Answer:
46.05 years
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
Given:
A = $1000P = $100r = 5% = 0.05Substitute the given values into the continuous compounding formula and solve for t.
[tex]\implies 1000=100e^{0.05t}[/tex]
[tex]\implies 10=e^{0.05t}[/tex]
[tex]\implies \ln 10=\ln e^{0.05t}[/tex]
[tex]\implies \ln 10=0.05t\ln e[/tex]
[tex]\implies \ln 10=0.05t[/tex]
[tex]\implies t=\dfrac{1}{0.05}\ln 10[/tex]
[tex]\implies t=20\ln 10[/tex]
[tex]\implies t=46.0517018... \rm years[/tex]
Therefore, it will take 46.05 years for the initial investment of $100 to reach $1000.
Water is flowing from a horizontal pipe 48 feet above the ground. The falling stream of water has the shape of a parabola whose vertex (0, 48) is at the end of the pipe (see figure). The stream of water strikes the ground at the point (10 sqrt3 , 0). Find the equation of the path taken by the water
The water stream's parabola has the equation y = 48 - (x2)/(20*sqrt(3)), with the vertex at (0, 48) and the point of impact at (10sqrt(3), 0).
The equation of the parabola created by the water stream has a vertex at (0, 48), which is where the pipe ends. It is a quadratic equation. The pipe serves as the middle of the parabola's base, which is symmetrical and has a vertex at that location. The vertex form of a parabola can be used to determine the equation of the parabola, which is y = 48 - (x2)/(20*sqrt(3)). The parabola opens downward, with the highest point at (0, 48) and the lowest point at (10sqrt(3), 0), where the water stream hits the ground, according to the equation. The parabola's vertex and point of impact with the ground are described by the equation for the water's journey.
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The units of an item available for sale during the year were as follows:
Jan. 1
Inventory
9 units at $39
$351
Aug. 13
Purchase
9 units at $41
369
Nov. 30
6 units at $42
252
Available for sale
24 units
There are 7 units of the item in the physical inventory at December 31. The periodic inventory system is used. Determine the inventory cost usin
first-in, first-out (FIFO) method; (b) last-in, first-out (LIFO) method; and (c) weighted average cost method (round per-unit cost to two decimal
your final answer to the nearest whole dollar).
Purchase
a. First-in, first-out (FIFO)
b.
Last-in, first-out (LIFO)
c. Weighted average cost
Feedback
M
$972
41 X
Check My Work
a. When the FIFO method is used, costs are included in cost of goods sold in the order in which they were purchased.
b. When the LIFO method is used, the cost of the units sold is the cost of the most recent purchases.
c. The average cost method is sometimes called the weighted average method. The average cost method uses the average unit cost for dete
cost of goods sold and the ending inventory.
Answer: a. First-in, first-out (FIFO) method:
Under FIFO, the first units purchased are assumed to be the first units sold.
9 units were sold at $39 each for a total cost of $351
9 units were sold at $41 each for a total cost of $369
6 units were sold at $42 each for a total cost of $252
So the total cost of goods sold is $351 + $369 + $252 = $972
The 7 units remaining in inventory at the end of the year were purchased at $41 each, so their cost is 7*41 = $287
b. Last-in, first-out (LIFO) method:
Under LIFO, the most recent units purchased are assumed to be the first units sold.
6 units were sold at $42 each for a total cost of $252
9 units were sold at $41 each for a total cost of $369
9 units were sold at $39 each for a total cost of $351
So the total cost of goods sold is $252 + $369 + $351 = $972
The 7 units remaining in inventory at the end of the year were purchased at $39 each, so their cost is 7*39 = $273
c. Weighted average cost method:
Under the weighted average cost method, the average cost of all the units is used to determine the cost of goods sold and ending inventory.
The total cost of the units available for sale is $351 + $369 + $252 = $972 and the total number of units available for sale is 24. So, the average cost per unit is $972 / 24 = $40.50
The cost of goods sold is $40.50 * 24 = $970.
The cost of the units remaining in inventory at the end of the year is $40.50 * 7 = $283.50
Note: The final answers were rounded to the nearest whole dollar.
Step-by-step explanation:
Explain how a $45 Timex watch and a $10,000 Rolex watch deliver value to respective target markets? Which factors account for the dramatic difference in watch prices?
Brand and product quality are the factors account for the dramatic difference in watch prices.
