The constant term is 8, which means that the y-intercept of the graph of g is (0, 8).
What is function?In mathematics, a function is a rule that assigns a unique output value for every input value in a set. It is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output. Functions are widely used in various fields of mathematics, science, engineering, and technology to model and analyze real-world situations, to describe how quantities depend on one another, and to solve problems.
Here,
If we set k=4, the function g(x) becomes:
g(x) = k(x+2) = 4(x+2)
The value of k affects the slope of the graph of g compared to the graph of f. In this case, since k=4, the slope of the graph of g is 4 times the slope of the graph of f.
The slope of the graph of f is 1, since the coefficient of x is 1. Therefore, the slope of the graph of g is:
4 * 1 = 4
This means that the graph of g is steeper than the graph of f.
The y-intercept of the graph of f is 2, since the constant term is 2. Setting k=4 does not affect the y-intercept of the graph of g, since the constant term remains the same:
g(x) = 4(x+2) = 4x + 8
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Spring fever! Epidemiologists and teachers alike have noticed the cyclic occurrence of the dreaded spring fever. Students afflicted with this disease exhibit certain listlessness in class, and they seem to stare out the windows with remarkable tenacity. At Metro University, teachers have been monitoring the situation and diagnosing spring fever. Their observations began with week 0, the first week in April. The teachers’ data are shown in the following table:
Spring Fever Cases: Raw Data Week Newly Diagnosed with SF No SF Diagnosed
0 0 1,025
1 105 920
2 180 740
3 390 350
4 325 25
For weeks 1–4, fill out the table below. Calculate the incidence and prevalence, show your fractions and answers in the table, and round to the nearest thousandths decimal place. (0.000)
Therefore, teachers should anticipate the greatest increase in spring fever during the 4th week.
A) Spring Fever: Incidence and PrevalenceWeek New Cases Total Cases So Far Individual at Risk at Start of Week Weekly Incidence Prevalence
1 105 105 920 0.102 0.102
2 180 285 740 0.196 0.278
3 390 675 350 0.527 0.659
4 325 1000 25 0.929 0.976
B) Spring Fever: Incidence and Prevalence per 100
Week Weekly Incidence per 100 Prevalence per 100
1 10.2 per 100 10.2 per 100
2 19.6 per 100 27.8 per 100
3 52.7 per 100 65.9 per 100
4 92.9 per 100 97.6 per 100
C) The 4th-week incidence is much higher, indicating an increase from 0.527 in the 3rd week to 0.929 in the 4th week.
Therefore, teachers should anticipate the greatest increase in spring fever during the 4th week.
Incidence= Number of new cases at particular week/total number of cases in that week
Prevalence= Total number of cases diagnosed/total number of subjects
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Let \( T_{1} \) and \( T_{2} \) be linear transformations given by \[ \begin{array}{l} T_{1}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 3 x_{1}+6 x_{2}
\[
T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 43 x_{1}+2 x_{2} \\ -10 x_{1}+4 x_{2}\end{array}\right]
\]
Let \(T_{1}\) and \(T_{2}\) be linear transformations given by
\[\begin{array}{l}
T_{1}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 3 x_{1}+6 x_{2} \\ 5 x_{1}-2 x_{2}\end{array}\right] \\
T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 8 x_{1}+4 x_{2} \\ 5 x_{1}+2 x_{2}\end{array}\right]
\end{array}\]
A linear transformation is a function that takes two input values and returns two output values in a way that preserves the linear structure of the data. It is described by a matrix that determines the output values from the input values. In the case of \(T_{1}\) and \(T_{2}\), the matrix is
\[
M=\left[\begin{array}{cc}
3 & 6 \\
5 & -2
\end{array}\right]
\]
and
\[
M=\left[\begin{array}{cc}
8 & 4 \\
5 & 2
\end{array}\right]
\]
respectively. The two linear transformations can be combined using matrix multiplication, which yields the transformation
\[
T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=M_{1} M_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)
\]
where
\[
M_{1}M_{2}=\left[\begin{array}{cc}
43 & 2 \\
-10 & 4
\end{array}\right].
