]t^9t-9x^9t=x^9t-9x^9x[/tex]Comparing both sides, we see that x = t, so:
x² - 9x - 1 = xx² - 10x - 1 = 0Solving this quadratic equation we get:
x = 5 ± √26Related Questions
Please help me with this
Answers
There is higher variability of y with large values of x.
There is a non linear relation between x and y.
How to explain the variabilityWe observe from figure b that for lower values of x the residuals are negative and as the values of x increases the residuals become positive but are distributed very close to the zero line.
Again for the extremely high values of x the residuals become negative following a decreasing non linear trend. Hence, from the residual plot we can conclude that the relation between x and y is a non linear one. Hence, the correct option is fourth option i.e, There is a non linear relation between x and y.
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Line n is perpendicular to the x-axis and passes through the point (–3,–7).
Write the equation for line n.
What is the slope of line n?
Answers
The equation for line n that is perpendicular to the x-axis and passes through the point (–3,–7) is x = -3, and its slope is undefined.
Since line n is perpendicular to the x-axis, it is parallel to the y-axis. Therefore, its slope is undefined since the y-axis is a vertical line with no defined slope.
To write the equation for line n, we know that the y-coordinate of every point on the line will be constant since the line is parallel to the y-axis. We also know that the line passes through the point (-3,-7), so we can write the equation as:
x = -3
This means that for any value of y, the x-coordinate will always be -3. Graphically, this represents a vertical line passing through the point (-3,-7) and parallel to the y-axis.
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2010 2008
$971 $812
$977 $943
$900 $873
$1071 $1023
$501 $486
3. Identify whether the mean or median is a more accurate reflection of the data.
Explain why.
Answers
The median is the accurate reflection of the data
How to solve for the mean501, 900, 971, 977, 1071
The mean would be
summation of the values
mean = 884
The median is the value that occurs in the middle = 971
The median would be more accurate reflection of the data. 501 is an outler. This is what caused us to have a mean that is c loser to 884. Hence we have 971 the median to be more accurate reflection of the data
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please help for this question
Answers
The single transformation that maps shape P onto shape Q is given as follows:
Reflection over the line y = 1.
What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Lateral or vertical movements.Reflections: A reflection is either over one of the axis on the graph or over a line.Rotations: A rotation is over a degree measure, either clockwise or counterclockwise.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, which can either enlarge or reduce the figure.The orientation of the figure changed, hence it underwent a reflection.
The intercepts are given as follows:
y = 4 and y = -2.
The line of reflection is the mean of the coordinates of the intercepts, hence:
(4 - 2)/2 -> y = 1.
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. Evaluate
11! 11!
24!
.
Answers
The evaluations are:
i. 11! = 39916800
ii. 24! = 2.045 x 10^37
What is expansion by factorial?Expansion by factorial is a method of expanding a given number from 1 to the number given. An example is given thus;
5! = 5 x 4 x 3 x 2 x 1!
= 120
To evaluate the given expressions;
a. 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1!
= 39916800
Also,
b. 24! = 24 x 23 x 22 x 20 x ........ x 5 x 4 x 3 x 2 x 1!
= 204484017332398 x 10 ^23
= 2.045 x 10^37
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ACTIVITY 1: Find f−1 in each of the following.
Answers
The [tex]f^{-1}[/tex] inverse of f of each
1) (x + 1)/2
2) [tex]\sqrt{\frac{x+1}{4} } \\[/tex]
3) 3 - 4x
4) [tex](x+5)^{1/3}[/tex]
5) [tex]\sqrt{x + 4}[/tex]
1) function f(x) = 3x + 1
let f(x) = y
y = 3x + 1
y - 1 = 3x
(y - 1)/3 = x
x obtained is [tex]f^{-1}[/tex]
and y will be x
[tex]f^{-1}[/tex] = (x-1)/3
2) equation f(x) = 4x² - 1
let f(x) = y
y = 4x² - 1
y + 1 = 4x²
(y + 1 )/4 = x²
x = [tex]\sqrt{\frac{x + 1}{4} }[/tex]
x obtained is [tex]f^{-1}[/tex]
and y will be x
[tex]f^{-1}[/tex] = [tex]\sqrt{\frac{x + 1}{4} }[/tex]
similarly,
3) f(x) = 3-x/4
y = 3-x/4
4y = 3 - x
x = 3 - 4x
[tex]f^{-1}[/tex] = 3- 4x
4) y = x³ - 5
y + 5 = x³
x = [tex](y + 5)^{1/3}[/tex]
[tex]f^{-1}[/tex] = [tex](x+5)^{1/3}[/tex]
5) y = x² - 4
y + 4 = x²
x = √y + 4
[tex]f^{-1} = \sqrt{x + 4}[/tex]
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Drag numbers to the table so it shows a proportional relationship between x and y.