What are Factors?The factors of production are resources that are the building blocks of the economy they are what people use to produce goods and services.
Given that the Timex watch is $45.
Rolex watch is $10000.
We have to find the factors account for the dramatic difference in watch prices.
The rolex watch quality is better than the Timex, so the price of Rolex watch is high compared to Timex.
The brand and product quality are the factors account for the dramatic difference in watch prices.
Hence, brand and product quality are the factors account for the dramatic difference in watch prices.
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Swimming Pool On a certain hot summer's day, 445 people used the public swimming pool. The daily prices are $1.75
for children and $2.50 for adults. The receipts for admission totaled $964.75. How many children and how many adults
swam at the public pool that day?
250 adults and 195 children swam at the public pool on that day.
What is the system of linear equations?
A system of linear equations is a set of two or more equations that contain two or more variables. The goal is to find the values of the variables that will satisfy all of the equations in the system.
This is a system of equations problem. We can start by using two variables, x for the number of children and y for the number of adults, and then set up two equations based on the information given.
The first equation is for the total number of people: x + y = 445
The second equation is for the total amount of money collected: 1.75x + 2.5y = 964.75
We can now use the first equation to solve for one of the variables in terms of the other, and then substitute that expression into the second equation.
x + y = 445
x = 445 - y
Now we substitute x = 445 - y into the second equation
1.75(445 - y) + 2.5y = 964.75
after solving this equation we get
y = 250
x = 195
Hence, 250 adults and 195 children swam at the public pool on that day.
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avin was reviewing a scatterplot and noticed several negative coefficients on the scatterplot. which of the following does that tell avin about the correlation coefficients?
A negative correlation coefficient indicates that as one variable increases, the other variable decreases. This means that the points on the scatterplot are spread in a downward direction, which suggests a negative correlation between the two variables.
A scatterplot is a graph that shows the relationship between two variables by plotting points that represent the values of the two variables. When reviewing a scatterplot, one can look for the correlation coefficient, which is a statistical measure that describes the strength of the relationship between the two variables. A negative correlation coefficient indicates that as one variable increases, the other variable decreases. This means that the points on the scatterplot are spread in a downward direction, which suggests a negative correlation between the two variables. A scatterplot with several negative coefficients indicates that the correlation between the two variables is negative, meaning that when one variable increases, the other one decreases. The strength of the correlation is determined by how close the points on the scatterplot are to the line of best fit. A strong negative correlation means that the points are close to the line of best fit and are spread in a downward direction, while a weak negative correlation means that the points are further away from the line of best fit and are spread in a more random pattern.
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what is the y-interpect on this graph
Answer:
16
Step-by-step explanation:
It's the number where the line crosses the y-axis
(a) Suppose that to provide additional funds for higher education, the federal government adopts a new income tax plan that consists of the 2010 income tax plus an additional 200 dollars per taxpayer. Let gg be the function such that g(x)g(x) is the 2010 federal income tax for a single person with taxable income xx dollars, and let hh be the corresponding function for the new income tax plan.
Write a formula for h(x)h(x) in terms of g(x)g(x):
h(x)=
⋅g(=
)+=
(b) Suppose that in order to pump more money into the economy during a recession, the federal government adopts a new income tax plan that makes income taxes 95 percent of the 2010 income tax. Let gg be the function such that g(x)g(x) is the 2010 federal income tax for a single person with taxable income xx dollars, and let hh be the corresponding function for the new income tax plan.
Write a formula for h(x)h(x) in terms of g(x)g(x):
h(xh(x)=
⋅g(=
)+=
h(x) = g(x) + 200, which means the average new income tax is the sum of the original income tax and an additional flat fee of 200 dollars per taxpayer.
h(x) = g(x) + 200
h(x) is the new income tax for a single person with taxable income x dollars.
g(x) is the 2010 federal income tax for a single person with taxable income x dollars.
Therefore, h(x) = g(x) + 200, which means the new income tax is the sum of the original income tax and an additional flat fee of 200 dollars per taxpayer.
The new income tax plan consists of the 2010 income tax plus an additional 200 dollars per taxpayer. To represent this mathematically, we let g(x) be the function such that g(x) is the 2010 federal income tax for a single person with taxable income x dollars, and let h(x) be the corresponding function for the new income tax plan. By examining the new income tax plan, we can see that the new income tax is the sum of the original income tax plus an additional flat fee of 200 dollars per taxpayer. Thus, h(x) = g(x) + 200, which is a concise formula that captures the essence of the new income tax plan. This formula shows that the new income tax is simply the original income tax increased by a fixed amount of 200 dollars.
