The reasonable domain and range of the function is option (A) Domain: {1, 2, 3, 4, 5, …}; Range: {2, 6, 18, 54, 162, …}.
The sequence appears to be an exponential sequence with a common ratio of 3. That is, each term is obtained by multiplying the previous term by 3.
If this sequence defines a function, a reasonable domain would be the set of positive integers starting from 1 since the sequence begins with the first term being 2.
The range of the function appears to be the set of positive powers of 3 since each term is a power of 3 multiplied by the initial term, 2. Therefore, a reasonable range would be the set {2, 6, 18, 54, 162, ...}.
Therefore, the correct option is (A) Domain: {1, 2, 3, 4, 5, …}; Range: {2, 6, 18, 54, 162, …}.
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12 Workers can do a piece of work in 30 days. Find how many workers should be added to finish the work in 24 days?
The answer is in the attachment given below ...
Thank you :)
Which line is perpendicular to the line y = -3x + 2
Answer:d
Step-by-step explanation:
real cube root of 64
The real cube root of 64 is 4.
What is Real cube root ?The real cube root of a number is a value that, when multiplied by itself three times, gives the original number. In other words, the cube root of a number x is a number y such that y * y * y = x.
the prime factorization using the exponent found in the previous step. We can write the number 64 as:
64 = 2^2 * 2^2 * 2^2
Step 4: Take the cube root of the factor that appears with the exponent found in Step 2. In this case, the factor is 2:
∛2 = 1.259921...
Step 5: Multiply the factors together to get the final result:
∛64 = ∛(2^2 * 2^2 * 2^2) = ∛2^6 = (∛2)^2 = 1.259921...^2 = 4
Therefore, the real cube root of 64 is 4.
On the other hand we can easily find out by, the real cube root of 64 is 4, because 4 multiplied by itself three times gives 64:
4 * 4 * 4 = 64
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The real cube root of 64 is 4.
What is a Real cube root?
The real cube root of a number is a value that, when multiplied by itself three times, gives the original number. In other words, the cube root of a number x is a number y such that y * y * y = x.
the prime factorization using the exponent found in the previous step. We can write the number 64 as:
64 = 2² * 2² * 2²
Step 4: Take the cube root of the factor that appears with the exponent found in Step 2. In this case, the factor is 2:
∛2 = 1.259921...
Step 5: Multiply the factors together to get the final result:
∛64 = ∛(2² * 2² * 2²) = ∛2⁶ = (∛2)² = (1.259921...)² = 4
Therefore, the real cube root of 64 is 4.
On the other hand, we can easily find out by, the real cube root of 64 is 4 because 4 multiplied by itself three times gives 64:
4 * 4 * 4 = 64
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Tableau DA 3-2: Exercise, Computing cost per equivalent unit and assigning costs to output LO P1
The equivalent unit of production- Weighted Average Method is given in the attached image.
What is the equivalent unit of production- Weighted Average Method?The equivalent units of production (EUP) in the weighted average method refer to the units of output that have been partially completed during a period, and are expressed in terms of fully completed units.
In the weighted average method, the costs incurred during the period are combined with the costs of beginning work in process (BWIP) to determine the cost per equivalent unit. This cost per equivalent unit is then used to assign costs to the units completed and transferred out and to the units still in process at the end of the period.
The EUP in the weighted average method is calculated by adding together the units completed during the period with the equivalent units of work done on the units that are still in process at the end of the period.
The equivalent units are calculated by multiplying the number of partially completed units by the percentage of completion for the period.
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PLEASE HELPPP AND SHOW THE WORKKKK
The answer will be as follows after answering the supplied question As a result, the equation of the line connecting the points (-1, -3) and (3, 5) is y = 2x - 1.
What is equation?A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.
y - y1 = m(x - x1) (x - x1)
where (x1, y1) is the location of one of the points and m is the line's slope.