\]
Therefore, the result of applying both transformations to a given input vector is given by
\[
T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 43 x_{1}+2 x_{2} \\ -10 x_{1}+4 x_{2}\end{array}\right]
\]
This is an example of a linear transformation, where two transformations are combined to produce a single result.
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Mark Twain was the pen name of Samuel Clemens, who spent several years as a steamboat pilot. He chose the name because the leadsman on a steamboat would call out "mark twain" to indicate that the water depth was 12 feet and safe for the boat to pass. Convert this depth to fathoms.
The depth of water is fount to be 2.0 fathom when its was 12 feet.
Explain about the unit conversion?The same attribute is expressed using a unit conversion, but in a different measurement system. For illustration, time can be defined in minutes rather than hours, and distance can be specified in kilometres, feet, or a different measurement unit though rather than miles.Given:
Samuel Clemens, who worked as a steamboat pilot for several years, wrote under the pseudonym Mark Twain. He chose the name because a steamboat's leadsman would yell "mark twain" when the water was 12 feet deep and it was safe is for boat to pass.Conversion unit:
1 foot = 0.167 fathom
Then,
12 feet = 0.167*12 fathom
12 feet = 2.004 fathom
12 feet = 2.0 fathom
Thus, the depth of the water is fount to be 2.0 fathom when its was 12 feet.
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If figure QRST is reflected across the x-axis and then translated 3 units down which of the following will be the coordinates for point R?
To find the coordinates of point R after the reflection and translation, we would need to know its original coordinates in the figure QRST. Then we could apply the above rules to get its new coordinates.
What are coordinates ?
Coordinates are numerical values that specify the position or location of a point in a given space. In mathematics, coordinates are often expressed as ordered pairs or triplets of numbers, which correspond to the distances of the point from a set of fixed reference points or axes.
Without seeing the figure QRST, it is not possible to give the exact coordinates for point R after the reflection and translation. However, we can use some general knowledge about the effects of reflection and translation on the coordinates of a point.
When a figure is reflected across the x-axis, the x-coordinates of all its points remain the same, but the y-coordinates are negated. That is, if a point has coordinates (x, y) before the reflection, its coordinates after the reflection will be (x, -y).
When a figure is translated down by 3 units, the y-coordinates of all its points are decreased by 3. That is, if a point has coordinates (x, y) before the translation, its coordinates after the translation will be (x, y - 3).
Therefore, to find the coordinates of point R after the reflection and translation, we would need to know its original coordinates in the figure QRST. Then we could apply the above rules to get its new coordinates.
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Find the value of cos J rounded to the nearest hundredth, if necessary.
The value of cos J rounded to the nearest hundredth is 0.384.
Describe the cosine function.A mathematical function known as the cosine is used in many branches of mathematics, such as geometry and trigonometry. It is described as the proportion between the hypotenuse and the adjacent side of a right triangle. It is represented by the symbol cos-1 or arc cos and is also known as the inverse cosine or arc cosine.
Using Pythagoras theorem lets find IJ
IJ = [tex]\sqrt{13^2 - 12^2}[/tex]
IJ = √25
IJ = 5
Now,
cos θ = Adjacent side/Hypotenuse
cos J = IJ/HJ
= 5/13
= 0.384
Thus, the value of cos J rounded to the nearest hundredth is 0.384.
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Complete question:
Find the value of cos J rounded to the nearest hundredth, if necessary.
A ball is thrown from a height of 154 feet with an initial downward velocity of 10 ft/s. The balls height (in feet) after t seconds is given by the following. h=154-10t-16t^2. how long after the ball is thrown does it hit the ground?
Answer:
Step-by-step explanation:
The ball hits the ground when h=0.
[tex]0=154-10t-16t^{2}[/tex]
Solve for t. You can use the quadratic formula.
[tex]t=\frac{-(-10)+-\sqrt{10^{2}(-16\cdot154) } }{2(-16)}[/tex]
[tex]t=\frac{5+-\sqrt{2489} }{16} \\t=-3.43 t=2.81[/tex]
Time cannot be negative. So, the answer is t=2.81 seconds.
HELP! i dont know what the answer is and need HELP!
The situation in which the quantities combine to make 0 is D.
What is a combination of quantities?