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Basketball Baseball Soccer Football 6th grade 7th grade 8th grade 2 1 7 8 4 6 4 15 Explain what the ratio 8:73 represents. 5 4 10 O The ratio 8:73 represents the ratio of total athletes to 7th grade football players. OThe ratio 8:73 represents the ratio of 6th grade football players to total athletes. O The ratio 8:73 represents the ratio of 8th grade baseball players to total athletes. OThe ratio 8:73 represents the ratio of 6th grade athletes to total athletes.
Answer:
Step-by-step explanation:
can u send the story or did you lie?
if not please e mail to ahmadhardy590 . com
Rob runs at a constant speed of 3.4 meters per second for one half hour. Then, he walks at a rate of 1.5 meters per second for one half hour. How far did Rob run and walk in 60 minutes?
The total distance that rob ran and walked for 60 minutes is; 8820 meters
How to calculate the distance covered?The parameter for the constant speed is that Rob runs at a speed of 3.4 meters per second for one half hour. Thus;
V1 = 3.4 m/s
t1 = 1.5 hours =
30 * 60 = 1,800 seconds.
The distance he runs at that speed and time is;
S1 = V1 * t1
= 3.4 * 1,800
= 6,120 meters
He walks at V2 = 1.5 m/s for t2 = 1,800 seconds.
The distance he walks;
S2 = V2 * t2
= 1.5 * 1,800
= 2,700 meters
The total distance he runs and walks;
S = S1 + S2
= 6120 + 2700
= 8820 meters
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For the expression, write an equivalent expression that uses only addition.
The expressions using only addition are (a) 4x + (-7y) + (-5z) + 6 and (a) -3x + (-8y) + (-4) + (-8/7z)
How to determine the equivalent expressionExpression 1
From the question, we have the following expression that can be used in our computation:
4x - 7y - 5z + 6
When represented using only addition, we have
4x + (-7y) + (-5z) + 6
Expression 2
From the question, we have the following expression that can be used in our computation:
-3x - 8y - 4 - 8/7z
When represented using only addition, we have
-3x + (-8y) + (-4) + (-8/7z)
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Charlie’s runs 8 miles in 74 minutes. How many minutes does he take per mile?
Answer: 9.25
For this equation you will need to use division. 74min. divided by 8mi.
To double check your answer is correct you have to multiply. 9.25min times 8mi.
please help !! JK is parallel to what?
A parachutist's rate during a free fall reaches 60 meters per second. What is this rate in feet per second? At this rate, how many feet will the parachutist fall during 2 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
Answer:
Question 1.) The rate is 198 feet per second.
Question 2.) The parachutist will fall 396 feet in 2 seconds of free fall.
Step-by-step explanation:
We have to first convert 60 meters into feet.
According to the question, we know that 1 meter is 3.3 feet. So use this equation to get 60 meters into feet.
3.3 x 60 = 198
This is in 1 second of free fall. We have to find 2 seconds of freefall so we multiply this by 2.
198 x 2 = 396 feet in 2 seconds of free fall.
I hope this was able to help you :D
Using trial and improvement, find the numbers that should replace A and B in the
rule for this sequence.
Rule:
Start at 6
Multiply by A then subtract B each time
6-8->
-36->
Using trial and improvement the numbers that should replace A and B is 20 and 34.
What is the trial and improvement process?If you are unable to solve a problem using standard algebraic techniques, try using the trial and improvement approach. If you want to get a C in math, you must comprehend this question because it typically is worth 3 marks.
According to the topic
6 = A * 2 - B = 2A - B
SZ = A - S - B = SA - B {Find the relationship}
:: 3A = 36 - 8 = 28
/ A = 28/3 = 9
; B = 2A - 8 = 18 - 8 = 10
the rule expression. 14n-10
: n = 3 , 10 . 3 - 10 = 20
n = 4 11 . 4 - 10 = 34
Using trial and improvement the numbers that should replace A and B is 20 and 34.