Answers
The table is completed as follows:
x = 0.6, y = 6.x = 1.8, y = 18.What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
From the first row, when x = 0.2, y = 2, hence the constant is given as follows:
k = y/x
k = 2/0.2
k = 10.
Hence the equation is:
y = 10x.
Then the numeric values are given as follows:
x = 0.6, y = 10 x 0.6 = 6.x = 1.8, y = 10 x 1.8 = 18.More can be learned about proportional relationships at https://brainly.com/question/7723640
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Use synthetic division to rewrite the following fraction in the form q(x)+r(x)d(x)
, where d(x) is the denominator of the original fraction, q(x)is the quotient, and r(x) is the remainder.
Answers
The result of the synthetic division is:4x⁵+17x⁴+14x³-3x²+2 = (4x⁴ + 5x³ - x²) (x + 3) + 56
what is synthetic division ?
Synthetic division is a simplified method of dividing a polynomial by a linear factor. It is commonly used in algebra to find the quotient and remainder when dividing a polynomial by a linear factor of the form (x-a).
In the given question,
To use synthetic division to rewrite the fraction, we first set up the problem like this:
-3 | 4 17 14 -3 0 2
| -12 -15 3 0
+----------------------------------
4 5 -1 0 0 2
The coefficients of the polynomial are written in descending order of powers of x, with any missing terms replaced by zeros. The divisor, x + 3, is written on the left, and the first coefficient of the polynomial is written on the top of the vertical line.
We then proceed to perform synthetic division as follows:
Bring down the first coefficient, which is 4, and write it under the horizontal line.
Multiply the divisor, -3, by the number we just brought down, which gives -12. Write this number under the next coefficient, 17.
Add the two numbers, 17 and -12, to get 5. Write this number under the next coefficient, 14.
Multiply the divisor, -3, by 5, which gives -15. Write this number under the next coefficient, -3.
Add the two numbers, -3 and -15, to get -18. Write this number under the next coefficient, 0.
Multiply the divisor, -3, by -18, which gives 54. Write this number under the next coefficient, 2.
Add the two numbers, 2 and 54, to get 56. This is the remainder, which we write above the divisor.
The result of the synthetic division is:
4x⁵+17x⁴+14x³-3x²+2 = (4x^4 + 5x³ - x²) (x + 3) + 56
Therefore, we have rewritten the fraction in the desired form:
4x⁵+17x⁴+14x³-3x²+2
---------------------- = 4x⁴ + 5x³ - x² + 56/(x+3)
x+3
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The Problem Rodeos have long been a part of the culture in the southernmost part of the country and the growing popularity of the annual Easter event across South America prompted the Rupununi Development Corporation to construct a luxury resort with 60 two-bedroom suites for the visiting cultural troupes (troupe leaders and artistes). Capacity is ten troupe leaders and fifty artistes. Each suite is equipped with a small kitchenette, which contains a 7.3 cu ft. refrigerator, a microwave, and a coffee maker. A Drystan 6-piece bedroom set and the Ashley stationary sofa and love seat (all imported from Manaus at considerable cost) are also part of the furnishings. Each accommodation also has an excellent view if the Kanuku Mountains and nearby savannahs. The facility cost the Corporation $1,920,000 to build and equip and depreciation $160,000 per year (a fixed cost). Other operating costs include: Labor $320,000 per year plus $5 per suite per day Utilities $158,000 per year plus $1 per suite per day Miscellaneous $100,000 per year plus $6 per suite per day In addition to these costs, costs are also incurred on food and beverage for each guest. These costs are strictly variable, and (on average), are $40 per day for troupe leaders and $15 per day for artistes. Required Part A Assuming that the facility can maintain an average annual occupancy of 80% in both troupe leader and artistes suites (based on a 360 -day year), calculate the following: i. the annual fixed costs ii. the variable cost per guest by type of guest iii. the annual number of guest days by type of guest
Answers
Part A:
i. Annual fixed costs:
Depreciation is a fixed cost, and it is given that the facility's annual depreciation cost is $160,000. Therefore, the total annual fixed costs would be:
Total annual fixed costs = Depreciation cost = $160,000
ii. Variable cost per guest by type of guest:
The variable cost per day for troupe leaders is $40, and for artistes, it is $15. The variable cost per guest can be calculated by multiplying the variable cost per day by the number of days of stay:
Variable cost per troupe leader guest = $40 x 1 guest x 360 days = $14,400
Variable cost per artiste guest = $15 x 1 guest x 360 days = $5,400
iii. Annual number of guest days by type of guest:
Assuming an average annual occupancy of 80% in both troupe leader and artistes suites, the annual number of guest days can be calculated as follows:
Number of troupe leader guest days = 10 guests x 360 days x 80% occupancy = 2,880 guest days
Number of artiste guest days = 50 guests x 360 days x 80% occupancy = 14,400 guest days
Therefore, the annual fixed costs are $160,000, the variable cost per troupe leader guest is $14,400, the variable cost per artiste guest is $5,400, and the annual number of troupe leader guest days is 2,880 and the annual number of artiste guest days is 14,400.
algebra hw I will give brainlyest
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The other value of x where g(x) = 15 is 16 in the absolute value function
Finding the value of xSince the vertex of the absolute value function is at (10,0), the equation for the function can be written as:
g(x) = a|x - 10|
To find the value of a, we can use the fact that the function passes through the point (4,15):
15 = a|4 - 10|
15 = 6a
a = 2.5
So the equation for the absolute value function is:
g(x) = 2.5|x - 10|
To find another value of x where g(x) = 15, we can set the equation equal to 15 and solve for x:
2.5|x - 10| = 15
|x - 10| = 6
x - 10 = 6 or x - 10 = -6
x = 16 or x = 4
Therefore, there are two possible values of x where g(x) = 15: x = 16 and x = 4.
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Please answer correctly and explain reasoning for brainliest (If correct) and thanks!
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Therefore, the correct answer is option C that is LM is reflected over the y-axis to L'M.
What is transformation?In mathematics, a transformation refers to a change in the position, shape, or size of a geometric figure. Transformations can be classified into four types: translation, rotation, reflection, and dilation.
Here,
The transformation of LM to L'M' involves both translation and reflection. To see the translation, we can compare the x- and y-coordinates of L and L', as well as M and M':
The x-coordinate of L' is 5 units more than the x-coordinate of L: -2 = -7 + 5.
The y-coordinate of L' is 2 units less than the y-coordinate of L: -4 = -2 - 2.
The x-coordinate of M' is 5 units more than the x-coordinate of M: 5 = 0 + 5.
The y-coordinate of M' is 2 units less than the y-coordinate of M: 3 = 5 - 2.
Therefore, we can conclude that LM is translated 5 units right and 2 units down to L'M'. This eliminates options OB and OD. To see the reflection, we can compare the x-coordinates of L and M, and their respective x-coordinates in L' and M':
The x-coordinate of L is negative and the x-coordinate of M is positive.
The x-coordinate of L' is negative and the x-coordinate of M' is positive.
Therefore, we can conclude that LM is reflected over the y-axis to L'M'. This eliminates option OA. Therefore, the correct answer is option OC.
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Factor the polynomial completely. If the polynomial is prime, so state.
15y2 - 19y + 6
Answers
Answer: 15y2 - 19y + 6 = 0
Step-by-step explanation:
The first term is, 15y2 its coefficient is 15 .The middle term is, -19y its coefficient is -19 .The last term, "the constant", is +6 Step-1 : Multiply the coefficient of the first term by the constant 15 • 6 = 90 Step-2 : Find two factors of 90 whose sum equals the coefficient of the middle term, which is -19 .
Find the perimeter of each figure
Answers
The perimeter of the composite figure is 46 metres.