We may use the slope formula to calculate the slope:
m = (y2 - y1) / (x2 - x1) (x2 - x1)
where the coordinates of the two points are (x1, y1) and (x2, y2).
m = (5 - (-3)) / (3 - (-1)) = 8 / 4 = 2
As a result, the slope of the line is 2. We can now use one of the two locations to get the equation of the line. Let's take (-1, -3) as an example:
y - (-3) = 2(x - (-1))
y + 3 = 2(x + 1)
y + 3 = 2x + 2
y = 2x - 1
As a result, the equation of the line connecting the points (-1, -3) and (3, 5) is y = 2x - 1.
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The height of a basketball thrown by a 6 foot tall man follows a path defined by the function h(x) = -0. 5x^{2} + 3x + 6 h(x)=−0. 5x2+3x+6, where x is the horizontal distance from where it is thrown. How far away from the basket should the player stand in order for the ball to go in the basket (10 feet high) on its way down? Show all work
Answer:
Step-by-step explanation:
Multiply both sides by 2.
Splitting the middle term, we get
In the given function the leading coefficient is negative, so the given function represents a downward parabola. It means, first the function is increasing after that the function is decreasing.
So, the value of the function is 10 at (its way up) and at (its way down.
Therefore, the player should stand 4 units away from the basket in order for the ball to go in the basket (10 feet high) on its way down.
A number from 1-54 is chosen at random. Find each probability as a fraction (in simplest form), decimal, and percent.
P(odd or at most 14)
a: 7/27, 0.2593, 25.93%
b: 17/27, 0.62, 62%
c: 7/27, 0.25, 25%
d: 17/27, 0.6296, 62.96%
-------------------------------------
A card is chosen at random from a standard deck. Find each probability as a fraction in simplest form.
P(king)
a:1/52
b: 1/13
c: 4/52
d: 13/52
-----------------------
A card is chosen at random from a standard deck. Find each probability as a fraction in simplest form.
P(spade or heart)
Group of answer choices
a: 1/26
b: 1/2
c: 26/52
d: 2/52
------------------------
i dont need any explanations, so just the answers please ^^
Answer:
P(odd or at most 14)
Answer: (a) 7/27, 0.2593, 25.93%
P(king)
Answer: (d) 13/52
P(spade or heart)
Answer: (b) 1/2
a youth basketball team is made up of 7 girls and 6 boys. the coach assigns five players at a time to specific positions. how many ways can the thirteen players be assigned to the five different positions? provide your answer below:
After using the npr formula, there are 154440 ways that the thirteen players on the youth basketball team can be assigned to the five different positions.
There are a total of 13 players on the youth basketball team, and there are five different positions that need to be filled. To determine the number of ways that the players can be assigned to these positions, we can use the formula for permutations:
P(n, r) = n! / (n - r)!
Where n is the total number of players, and r is the number of positions. In this case, n = 13 and r = 5. Plugging these values into the formula, we get:
P(13, 5) = 13! / (13 - 5)!
= 13! / 8!
= (13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
= (13 * 12 * 11 * 10 * 9) / 1
= 154440
Therefore, there are 154440 ways that the thirteen players on the youth basketball team can be assigned to the five different positions.
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Find the probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker. The probability is (Round to six decimal places as needed.)
The probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker is 0.0032.
The probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker is given by 0.0032. Probability is a concept of Mathematics. It is a measure of the likelihood of an event taking place. The concept of probability is very essential in the study of Mathematics. It helps us in determining the chance of occurrence of an event.What is the formula for probability?The probability of an event is represented by a number between 0 and 1. A probability of 0 indicates that the event is impossible while a probability of 1 indicates that the event is certain to happen.
The formula for probability is given by;Probability (P) = Number of favourable outcomes/ Total number of outcomes.The given event is to find the probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker.In a deck of cards, there are 13 clubs. Out of these, we have to select 4 cards. This can be done in (13C4) ways. Similarly, one card can be chosen from each of the remaining three suits. This can be done in (13C1) * (13C1) * (13C1) ways.