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light and sound waves quick check 1 of 51 of 5 items question a ringing alarm clock is put under a glass jar. the air is slowly removed from the space around it. what will happen as the air is removed? (1 point) responses the appearance of the clock will not change, but its sound will become fainter. the appearance of the clock will not change, but its sound will become fainter. the clock will slowly become less visible, until you can only hear it. the clock will slowly become less visible, until you can only hear it. the clock will slowly become quieter and will ultimately fade from view. the clock will slowly become quieter and will ultimately fade from view. the appearance of the clock and the sound of the clock will not change.
Answer:
c
Step-by-step explanation:
The sound of the alarm clock will become fainter as the air is removed from the space around it. As the air is removed, the sound waves will be unable to travel and will become more and more muffled until you can only hear a faint sound from the clock. The appearance of the clock will not change.
As the air is slowly removed from the space around an alarm clock, the sound of the clock will become fainter. This is because the sound waves will be unable to travel properly through the airless space, and will become more and more muffled until you can only hear a faint sound from the clock. The appearance of the clock will not change, however. This phenomenon is caused by sound waves being unable to travel through airless spaces, which is why sound can be muffled when you cover your ears or put something between you and the sound source. Although the clock will become quieter and its sound will become fainter, the appearance of the clock will remain the same.
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The top selling brand of vape machines sold 10000 units at $89 per unit in 2018. what is their market share if the vape machine market had sales of $1.4M?
Solve the equation on the
interval [0, 2π).
2sin(x) + √3 = 0
X =
?]π
5TT
The equation on the interval [0, 2π).x is 4π / 3 ,5π / -2
How should an interval equation be written?Intervals are expressed using parentheses or rectangular brackets, and a comma is used to separate two integers. The two numbers are referred to as the interval's endpoints. The least element or lower bound is shown by the number on the left. The biggest element or upper bound is shown by the number on the right.
As a result, when x = 4 and 5 4, f (x) has its maximum value of 1, which is 1.
A range of numbers between two specified numbers that include all real numbers in that range is known as an interval.
2sinx+ [tex]\sqrt{}[/tex]3 =0
⇒sinx= [tex]\sqrt{}[/tex] 3− 2
⇒x=nπ+(−1) ^-n 4π /3 (∵sin3 4π = [tex]\sqrt{}[/tex]3/-2 )
X =?]π5TT
x = 4π / 3 ,5π / -2
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find the largest zero for the function below. f(x)=x^3-2x^2-3x
Answer: The zeros of the function f(x) are the values of x that make f(x) equal to zero. To find the zeros of the function, we can set f(x) equal to zero and solve for x.
f(x) = x^3 - 2x^2 - 3x = 0
One way to find the zeros of the function is to factor it:
x(x-3)(x+1)=0
Thus the zeros of the function are x=0, x=3, x=-1
The largest zero of the function is 3.
Another way to find the zeros of the function would be using synthetic division or other root-finding techniques like the Newton-Raphson method.
Step-by-step explanation:
Find the area help asap!!!
Answer:
First let 'A' stand for area.
So, there's 3 areas so we write it like this:
A1: 14 ft × 3ft = 42 ft
A2: (14 ft - 2 ft) × 2 ft = 24 ft
A3: 8 ft × 3 ft = 24 ft
So when you add all of them = 90 ft
Have a wonderful day! :-)
80 items to ship full case and 7 items per case
Answer: You want to ship 80 items, and each case holds 7 items. To find the number of cases needed to ship the 80 items, you can use the formula:
Number of cases = (Number of items) / (Items per case)
So in this case, the number of cases needed to ship 80 items is:
Number of cases = 80 / 7
Which simplifies to 11.428571428571429, so you will need 12 cases to ship 80 items.
Step-by-step explanation:
on Saturday there was a -4 change in inventory. How many phones were In inventory on Sunday?
Answer:
14
Step-by-step explanation:
First we can find Wednesdays inventory by doing 16-5, giving us 11
We can do the same thing for Saturday. Doing -2+20 because the change was positive 20, not negative. That brings Saturdays inventory to 18
They said Saturdays change was -4
So taking the 18 and subtracting 4 gets you Sundays inventory of 14
A cross between a plant with flowers and a plant with white flowers yielded 47 plants with red flowers and 51 plants with white flowers. What are the genotypes of the parent plant? Explain
The result is close to the 1:1 ratio of red to white flowering plants, so the genotype must be Rr and rr. Option A is correct.
What is Law of DominanceMendel's law of dominance states that in a heterozygote, one trait will conceal the presence of another trait for the same characteristic.