How to find the perimeter of a figure?The perimeter of a figure is the sum of the whole sides of the 2 dimensional figure. Therefore, the perimeter of the composite figure is the sum of the whole sides.
Therefore, the perimeter of the figure can be found as follows:
perimeter of the shape = 5 + 6 + 9 + 11 + 3 + 12
perimeter of the shape = 11 + 9 + 11 + 15
perimeter of the shape =20 + 11 + 15
perimeter of the shape = 31 + 15
perimeter of the shape = 46 metres
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PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
Answers
A. The expression that represents the total amount of canned food they have collected so far is: 4x² + 2xy + 3
B. Number of canned food still remaining to be collected is: 2x² - 4xy + 5
How to Solve Polynomial Expressions?A polynomial expression is a mathematical expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication of non-negative integer exponents.
Part A: To find the expression that represents the total amount of canned food they have collected so far, add the expression for each person given together.
3x² - 2 + x² + 2xy + 5
Combine like terms:
4x² + 2xy + 3
Part B: Number of canned food still remaining to be collected is calculated below.
(6x² - 2xy + 8) - (4x² + 2xy + 3)
Open bracket:
6x² - 2xy + 8 - 4x² - 2xy - 3
Combine like terms:
2x² - 4xy + 5
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Help I have to turn this in tmw!!
Answers
Answer:
[tex]\large\boxed{\tt Area = Length \times Width}[/tex]
[tex]\large\boxed{\tt Area = 8.6 \ cm. \times 3 \ cm.}[/tex]
[tex]\large\boxed{\tt Area = 25.8 \ cm.^{2}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked for the area of a 2D Rectangle.}[/tex]
[tex]\large\underline{\textsf{What is Area?}}[/tex]
[tex]\textsf{Area for 2D shapes is how much space is inside between edges. Consider edges}[/tex]
[tex]\textsf{as the sides of a shape.}[/tex]
[tex]\underline{\textsf{How are we able to find Area?}}[/tex]
[tex]\textsf{Many shapes require different formulas to find the area. Some have the same}[/tex]
[tex]\textsf{formulas however it depends on how many sides the shape has, and the number of}[/tex]
[tex]\textsf{dimensions shown in the shape. For a Rectangle it's simple. Because a Rectangle}[/tex]
[tex]\textsf{has 2 Dimensions (Length and Width), to find the area we should multiply}[/tex]
[tex]\textsf{the dimensions together, hence resulting in the amount of space inside the shape.}[/tex]
[tex]\large\underline{\textsf{Formula;}}[/tex]
[tex]\large\boxed{\tt Area = Length \times Width}[/tex]
[tex]\large\underline{\textsf{Plug in Values;}}[/tex]
[tex]\textsf{The Length and Width aren't mentioned in the question, but it doesn't matter}[/tex]
[tex]\textsf{since we're still going to get the same answer no matter which place they're in.}[/tex]
[tex]\large\boxed{\tt Area = 8.6 \ cm. \times 3 \ cm.}[/tex]
[tex]\large\underline{\textsf{Solving for the Area;}}[/tex]
[tex]\textsf{We have our formula, now multiply the dimensions together.}[/tex]
[tex]\large\boxed{\tt Area = 25.8 \ cm.^{2}}[/tex]
HELP PLS 65.1 + WHAT = 100 !!!
Answers
Answer: 34.9
Step-by-step explanation: 100 - 65.1
Overview
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At a school there are five lessons in a day.
In total, the five lessons last for 4 hours.
a) Assume that each lesson lasts the same amount of time.
How many minutes long is the final lesson?
Optional working
+ Answer:
b) In fact, the first lesson of the day is shorter than the other lessons.
The other lessons last the same amount of time.
What does this tell you about the length of the final lesson?
A It is shorter than the answer to part a)
B It is the same as the answer to part a)
C It is longer than the answer to part a)
minutes
Submit Answering
Answers
Time taken by final lesson is 48 minutes and time consumption will not be affected if first lesson takes less time to finish.
Given that;
The time to finish five lessons = 4 hours
Then one lesson takes = 4/5 hours to finish
(a) Since each lesson takes equal amount of time
Therefore,
The time taken by final lesson in minutes = (4/5)x60
= 48 minutes
(b) Since each lesson has own capacity of time so the time consumption for other lesson is not affected if first lesson takes less time.