In mathematics, a combination of quantities usually means taking a group of items or values and selecting some of them without regard to their order. A combination is different from a permutation in that order does not matter in a combination, whereas it does matter in a permutation.
For example, if you have three objects labeled A, B, and C, then the possible combinations of two objects are AB, AC, and BC. These combinations are different from the permutations of two objects, which include AB and BA, AC and CA, and BC and CB.
Combinations are often used in probability, statistics, and combinatorics to calculate the number of ways that objects or values can be selected from a set, without regard to their order.
The situation in which the quantities combine to make 0 is:
D. In the morning, the temperature rises 30 degrees. In the evening, it falls by 30 degrees.
In situation D, the temperature rises by 30 degrees in the morning and then falls by 30 degrees in the evening, which means that the overall change in temperature is 0. In situations A, B, and C, the quantities do not combine to make 0. In situation A, the hot air balloon rises a total of 80 feet, which is not 0. In situation B, Kathy has $10 left after giving half to her friend, which is not 0. In situation C, the player earns a total of 8 points, which is not 0.
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USING R STUDIO( only answer number 2)
HOW DO I INPUT THIS, EXACT COMMANDS
PLEASE
2) Now, we'll use the means and standard deviations we've found to predict what proportion of people should different heights if the height variables follow a normal distribution. This will involve finding Z-scores and then using the pnorm command. See these notes on doing calculations with the normal distribution.
Task. Assuming that height follows a normal distribution with the mean and standard deviation you found in the previous exercise, find the Z-scores for heights 6'4", 5'8", and 5'2". Then, answer the following questions:
• What percentile is the height 5'2"?
• What portion of people are taller than 6'4"?
• What portion of people are between 5'2" and 5'8"?
that question above is based on the question/data below which is answered
Now, let's find the means and standard deviations
of height and weight
Task. Store the mean and standard deviation of
the height and weight variables under the
names height.xbar, weight.xbar, height.s
and weight.s (recall that & and s are the
mathematical symbols used most commonly for a
sample mean and a sample standard deviation).
Also, output the means and standard deviation.
Recall that mean and sd are the commands to find
the mean and standard deviation of a variable.
When I say to store these values under the
names height.bar, weight.bar, height.s
and weight.s, I mean to write a command like
height.xbar
<- mean(...)
This won't output the mean, but it will save it
as height.sbar, and then in future problems you
can write height.bar rather than copying and
pasting the actual number. To output the mean, you
can issue a command consisting of just the variable
name on a line by itself, like this:
height.xbar
## 111 67.145
ANSWER TO THIS IS "mean(cdc$weight) and height.xbar <- mean(cdc$weight)
To input the given commands and find the Z-scores for the different heights, you will need to use the following steps:
1. Convert the heights from feet and inches to inches. For example, 6'4" would be 76 inches, 5'8" would be 68 inches, and 5'2" would be 62 inches.
2. Use the formula Z = (X - mean) / standard deviation to find the Z-scores for each height. For example, for the height of 6'4", you would use the formula Z = (76 - height.xbar) / height.s.
3. Use the pnorm command to find the percentiles for each Z-score. For example, for the Z-score of the height 6'4", you would use the command pnorm(Z).
4. Use the pnorm command with the lower.tail = FALSE argument to find the portion of people taller than a given height. For example, for the height of 6'4", you would use the command pnorm(Z, lower.tail = FALSE).
5. Use the pnorm command with the lower and upper limits to find the portion of people between two heights. For example, for the heights of 5'2" and 5'8", you would use the command pnorm(upper limit) - pnorm(lower limit).
Using these steps, you can input the given commands and find the Z-scores and percentiles for the different heights. Remember to use the variable names height.xbar and height.s for the mean and standard deviation of the height variable, and to use the number, variable, and height terms in your answer.
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Need help pleaseeeeeeee
The volume of the right square pyramid with the dimensions e = 5m, h = 4m, and s = 6m is 48m³.
What is pyramid?Pyramid is a structure with a polygonal base and triangular sides that meet at a point. Pyramids have been used throughout history as tombs, temples and monuments. Many of the most famous pyramids are located in Egypt, such as the Great Pyramid of Giza.
The volume of a right square pyramid is equal to one-third of the base area multiplied by the height. To find the volume of this pyramid, we first need to calculate the base area.