According to this law, the offspring of the first generation from pure breed parents will show only dominant traits.
When a Heterozygous dominant parent mates with a pure recessive parent the ratio of the dominant and recessive characters will be 1:1.
The cross:
r r
R Rr Rr
r rr rr
Therefore, the result is close to the ratio of red to white flowering plants, so the genotype must be Rr and rr.
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The complete option are:
A. The results are close to a 1:1 ratio of plants with red flowers to plants with white flowers. Therefore, the genotypes of the
Rr and ir
B.
The results should yield plants with red flowers and plants with white flowers in a 3:1 ratio due, so the geneotype of each parent is Rr.
The number of offspring was not large enough to produce the expected results
C. The results differ from the predicted values. Therefore, the genotypes of the parents cannot be determined.
D
. The results should show a ratio of 3 plants with white flowers to 1 plant with red flowers, so the genotypes of the parent plants are RR
The sports store donates basketballs and soccer balls to the boys and girls club. The ratio of basketballs to soccer balls is 7: 6. The store donates 24 soccer balls. How many basketballs does the store donate?
The number of basketballs that were donated is equal to 28 basketballs.
How to determine the number of basketballs that were donated?In Mathematics, a proportion can be defined as an equation which is typically used to represent the equality of two (2) ratios.
This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities as follows;
7:6 = x:24
7/6 = x/24
Cross-multiplying, we have the following:
6x = 7 × 24
6x = 168
x = 168/6
x = 28 basketballs.
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Solve the equation for all real values of x.
3 tan²x =√3 tanx
The trigonometric equation has the following roots: x₁ = ± i · π, x₂ = π / 6 ± i · π, where i are integers. (Correct choice: D)
How to solve a trigonometric equation
Trigonometric equations are equations that involve trigonometric functions. Trigonometric functions are periodic trascendent functions. In this problem we must determine the roots of a trigonometric equations by means of algebra properties and trigonometric formulas:
3 · tan² x = √3 · tan x
3 · tan² x - √3 · tan x = 0
tan x · (3 · tan x - √3) = 0
The roots of the equation are tan x = 0 or tan x = √3 / 3, whose angles are: x₁ = ± i · π, x₂ = π / 6 ± i · π, where i are integers.
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What is 28/50 in the simplest form
Answer:
Exact Form:
14/25
Decimal Form:
0.56
Step-by-step explanation:
the module `math` also provides the name `e` for the base of the natural logarithm, which is roughly 2.71. compute $\sqrt{e^{2\pi} 30\pi}$, giving it the name `near twentyfive`.
The value of `near twentyfive` is approximately equal to 25.3 and is calculated by taking the square root of the product of `e` raised to the power of[tex]$2\pi$[/tex], and 30[tex]$\pi$[/tex].
The designation "e" for the natural logarithm's base, which is around 2.71, is provided by the math module. We must take the square root of the product of "e" raised to the power of $2 pi and of "30 pi" in order to determine the value of "near twentyfive." The mathematical notation for this is sqrt(e(2)pi, pi). 'near twentyfive' has a value that is roughly equivalent to 25.3. This is due to the fact that $e2pi$ is roughly equivalent to 19.7, and $30pi$ is roughly equivalent to 94.2. 1867.4 is the result of adding these two integers together, while 43.4 is the result of taking 1867.4 as its square root. Finally, when 43.4 is divided by 2, the result is 25.3
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at a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. which of the following is closest to the proportion of orders that are processed in less than 240 seconds? following is closest to the proportion of orders that are processed in less than 240 seconds?
А
0.17
B
0.25
0.36
D
083
E
0.95
As per the interpolation method, the proportion of orders that are processed in less than 240 seconds is 0.17
The interpolation method is defined as a method of deriving a simple function from the given discrete data set such that the function passes through the provided data points.
Here we have given that at a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds.
And the proportion of orders that are processed in less than 240 seconds is calculated as,
Here we know that 1 standard deviation below mean = 16% = M - d
Then we apply the value on it, then we get,
=> 276 s - 38 s = 238 s
Here we know that the mean of distribution is,
=> 50% which is equal to 276 s
And the proportion less than 240 s is consider that x%, then by using the interpolation method it can be calculated as,
=> (240 - 238) / (276 - 238) = (x - 16) / (50 - 16)
When we simplify this one then we get,
=> 1/19 = x - 16 / 34
Which can be rewritten as,
=> 19(x - 16) = 34
=> 19x - 304 = 34
=> 19x = 338
=> x = 17.78%.
