Answers
The description of the transformations of the parent functions to produce the graphs of f(x) = sin(2x) and g(x) = csc(2x) are
a. The graphs of f(x) = sin(2x) and g(x) = csc(2x) are a horizontal compression by a factor of (1/2) of the graphs of y = sin(x) and y = csc(x).
b. 0, π/2, π, 3·π/2
c. 0, π/2, π, 3·π/2
What is the transformation of a function?A transformation of a function is an operation that changes the function's graph in some way.
a. The graph of f(x) = sin(2x) is obtained by taking the graph of sin(x) and horizontally compressing it by a factor of 1/2. This is because the argument of the sine function has been multiplied by 2, which causes the period of the function to be halved.
The graph of g(x) = csc(2x) is obtained by taking the graph of y = csc(x) and horizontally compressing it by a factor of 1/2. This is because the argument of the cosecant function has been multiplied by 2, which causes the period of the function to be halved.
b. The x-intercepts of the graph of f(x) = sin(2x) are the values of x for which f(x) = 0. Since sin(2x) = 0 when 2x is an integer multiple of π, we can find the x-intercepts by solving the equation 2x = n·π for x, where n is an integer. This gives us x = n·π/2. o four x-intercepts of the graph of f are x = 0, x = π/2, x = π, and x = 3·π/2.
c. The vertical asymptotes of the graph of the function g(x) = csc(2x) are the values of x for which g(x) is undefined. Since csc(2x) is undefined when 2x is an integer multiple of π, we can find the vertical asymptotes by solving the equation 2x = n·π for x, where n is an integer. This gives us x = (n·π)/2. So, four vertical asymptotes of the graph of g are x = π/2, x = 3·π/2, x = 5·π/2 and x = 7·π/2.
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Related Questions
A gamer is observing her score, y, as she plays a video game. She currently has 3,200 points and is gaining 200 points for every minute, x, she plays.
Which of the following equations can be used to describe this linear relationship?
A. y = 3,200x − 200
B.y = 3,200x + 200
C. y = 200x − 3,200
D. y = 200x + 3,200
Answers
Answer: d
Step-by-step explanation:
the slope is positive 200 because she is gaining 200 points for every minute which is x. 200x or 200 multiplied by x is her slope and her y intercept is 3200
10 ft
20 ft
15 ft
Find the area.
A = [?] ft²
Round to the nearest
hundredth.
Answers
The total area of the composite figure is 114.25 square feet.
How to find the area of the shape?The area of a circle of diameter D is:
A = 3.14*(D/2)²
And the area of a triangle of base B and height H is:
A = B*H/2
We can decompose the figure into two simpler ones, a triangle of base of 10ft and height of 15 ft, whose area is:
A = 10ft*15ft/2 = 75ft²
And half of a circle of diameter of 10ft, whose area is:
A = 0.5*3.14*(10ft/2)² = 39.25 ft²
Then the total area of the figure is:
area = 75ft² + 39.25 ft² = 114.25 ft²
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For each pair of figures below, choose how they are related.
O Translation
O Reflection
• Rotation
• None of these
• Translation
• Reflection
• Rotation
None of these
O Translation
© Reflection
• Rotation
• None of these
• Translation
• Reflection
O Rotation
O None of these
Answers
The type of transformation that occurred in each object are:
1) Rotation
2) Translation
3) Reflection
4) Translation
How to Identify the object Transformation?There are different types of transformations of objects such as:
Translation: Translation is said to occur when we slide a figure in any direction.
Reflection: Reflection is said to occur when we flip a figure over a line.
Rotation: Rotation is said to occur when we rotate a figure a certain degree around a point.
Dilation: Dilation is said to occur when we enlarge or reduce a figure.
1) The given transformation is rotation because the original object was clearly rotated.
2) The given transformation is said to be translation because the object just changed position.
3) The transformation that occurred is said to be a reflection because it is a mirror image.
4) The given transformation is said to be translation because the object just changed position.
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g suppose that you are an elementary school teacher and you are evaluating the reading levels of your students. you find an individual that reads 46.2 word per minute. you do some research and determine that the reading rates for their grade level are normally distributed with a mean of 85 words per minute and a standard deviation of 22 words per minute. a. at what percentile is the child's reading level (round final answer to one decimal place).