The base area of a square pyramid is equal to the length of one side (s) squared. Since the length of one side of this pyramid is 6m, the base area is 6m x 6m, which equals 36m².
Now that we know the base area, we can calculate the volume of the pyramid. The volume is equal to one-third of the base area multiplied by the height. In this case, the volume of the pyramid is one-third of 36m² multiplied by 4m, which equals 48m³.
Therefore, the volume of the right square pyramid with the dimensions e = 5m, h = 4m, and s = 6m is 48m³.
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7.1 is what percent of 32? Round to the nearest hundredth.
if we take 32(origin amount) to be the 100%, what's 7.1 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 32 & 100\\ 7.1& x \end{array} \implies \cfrac{32}{7.1}~~=~~\cfrac{100}{x} \\\\\\ 32x=710\implies x=\cfrac{710}{32}\implies x\approx 22.19[/tex]
Help!!!!
I’m on the last question
Answer: 28
Step-by-step explanation: Both Of Those Triangles Are Equal. That Means They Both Equal 14. So If We Multiply 14 With 2, We Would Get 28 cm!
Hoped This Helped!
Answer:
28cm
Step-by-step explanation:
its a perfect rectangle so both triangle are Reflexive property so they would be the same size
Suppose that 511,969 is invested at an interest rate of 5 2% per year, compounded continuously a) Find the exponential function that describes the amount in the account after timet in years b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time?
The doubling time.
A) The exponential function that describes the amount in the account after time t in years is A(t) = 511969*e^(0.052*t), where A(t) is the amount in the account after time t, e is the base of the natural logarithm, and t is the time in years.
B) The balance after 1 year is A(1) = 511969*e^(0.052*1) = 538,926.41
The balance after 2 years is A(2) = 511969*e^(0.052*2) = 567,639.77
The balance after 5 years is A(5) = 511969*e^(0.052*5) = 661,234.83
The balance after 10 years is A(10) = 511969*e^(0.052*10) = 872,032.74
C) The doubling time is the time it takes for the amount in the account to double. We can find this by setting A(t) = 2*511969 and solving for t.
2*511969 = 511969*e^(0.052*t)
2 = e^(0.052*t)
ln(2) = 0.052*t
t = ln(2)/0.052
t = 13.33 years
So the doubling time is 13.33 years.
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Two factories blow their whistles at exactly the same time. If a man hears the two blasts
exactly 6.1 seconds and 2.7 seconds after they are blown and the angle between his lines of
sight to the two factories is 42.4°, how far apart are the factories? Give your result to the
nearest meter. (Use the fact that sound travels at 344 m/sec.)
Distance between both factories is 1543 m
What is cosine law?In Trigonometry, the law of Cosines, also known as Cosine Rule or Cosine Formula basically relates the length of the triangle to the cosines of one of its angles. It states that, if the length of two sides and the angle between them is known for a triangle, then we can determine the length of the third side. It is given by:
c² = a² + b² – 2ab cosγ
Given,
A man hears the two blasts exactly 6.1 seconds and 2.7 seconds from two factories.
Angle between line of sight γ = 42.4°
Speed of sound = 344m/sec
Distance of factory A from man (a)
6.1 × 344 = 2098.4 m
Distance of factory B from man (b)
2.7 * 344 = 928.8 m
The side opposite the angle between his lines of sight will be the distance between the factories.
Using cosine law
c² = a² + b² – 2ab cos γ, where
c = distance between the factories
c² = 2098.4² + 928.8² – 2(2098.4)(928.8) cos 42.4°
c = √(2098.4² + 928.8² – 2(2098.4)(928.8) cos 42.4°)
c = √(4403282.56 + 862669.44 - 3897987.84(0.74))
c = √(5265952 - 2884511)
c = √2381441
c = 1543.19 m
≈ 1543 m
Hence, 1543 m is the distance between both factories.
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speed=_______÷_______
Answer:
i need more details i cant answer.
the perimeter of the rectangle is 22 feet. The perimeter of the triangle is 12 feet. Find the dimensions of the rectangle.