Therefore the closest to the proportion of orders that are processed in less than 240 seconds is 17% that is equal to the value of 0.17.
Hence the correct option is (A).
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Find three consecutive integers such that triple the sum of the first two integers is 19 less than larger integer
The three consecutive integers are given as follows:
-4, -3 and -2.
How to obtain the three consecutive integers?The three consecutive integers are obtained using a system of equations, for which the variables are given as follows:
x, y and z.
They are consecutive, thus:
y = x + 1.z = x + 2.Triple the sum of the first two integers is 19 less than larger integer, hence:
3(x + y) = z - 19
Replacing into the equation, the value of x is obtained as follows:
3(x + x + 1) = x + 2 - 19
6x + 3 = x - 17
5x = -20
x = -4.
Hence the remaining integers are -3 and -2.
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A meteorologist drew the accompanying graph to show the changes in relative humidity during a 24-hour period in New York City. What is the range of this set of data?
The range of this set of data is 30 ≤ y ≤ 80.
What is a range?In Mathematics, a range is the set of all real numbers that connects with the elements of a domain.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown above, we can reasonably and logically deduce the following domain and range:
Domain = 0 ≤ x ≤ 24 or [0, 24].
Range = 30 ≤ y ≤ 80 or [30, 80].
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Find the measure of the numbered angles.
The measure of the numbered angles of the quadrilaterals in the question are presented as follows;
14. m∠1 = 54°, m∠2 = 36°, m∠3 = 54° m∠4 = 108°, m∠5 = 72°
15. m∠1 = 90°, m∠2 = 45°, m∠3 = 45°, m∠4 = 45°, m∠5 = 45°
16. m∠1 = 64°, m∠2 = 64°, m∠3 = 26°, m∠4 = 90°, m∠5 = 64°
What is a quadrilateral?A quadrilateral is a four sided polygon.
14. The figure is a rectangle
The two diagonals of a rectangle are the same length and the diagonals of a rectangle bisect each other, therefore;
The triangles formed by the diagonals of the rectangle are isosceles triangles.
The angle at the vertex of the isosceles triangle that has 36° as the base angle of the triangle is therefore; (180° - 2 × 36°) = 108°
The angle ∠4, is a vertical angle to the angle calculated above, therefore;
m∠4 = 108°
m∠5 = (360° - 2 × 108°) = 72°
m∠5 = 72°
The similar triangles formed by the diagonals indicates that we get;
m∠2 = 36°
m∠1 = (180° - m∠5)/2
Therefore; m∠1 = (180° - 72°)/2 = 54°
m∠1 = 54°
∠1 ≅ ∠3
Therefore; m∠3 = m∠1 = 54°
m∠3 = 54°
15. The quadrilateral is a square, therefore;
The diagonals bisect each other and are perpendicular.
m∠1 = 90° (Definition of perpendicular angles)
m∠5 = (180° - 90°)/2 = 45°
m∠5 = 45°
∠3 ≅ ∠5, therefore;
m∠3 = m∠5 = 45°
m∠3 = 45°
m∠3 + m∠2 = 90° (The vertex angles of a square are 90°)
m∠2 = 90° - m∠3
m∠2 = 90° - 45° = 45° (Substitution property)
m∠2 = 45°
16. The quadrilateral is a rhombus, therefore;
The diagonals of a rhombus perpendicular
Adjacent angles are supplementary
The opposite angles of a rhombus are congruent
The opposite sides of a rhombus are parallel
Diagonals of a rhombus bisect the interior angles
The above properties indicates that we get;
90° + m∠1 + 26° = 180°
m∠1 = 180° - 26° - 90° = 64°
m∠1 = 64°
m∠4 = 90°
The angle ∠3 and the 26° angle are alternate interior angles. Alternate interior angles between parallel lines are congruent, therefore;
m∠3 = 26°
m∠1 = m∠2 (definition of bisected angle), therefore;
m∠2 = m∠1 = 64°
m∠2 = 64°
∠2 and ∠5 are alternate interior angles, therefore;
∠2 ≅ ∠5
m∠5 = m∠2 = 64°
m∠5 = 64°
Learn more about the properties of quadrilaterals here: https://brainly.com/question/3509769
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