Therefore, the total number of ways in which we can choose 7 cards is given by (52C7).Thus, the required probability is given by;Probability = Number of favourable outcomes/ Total number of outcomes.Number of favourable outcomes = (13C4) * (13C1) * (13C1) * (13C1)Total number of outcomes = (52C7)Probability = Number of favourable outcomes/ Total number of outcomes= [(13C4) * (13C1) * (13C1) * (13C1)]/ (52C7)= 0.0032 (rounded to 6 decimal places).Therefore, the probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker is 0.0032.
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The frequency table shows the scores from rolling a dice 10 time 1 1 2 2 3 1 4 2 5 4 6 2 find the mean
On answering the provided question, we have got that 3.3 is the average equation result after rolling the dice ten times.
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
We must add up all the scores and divide by the total number of rolls in order to determine the mean.
The total of every score is:
1 + 1 + 2 + 2 + 3 + 1 + 4 + 2 + 5 + 4 + 6 + 2 = 33
There are ten rolls in total.
The mean is as a result:
mean = total scores / total rolls = 33 / 10 = 3.3
3.3 is the average result after rolling the dice ten times.
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HELP PLEASE
its math
Thank you
Answer:
Option 2
Step-by-step explanation:
For two angles to be adjacent they need to have a common side/ray and a common vertex!
Hope this helps!!!
Answer:
Step-by-step explanation:
In geometry, two angles are adjacent if they have a common side and a common vertex. In other words, adjacent angles are directly next to each other and do not overlap.
->No, the two indicated angles do not share common vertex
now that we have determined that the problem deals with combinations, calculate the number of ways that six letters can be grouped from nine letters total. fill in the blanks below with the correct numbers. provide your answer below:
Answer : There are 84 different ways that six letters can be grouped from nine letters total.
Now that we have determined that the problem deals with combinations, we can use the formula for combinations to calculate the number of ways that six letters can be grouped from nine letters total. The formula for combinations is:
C(n,k) = n! / (k! * (n-k)!)
Where n is the total number of items, and k is the number of items being chosen. In this case, n = 9 and k = 6. Plugging these values into the formula gives us:
C(9,6) = 9! / (6! * (9-6)!)
C(9,6) = 9! / (6! * 3!)
C(9,6) = 362880 / (720 * 6)
C(9,6) = 362880 / 4320
C(9,6) = 84
Therefore, there are 84 different ways that six letters can be grouped from nine letters total.
Answer: 84.
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Find the mean of the first five natural numbers
Answer:
The first five natural number are 1, 2, 3, 4 and 5. Hence, the mean of the five natural numbers is 3.
Answer:
3
Step-by-step explanation:
[tex]\frac{1+2+3+4+5}{5}[/tex] = [tex]\frac{15}{5}[/tex] = 3
The natural numbers are also called the counting numbers. They are the set of numbers: 1, 2, 3, ....
Helping in the name of Jesus.
The value of a second-hand car is £8000
Each year it loses 20% of it value at the start of this year. work out its value an year ago
pls pls help quick
Answer:
£10,000
Step-by-step explanation:
100%-20%= 80% --> 0.8
£8000 divided by 0.8 = £10,000
Which function is the inverse of f(x)= -x^3 -9?
Answer:
B. [tex]\sqrt[3]{-x-9}[/tex]
Step-by-step explanation:
Switch x and y, and then solve for y.
[tex]y = -x^3-9\\x=-y^3-9\\x+9=-y^3\\-x-9=y^3\\\sqrt[3]{-x-9} =y[/tex]
Please I need help. Using y=k/x, you get k=1.5. So applying this, the first two are correct and in inverse proportion, however the last one doesn’t seem to work. Please help
Answer:
The last one doesn't work because s and t aren't inversely proportional. If they were inversely proportional, k would remain constant.