The dimensions of the rectangle is 3.33 by 5.33
How to find the dimensions of the rectangle.From the question, we have the following parameters that can be used in our computation:
The perimeter of the rectangle is 22 feet. The perimeter of the triangle is 12 feet.Using the above as a guide, we have the following:
Third side of triangle, w = 12 - 5 - 1/2l
The perimeter of the rectangle is then calculated a
2 * (1/2l + 1/2l + 12 - 5 - 1/2l) = 22
So, we have
(1/2l + 1/2l + 12 - 5 - 1/2l) = 11
Evaluate
1 1/2l + 7 = 11
This gives
3/2l = 5
Evaluate
l = 10/3
The dimension is then represented as
l by 12 - 5 - 1/2l
This gives
10/3 by 12 - 5 - 1/2 * 10/3
Evaluate
3.33 by 5.33
Hence, the dimension is 3.33 by 5.33
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of a The cumulative distribution function handon variable X is given by Ex (x) = 0 X 4 for xco for 8 OcXL4 for x7,4 1 Find. a) The pdf of a b) P(X=-1) c) PC z cx
a)f(x) = { 0, if x < 0 \\ 4x, if 0 ≤ x < 4 \\ 0, if x ≥ 4 }
b)P(X=-1) = 0
c)P(X ≤ 3) = 4 * 3 = 12
a) The pdf (probability density function) of the variable X is given by
f(x) =
{
0, if x < 0 \\
4x, if 0 ≤ x < 4 \\
0, if x ≥ 4
}
b) P(X=-1) = 0, since x < 0
c) P(X ≤ 3) = 4 * 3 = 12
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The selling price of each cup of lemon juice is 3/2 times as much as the selling price of a cup of apple juice. For every 2 cups of lemon juice sold, Mr Tan sells 5 cups of apple juice. He earns $12 more from apple juice than from lemon juice. How much does Mr Tan earn altogether?
Therefore , the solution of the given problem of unitary method comes out to be Mr. Tan makes a total of $30 Plus $18 = $48.
An unitary method is what?To finish the job using the unitary technique, the equation from this nano section should be multiplied by two. In essence, when a wanted object is present, both the characterised by either a group and the pigment sections are omitted from the unit method. A variable fee of Inr ($1.01), for instance, would be paid for 40 pens. It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.
Here,
Let's name the CDs' pre-tax cost "x" for simplicity. The overall cost of the CDs before tax is two times because Lena purchased two of them for the same price. The cost of the Discs, with the addition of the $1.80 sales tax, is:
=> 2x + $1.80
Given that we know the final price, including tax, was $23.40, we can create the following equation:
=> 2x + $1.80 = $23.40
By deducting $1.80 from each half, we arrive at:
=> 2x = $21.60
When you divide both parts by 2, you get:
=> x = $10.80
As a result, each Disc cost $10.80 before taxes.
We can create another equation now that we know his revenues from selling apple juice are $12 higher than his profits from selling lemon juice:
=> 30n - 18n = 12
=> 12n = 12
=> n = 1
As a result, Mr. Tan sells 2n + 5n = 7n = 7 glasses of juice, for a total profit of 30n = $30 from the sale of apple juice and 18n = $18 from the sale of lemon juice.
Therefore, Mr. Tan makes a total of $30 Plus $18 = $48.
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How much greater is the fractional part of a college student's daily servings that comes from grains than from fruits?
To determine how much greater the fractional part of a college student's daily servings that comes from grains than from fruits, we would need to know the specific fractions or percentages of each type of food that the student consumes. Without this information, it is impossible to accurately answer the question.
For example, if the student consumes 1/2 of their daily servings from grains and 1/4 of their daily servings from fruits, then the difference would be 1/2 - 1/4 = 1/4 or 25%. However, without knowing the specific fractions or percentages, we cannot determine the difference.
It is important to remember that a balanced diet should include a variety of food groups, including grains, fruits, vegetables, proteins, and dairy. The specific amounts of each will vary depending on individual dietary needs and preferences.
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please i need help im in a desperate situation
Answer:
Step-by-step explanation:
When calculating this equation you simply insert the x value into the equation given, in this case (x-2)^2
for example you are given 4 to 4 which is achieved by the method previously described, like this (4-2)^2 = (2)^2 = 4
so the answers would be
6 -> 16 (6 - 2 = 4 and 4^2 is 16)
10 -> 64 (10 - 2 = 8 and 8^2 is 64)
Please answer number 10, make sure to answer both parts. Thank you.