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Given that a function, g, has a domain of -20 s × s 5 and a range of -5 s g(x) s 45 and that g(0) = -2 and g(-9) = 6, select the statement that could true for g.
A. g(-4)= -11
B. g(-13)= 20
C. g(0) = 2
D. g(7) = -1
Answers
The statement that could be true for the domain of g is g(-4) = -11.
option A.
Which statement is true for domain of g?
The function g has a domain of -20 s × s 5 and a range of -5 s g(x) s 45 and that g(0) = -2 and g(-9) = 6.
The given statements that could be true for g is calculated as follows;
Option A: g(-4) = -11
Since the range of g is -5 s g(x) s 45, it is possible for g(-4) to be -11.
Therefore, this could be true.
Option B: g(-13) = 20
Since the domain of g is -20 s × s 5, it is not possible for g(-13) to be defined. Therefore, option B is not true.
Option C: g(0) = 2
We are given that g(0) = -2, so option C is not true.
Option D: g(7) = -1
Since the domain of g is -20 s × s 5, it is not possible for g(7) to be defined. Therefore, option D is not true.
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an expression that is equivelent to 12x-3x
Answers
Answer:
it would be 9x
Step-by-step explanation:
because subtract 3 from 12 and leave the x
3. How many different numbers can be created by selecting 4 of the digits from the number 8712395?
Answers
840 different numbers can be created selecting 4 of the digits from the number
How many different numbers can be created selecting 4 of the digits from the numberFrom the question, we have the following parameters that can be used in our computation:
Number = 8712395
Digits = 4
The count of digits in the number is 7
Using the above as a guide, we have the following:
First digit = any of the 7second digit = any of the remaining 6Third digit = any of the remaining 5Fourth digit = any of the remaining 4So, we have
Numbers = 7 * 6 * 5 * 4
Evaluate
Numbers = 840
Hence, 840 numbers can be formed
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A 45-year-old man puts $2500 in a retirement account at the end of each quarter until he reaches the age of 66, then makes no further deposits. If the account pays 4% interest compounded quarterly, how much will be in the account when the man retires at age 71? There will be $ in the account.
Answers
Answer: The man will make deposits for 66 - 45 = 21 years, or 21 x 4 = 84 quarters.
The quarterly interest rate is 4% / 4 = 1%.
Let's use the formula for the future value of an annuity:
FV = PMT x ((1 + r)^n - 1) / r
where FV is the future value of the annuity, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.
In this case, PMT = $2500, r = 1%, and n = 84. Substituting these values into the formula, we get:
FV = $2500 x ((1 + 0.01)^84 - 1) / 0.01
FV = $2500 x (5.409 - 1) / 0.01
FV = $2500 x 540.9
FV = $1,352,250
Therefore, there will be $1,352,250 in the account when the man retires at age 71.
Which of the following represents vector w = ❬–27, 35❭ in linear form?
w = –27i + 35j
w = 27i – 35j
w = –35i + 27j
w = 35i – 27j
Answers
Answer: w = –27i + 35j
Step-by-step explanation:
A restaurant manager tracks the number of people in every party to sit at a specific table every day for a week, then compiles the results into a probability distribution as shown in the table:
a.) There is a 25% chance that a party will contain 5 or more people. b.) There is a 50% chance that a party will contain 4 or more people. c.) There is a 50% chance that a party will contain 2 or fewer people.
d.) There is a 75% chance that a party will contain 3 or more people.
Answers
There are 25% chance of 5 more people in the party.
Hence option (a) is correct.
Relative frequency = (number of times of occurrence of an event )/ (number of trials)
For the given table
relative frequency for 1 people = 0.05 = 5%
relative frequency for 2 people = 0.46 = 46%
relative frequency for 3 people = 0.18 = 18%
relative frequency for 4 people = 0.22 = 22%
relative frequency for 5 people = 0.06 = 6%
relative frequency for 6 people = 0.03 = 3%
Since relative frequency for 1 people is 5%
Therefore,
Relative frequency for 5 people is = 5x5%
= 25 %
Hence,
Relative frequency of 5 more people 25%.
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Solve for x. Round to the nearest tenth of a degree, if necessary.