Use the central limit theorem(CLT) to compute the expected amount of sampling error with a sample size of 25 for the population with a mean of μ= 16 and a standard deviation of σ= 5 show work.
The expected amount of sampling error with a sample size of 25 is 1.
The Central Limit Theorem (CLT): What is it?According to the Central Limit Theorem (CLT), a statistical theory, regardless of the population distribution's form, the distribution of sample means tends to resemble a normal distribution as sample size grows. This indicates that the distribution of the means of multiple samples of the same size taken from a population will be roughly normal. Since it enables us to utilise normal distribution features to draw conclusions about a population even when the population distribution is unknown or non-normal, the CLT is crucial to statistics.
Given that, μ= 16 and σ= 5.
The formula for the standard error of the mean (SEM) is:
SEM = σ / √(n)
SEM = 5 / √(25)
SEM = 1
Hence, the expected amount of sampling error with a sample size of 25 is 1.
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Combine the like terms to create an equivalent expression.
7+4c+2d+3=7+4c+2d+3=7, plus, 4, c, plus, 2, d, plus, 3, equals
Answer:
4c + 2d + 10
Step-by-step explanation:
The expression given is mostly already simplified, and the like terms that have variables are already combined.
As for 7 and 3, they are like terms because neither of them are attached to a variable.
Combining these like terms:
7 + 3 = 10The equivalent expression is now 4c + 2d + 10.
8. Theo went to a bakery on Saturday morning. He bought a cup of hot chocolate and some bagels. The hot
chocolate cost $3.50 and each bagel costs $0.75 each.
(a) Write a linear function, that models the total cost, c, in dollars, of Theo's order based on the number of
bagels, b, he buys.
(b) Explain what the statement below means in the context of the problem.
c(6)=8
a) The total cost, c, in dollars, of Theo's order based on the number of
bagels, b, he buys is: c = 0.75b + 3.5
b) The statement c(6) = 8 represents that the number of bagels bought was 6 which resulted in a total cost of $8
How to solve Linear Equation Word Problems?The general expression for a linear equation in slope intercept form is:
y = mx + b
Where:
m is slope
b is y-intercept
a) Let the number of bagels bought be b
Cost of each bagel = $0.75
Cost of chocolate = $3.50
Thus:
Total cost is:
c = 0.75b + 3.5
b) c(6)=8
This means the number of bagels bought was 6 which resulted in a total cost of $8
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Sam and terry contribute money to buy 2 litre tub of juice in the ratio of 2:3 calculate the amount of juice each one received after sharing in the ratio of 2:3
Sam will receive 0.8 litres of juice, and Terry will receive 1.2 litres of juice after sharing the 2-litre tub of juice in the ratio of 2:3.
To solve this problem, we need to use the concept of ratio and proportion.
Let's first find the total amount of money contributed by Sam and Terry. Since the ratio of their contributions is 2:3, we can write:
Total contribution = Sam's contribution + Terry's contribution
Let's assume that Sam contributed $2x and Terry contributed $3x. Then, we have:
Total contribution = $2x + $3x = $5x
Now, we know that the total contribution is equal to the price of the juice, which is not given in the problem. So, let's assume that the price of the 2-litre tub of juice is $10. Then, we have:
Total contribution = Price of juice = $10
Therefore,
$5x = $10
Solving for x, we get:
x = $2
So, Sam contributed $4 and Terry contributed $6.
Now, to find the amount of juice each one received, we need to share the 2-litre tub in a ratio of 2:3.
The total ratio is 2+3 = 5.
So, Sam will receive 2/5 of the juice and Terry will receive 3/5 of the juice.
Therefore, Sam will receive (2/5) × 2 litres = 0.8 litres of juice, and Terry will receive (3/5) × 2 litres = 1.2 litres of juice.
In conclusion, Sam will receive 0.8 litres of juice, and Terry will receive 1.2 litres of juice after sharing the 2-litre tub of juice in a ratio of 2:3.