The volume is 3x³ + 16x² + 3x - 10, while when the height is reduced by 50%, the new volume is (1/2)(3x³ + 16x² + 3x - 10)
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.
The volume of the triangular prism is:
Volume = area of base * height
Substituting:
Base area = (1/2) * (2x + 2) * (x + 5) = x² + 6x + 5; height = 3x - 2
Volume = area of base * height = (x² + 6x + 5)(3x - 2)
Volume = 3x³ + 18x² + 15x - 2x² - 12x - 10 = 3x³ + 16x² + 3x - 10
The volume is 3x³ + 16x² + 3x - 10
If the height is reduced by 50%, new height = (1/2)(3x - 2)
Volume = area of base * height = (x² + 6x + 5) * (1/2)(3x - 2)
Volume = (1/2)(3x³ + 16x² + 3x - 10)
The new volume is (1/2)(3x³ + 16x² + 3x - 10)
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Can someone help pls?!
Simplify arctan4/7 + arctan7/4
(round to the nearest degree).
a. 45°
b. 90°
c. 0°
arctan(4/7) + arctan(7/4) is 90 degrees
What is Trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the functions that describe those relationships. It has applications in fields such as engineering, physics, astronomy, and navigation.
We can use the following trigonometric identity to simplify the expression:
arctan(x) + arctan(1/x) = pi/2
where x is a positive number.
In this case, we can set x = 4/7, which is a positive number, and apply the identity to get:
arctan(4/7) + arctan(7/4) = pi/2
Therefore, the sum of the two arctan terms simplifies to pi/2.
So, the simplified expression is:
arctan(4/7) + arctan(7/4) = 90 degrees (rounded to the nearest degree).
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Question 4
Which is the equation of the line that is parallelto y = 2x +1 and goes through the point (3,9)?
y=2x+3
y= -1/2x +9
y=2x+9
y=-1/2x+3
Answer:
y=2x+3
Step-by-step explanation:
Using the point-slope form of the equation of a line, we can write:
y - 9 = 2(x - 3)
Simplifying, we get:
y - 9 = 2x - 6
y = 2x + 3
Therefore, the equation of the line that is parallel to y=2x+1 and goes through the point (3,9) is y=2x+3.
parallel → the same slope
slope: y = 2x +1 → m = 2
y=2x+3 ⇔ 2(3)+3=6+3=9
y=2x+9 ⇔ 2(3)+9=6+9=15≠9
⇒ answer: y=2x+3
how do i solve this?
Step-by-step explanation:
it is a quadrilateral.
the sum of all angles in a quadrilateral is always 360°.
so,
360 = x + x + 2x + 7 + 2x + 5 = 6x + 12
348 = 6x
x = 348/6 = 58°
that's it.
A store is having a holiday sale and offers no down payment on each credit items. A sound system will cost $29.99 per week for a year. What is the total price?
Answer:$20.40
Step-by-step explanation:
20% off means that the new price of the skirt will be 80% of the original price:
$30(100% – 20%) = $30(80%)
Converting the percent to a decimal gives:
$30(0.8) = $24.00
There is an additional 15% off the sale price of $24.00, so the final price is 85% of the sale price:
$24(100% – 15%) = $24(85%)
Again converting the percent to a decimal gives:
$24(0.85) = $20.40
Given :. f(X)=2/x²+1
Determine f(x-¹)-x²f(-1)
The given function evaluates to [tex]\frac{x^2(1-x)}{x^2 + 1}[/tex].
What is a Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837: A variable y is said to be a function of the independent variable x if there is a relationship between them such that whenever a numerical value is assigned to x, there is a rule that determines a specific value of y.