Answers
The value of x it the nearest tenth of degree is 25.6°
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Sin(tetha) = opp/ hyp
cos( tetha) = adj/ hyp
tan( tetha) = opp/ adj
Here, the hypotenuse is 92 and adjascent to the to the angle x is 63
therefore to calculate x we use cosine function
cos x = 83/92
cos x = 0.902
x = cos^-1( 0.902)
x = 25.6° ( nearest tenth)
therefore the value of x is 25.6°
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What is the perimeter and area of the Rhombus?
Z
6.2,
W
Y
7.4
9.7 cm
X
Answers
Answer:
Perimeter of rhombus = 4(9.7) = 38.8 cm
Area of rhombus = 4(1/2)(6.2)(7.4)
= 91.76 cm^2
How many more sunflowers with a height of 27 1/2 inches or more were there than sunflowers with a heigh less than 27 1/2 inches?
Answers
The number of sun flowers with a height of 27¹/₂ inches or more are 4 more than those with a height of less than 27¹/₂ inches
How to Interpret Dot Plots?A dot plot, which is also known as a strip plot or dot chart, is a simple form of data visualization that comprises of data points plotted as dots on a graph with an x- and y-axis. These types of charts are used to graphically depict certain data trends or groupings.
The number of heights below 27¹/₂ inches that exists in the given dot plot is seen to be 8 in number.
Similarly, the number of dot plots that exists above or equel to 27¹/₂ inches from the given dot plot are 12 in number.
Therefore, we can say that:
Difference in total number for both parameters = 12 - 8= 4
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Find f(-1).
Provide your answer below:
f(t)=-3t²-2t+1
Answers
Answer:
f(-1)=0
Step-by-step explanation:
To evaluate the function f(t) = -3t² - 2t + 1, we will start by plugging in -1 everywhere t occurs in the function :
[tex]\star \phantom{t-u} f(-1)=-3(-1)^2-2(-1)+1\\\\\\\star\phantom{t-u} f(-1)=-3*1+2+1\\\\\star\phantom{t-u} f(-1)=-3+3\\\\\underline{\star\phantom{t-u}f(-1)=0}[/tex]
[tex]\bigstar[/tex] Therefore the answer is f(-1) = 0
How would I solve this?
Answers
Answer:
f(1) = 1
Step-by-step explanation:
Open holes on a graph means that the function is not defined at that point, so we ignore the open hole.
At f(1), there is both an open hole at y=-2 and a closed hole at y=1
We ignore the open hole as it is not defined so the answer would be the closed hole, y = 1
So f(1) is 1
Find the area and central angle of the polygons given the apothem or side length. Thank you.
Answers
The missing parameters of the regular polygons are listed below:
Case 1: θ = 45°, a = 10.864 cm
Case 2: θ = 72°, s = 5.812 cm
How to compute parameters of regular polygons
In this problem we must determine missing parameters of regular polygons, that is, polygons with sides of equal length. All parameters are summarized below:
Central angle
θ = 360 / n
Relationship between apothema and side length
a = s / [2 · tan (180 / n)]
Where:
n - Number of sidesa - Apothemas - Side lengthNow we proceed to find missing parameters:
Case 1: s = 9 cm, n = 8
θ = 360 / 8
θ = 45°
a = (9 cm) / [2 · tan (180 / 8)]
a = 10.864 cm
Case 2: a = 8 cm, n = 5
θ = 360 / 5
θ = 72°
s = 2 · a · tan (180 / n)
s = 2 · (8 cm) · tan (180 / 5)
s = 5.812 cm
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I need to find both of the solutions to the equation 100+(n-2)^ = 149
Answers
The solutions to the equation 100+ (n - 2)² = 149 are n = 9 and n = -5
Finding the solutions to the equation 100+ (n - 2)² = 149From the question, we have the following parameters that can be used in our computation:
The equation 100+ (n - 2)² = 149
Express as
100+ (n - 2)² = 149
Subtract 100 from both sides of the equation
So, we have the following representation
(n - 2)² = 49
Take the square root of both sides
n - 2 = 7 and n - 2 = -7
Add 2 to both sides
n = 9 and n = -5
Hence, the solutions to the equation 100+ (n - 2)² = 149 are n = 9 and n = -5
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