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meters and feet are two different scales for measuring distance. Five meters is approximantly 16.41 ft, and 12 m is approximently 39.37ft. write an equation that shows the approximate distance in feet as a function of the distance in meters
Step-by-step explanation:
16.41 ft / 5 m = 'unit rate' (or conversion factor) = 3.282 ft/ m
then # ft = 3.282 ft / m * # meter (approximately )
The following table shows the number of attendees at each of the private dance events hosted by Fenel Arrangements.
Event Martha's Moonwalk Shirly's Shimmy Harry's Hoedown
# 48 33 ?
If the mean of the data set is 41 attendees, find the number of attendees at Harry's Hoedown
The number οf attendees at Harry's Hοedοwn is 42.
What is data set?A data set is a cοllectiοn οf cοnnected data. In the case οf tabular data, a data set is assοciated with οne οr mοre database tables, where each rοw alludes tο a particular recοrd in the assοciated data set and each cοlumn tο a particular variable.
Suppοse the number οf Harry's Hοedοwn attendees be "x"
Given, Mean οf the data = 41 attendees
We knοw,
Mean = sum οf οbservatiοns / number οf οbservatiοns
41 = (48+33+x) / 3
48 + 33 + x = 123
x = 123 - (48+33)
x = 42
Hence the correct answer is 42 attendees.
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Answer:
42
Step-by-step explanation:
A small country emits 150,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 0.5% per year for the next 5 years. In the first year of the agreement, the country will keep its emissions at 150,000 kilotons and the emissions will decrease 0.5% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 5 year period, to the nearest whole number?
Rounding to the nearest whole number, the total emissions over the 5-year period would be approximately 743,289 kilotons of carbon dioxide.
What is percentage ?Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". For example, 50% is equal to 50/100, which simplifies to 0.5. Percentages are often used to express proportions or ratios in a way that is easier to understand. For instance, if there are 20 red balls and 80 blue balls in a bag, we could say that the ratio of red balls to blue balls is 1:4, or we could express this as a percentage by saying that 20% of the balls are red and 80% are blue.
According to given information :To calculate the total carbon emissions over the 5-year period, we need to calculate the emissions for each year and then add them up.
Starting with the current emission level of 150,000 kilotons, the emissions in each of the next 5 years will be:
Year 1: 150,000 kilotons (no reduction)
Year 2: 150,000 * (1 - 0.005) = 149,325 kilotons
Year 3: 149,325 * (1 - 0.005) = 148,654 kilotons
Year 4: 148,654 * (1 - 0.005) = 147,987 kilotons
Year 5: 147,987 * (1 - 0.005) = 147,323 kilotons
To get the total emissions over the 5-year period, we add up the emissions for each year:
150,000 + 149,325 + 148,654 + 147,987 + 147,323 = 743,289 kilotons
Therefore, rounding to the nearest whole number, the total emissions over the 5-year period would be approximately 743,289 kilotons of carbon dioxide.
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Answer:742537
Step-by-step explanation: I did the math, and this is the correct answer
The function f(x)=4x-8 is reflected accross the y axis resulting in a new function write the equation of g(x)
A triangle with a height of 9 inches has an area of 36 square inches. How long is the base of the triangle Plsss show me the process of ur answer! Tyy
On his 25th birthday, Matthew started an annuity for his retirement. He deposits $630 each month into an account earning 8% annual interest compounded monthly. He determines that he will be able to retire once he has $1,000,000 in his retirement account. Determine how old Matthew will be when he is able to retire.
Matthew who started an annuity on his 25th birthday by depositing $630 monthly into an account earning 8% annual interest compounded monthly will become 55 years old when the retirement account will be $1,000,000.
What is an annuity?An annuity involves a series of payments made periodically.
The annuity attracts an interest rate compounded periodically.
Compounding involves charging interest on accumulated interest and the principal for each compounding period.