As per the given data:
The function is [tex]f(x) = \frac{2}{x^2 + 1}[/tex]
To determine the function: [tex]f(\frac{1}{x}) - x^2f(-1)[/tex]
Substituting (1/x) and (-1) respectively:
[tex]= \frac{2}{\frac{1}{x}^2 + 1} - x^2\frac{2}{(-1)^2 + 1}[/tex]
[tex]= \frac{2x^2}{x^2 + 1} - x^2\frac{2}{2}[/tex]
[tex]= \frac{2x^2}{x^2 + 1} - x^2[/tex]
Taking the LCM:
[tex]= \frac{2x^2 - x^3 - x^2}{x^2 + 1}[/tex]
[tex]= \frac{x^2 - x^3}{x^2 + 1}\\= \frac{x^2(1-x)}{x^2 + 1}[/tex]
Hence, the given function evaluates to [tex]\frac{x^2(1-x)}{x^2 + 1}[/tex]
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Brooklyn and Lincoln like to work on brain teasers. Brooklyn has 7 brain teasers. If together they have 15 brain teasers, then we can use the equation x + 7 = 15 to determine how many brain teasers Lincoln has. How many brain teasers does Lincoln have?
Brooklyn has 7 brain teasers and total of 15 brain teasers, then Lincoln has 8 brain teasers.
What is Linear equation?Linear equations are equations that can be written in the form ax + b = 0, where a and b are constants and x is a variable. Linear equations represent straight lines when graphed on a coordinate plane.
We can solve the Linear equation x + 7 = 15 to determine how many brain teasers Lincoln has.
First, we want to isolate the variable x on one side of the equation. To do this, we can subtract 7 from both sides of the equation:
x + 7 - 7 = 15 - 7
Simplifying the equation gives us:
x = 8
Therefore, Lincoln has 8 brain teasers.
In conclusion, if Brooklyn has 7 brain teasers and together they have 15 brain teasers, then Lincoln has 8 brain teasers.
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A city had a declining population from 1992 to 1998. The population in 1992 was 200,000. Each year for 6 years, the population declined by 3%. Write an exponential decay model to represent this situation.
The exponential decay model for this situation is P(t) = 200,000 * (1 - 0.03)^t
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
We need to Write the percent as a fraction in simplest form
16.24%
So, we can rewrite it as;
16.24 / 100
16 and 24/100 or 16 6/25
So the percent as a fraction is 16 6/25
We are given that;
Population in 1992=200000
Time=6years
Rate=3%
To write an exponential decay model to represent this situation, we can use the formula:
P(t) = P * (1 - r)ᵗ
where P(t) is the population after t years, P is the initial population, r is the annual rate of decline as a decimal, and t is the number of years. In this case, the initial population P is 200,000, the annual rate of decline r is 0.03 (since the population declines by 3% each year), and t is the number of years from 1992, so t = 0 corresponds to 1992 and t = 6 corresponds to 1998.
P(t) = 200,000 * (1 - 0.03)^t
where t is the number of years from 1992 to 1998.
Therefore, by the given percent answer will be P(t) = 200,000 x (1 - 0.03)^t
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The ratio of students who wear glasses to the total class is 2:5. If 5 of the students who didn’t wear glasses now do,what is the ratio of students who wear glasses to those who don’t?
Answer:
Let's say that the class has a total of 7x students, where 2x wear glasses and 5x don't.
After 5 of the students who didn't wear glasses now do, the number of students who don't wear glasses becomes 5x - 5.
So, the new ratio of students who wear glasses to those who don't wear glasses is:
2x : (5x - 5)
We can simplify this ratio by dividing both terms by the greatest common factor, which is x:
2 : (5 - 5/x)
We can't simplify this any further, but we can see that the ratio is not fixed and depends on the value of x.
You earned 75% on your badminton practical. If the practical was out of 88, what mark did you earn?
Answer:
66 (at least if that is an answer choice)
Step-by-step explanation:
[tex]\frac{75*88}{100} = 66[/tex]
66 is your answer!
Tell whether each equation is true for no real number, some real
number(s), or all real numbers. (a) x · 1 = x
The equation x · 1 = x is true for all real numbers. This is because any number multiplied by 1 is equal to itself.
For example, if x = 2, then 2 · 1 = 2. If x = 5, then 5 · 1 = 5. This is true for any value of x, so the equation is true for all real numbers.
In mathematical terms, 1 is known as the multiplicative identity because it does not change the value of a number when it is multiplied by it. Therefore, the equation x · 1 = x is always true for any real number x.
In conclusion, the equation x · 1 = x is true for all real numbers.
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