I/Y (Interest per year) = 8%
PV (Present Value) = $0
PMT (Periodic Payment) = $630
FV (Future Value) = $1,000,000
Results:
N = 368.641 months
= 30 years and 9 months
Sum of all periodic payments = $232,470
Total Interest = $767,530
Matthew's current age = 25 years
55 years old (25 + 30)
Thus, Matthew will be 55 years old when his retirement (annuity) account grows to $1,000,000.
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For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. 32.f(x)=x3−2x2−29x−423x2−7x−20
From the given data, the vertical intercept, vertical asymptotes and slant asymptote are 2, -5/3 and 4, y = x² - 5x + 13 respectively.
To find the horizontal intercepts, we need to set f(x) = 0 and solve for x:
x³ - 2x² - 29x - 42 / (3x² - 7x - 20) = 0
We can factor the denominator using the quadratic formula:
3x² - 7x - 20 = (3x + 5)(x - 4)
Now, we can write the function as:
f(x) = (x³ - 2x² - 29x - 42) / (3x + 5)(x - 4)
To find the vertical intercept, we need to set x = 0:
f(0) = -42/(-5)(-4) = 2.1
To find the vertical asymptotes, we need to find the values of x that make the denominator equal to zero:
3x + 5 = 0 or x - 4 = 0
Solving for x, we get:
x = -5/3 or x = 4
Therefore, the vertical asymptotes are x = -5/3 and x = 4.
To find the horizontal or slant asymptote, we need to look at the degree of the numerator and denominator. Since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. Instead, there is a slant asymptote, which we can find by dividing the numerator by the denominator:
x³ - 2x² - 29x - 42 / (3x + 5)(x - 4) = (x² - 5x + 13) + (-2x - 2) / (3x + 5)(x - 4)
The slant asymptote is the line y = x² - 5x + 13.
Now, we can sketch the graph of the function. The graph will approach the vertical asymptotes at x = -5/3 and x = 4. The function will intersect the x-axis at x = -2, x = 3, and x = 7. The function will intersect the y-axis at y = 2.1. The graph will approach the slant asymptote y = x² - 5x + 13 as x approaches infinity or negative infinity.
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If the bunny ran from −81 to 81 with average speed of 18 units per minute then, the distance is ?
units and it ran for ?
minutes.
Answer:
162 and 9
Step-by-step explanation:
The distance he ran for is from - 81 to 0 and to 81
81 +81 = 162 units
Time spent =distance/speed
Time = 162/ 18 = 9mins
Write tan x in terms of cos x.
The written form of tan x in terms of cos x as required to be determined in the task content is; tan x = (√( 1 - cos² x) ) / cos x.
What is tan x in terms of cos x?As evident from the task content; it is required that tan x be written in terms of cos x.
Hence, recall from trigonometric identities that;
tan x = sin x / cos x
However, since sin² x = 1 - cos² x from ( sin²x + cos²x = 1)
It follows that; sin x = √( 1 - cos² x)
Hence, it can be written that;
tan x = (√( 1 - cos² x ) ) / cos x.
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20. What is the value of x to the nearest tenth? The diagram is not drawn to scale. (1 point)
x
x=14.4
x 12.7
x=3.0
x=2.2
Using similar triangle theorem, to calculate the ratios of the length, the value of x is 14.4 units
What is similar triangle theoremThe similar triangle theorem, also known as the AA (angle-angle) similarity theorem, states that if two triangles have two corresponding angles that are congruent, then the triangles are similar. That is, the corresponding sides of the triangles are in proportion, and the ratios of the corresponding sides are equal. In other words, if ΔABC ~ ΔDEF, then:
AB/DE = BC/EF = AC/DF
This theorem can be used to solve problems involving similar triangles, such as finding unknown side lengths or angles.
To find the value of x, we need to apply similar triangle theorem.
Taking the ratios of sides from the two triangles;
13.5 / 6.2 = x / 6.6
Cross multiply both sides and solve for x
x = (13.5 * 6.6) / 6.2
x = 14.4 units
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