Answers
This shows that they read less frequently than 95.7% of their classmates in the same grade level.
what is percentile ?In statistics, a percentile is a metric that is used to express where one observation stands in relation to a larger group of data. It displays the proportion of data points that fall under a given value. For instance, if a student achieves a score in the 90th percentile on a standardised test, it signifies that they outperformed 90% of their peers who also took the test. As an alternative, if a child is taller than 25% of children their age and shorter than 75%, their height is in the 25th percentile for their age.
given
We must first compute the z-score using the following formula to determine the percentile of the child's reading proficiency.
z = (x - μ) / σ
where x represents the child's reading rate, represents the grade-level mean reading rate, and represents the standard deviation.
Inputting the values provided yields:
z = (46.2 - 85) / 22
z = -1.727
We can calculate or use a conventional normal distribution table to obtain the value of 0.0428 for the region to the left of z = -1.727. The child's reading rate is at the 4.28th percentile according to this statistic.
As a result, the child's reading proficiency is 4.3 percentile (rounded to one decimal place).
This shows that they read less frequently than 95.7% of their classmates in the same grade level.
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a rectangle has a length of 25 cm and a width of 12.25 cm. a larger, similar rectangle has a width 49 cm. what is the length of the larger rectangle?
Answers
Answer: 100 cm
Step-by-step explanation:
1. Since the problem tells us that they are similar, we can infer that this larger rectangle is the same rectangle, only bigger.
2. With this information, we can do the equation 49/12.25 because then we will get the amount the rectangle grows by.
3. 49/12.25=4
4. Now, we can multiply the length(25) by 4.
5. 25 x 4=100
6. The length of the larger rectangle is 100.
I hope this helps!
Whether the economy is in a recession is illustrated in the AD/AS model by how close the _____ is to the potential GDP line.
a. AD curve
b. AS curve
c. AS and AD curve
d. equilibrium
Answers
When the equilibrium point is above the potential GDP line, the economy is experiencing inflationary pressure.
In the AD/AS model, whether the economy is in a recession is illustrated by how close the equilibrium is to the potential GDP line. The potential GDP line represents the maximum level of output that an economy can produce with its existing resources and technology.What is the AD/AS model?The AD/AS model is a graphical representation of the macroeconomic relationship between aggregate demand (AD) and aggregate supply (AS). This model is used to explain the behavior of the economy by demonstrating how changes in the level of aggregate demand and aggregate supply can impact the economy's level of output and prices.
The model's AD curve represents the total demand for all goods and services in an economy at different price levels. The AS curve represents the total supply of all goods and services in the economy at different price levels.
The intersection of the AD and AS curves represents the equilibrium point where the economy's output level and price level are determined. The economy is in a recession when the equilibrium point is below the potential GDP line.
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Helppppppppppppppppppppppp
Answers
Answer:
no
Step-by-step explanation:
You want to know if a triangle with sides 54, 66, and 87 is a right triangle.
Pythagorean theoremThe side lengths of a right triangle will satisfy the relation given by the Pythagorean theorem. Here, that would require ...
54² +66² = 87²
2916 +4356 = 7569
7272 = 7569 . . . . . . . . . false — not a right triangle
Triangle WXY is not a right triangle, so XY is not tangent to circle W.
__
Additional comments
The parity of the integer side lengths of a right triangle is always even. That is, there can be two odd side lengths, but never just one odd side length.
Side lengths 54 and 66 are even, while length 87 is odd. There is only one odd side length, so this triangle cannot be a right triangle.
A tangent always meets a radius at right angles, so XY is a tangent if and only if angle X is a right angle.
2. The function f gives the dollar value of a bond t years after the
bond was purchased. The graph of Jis shown.
What is f(0)? What does it mean in this situation?
b. What is f(4.5)? What does it mean in this situation?
c. When is f(t) = 1500? What does this mean in this
situation?
Answers
The function f a. f(0) represents the bonds after 0 years. That is the immediate value of bond in dollars at 0 year. b. f(4.5) represents the value of the bond 4.5 years later.
What does a mathematical function mean?A function in mathematics is a rule that designates a certain output value for each input value. Each input from the domain has precisely one output in the range, forming a relationship between two sets known as the domain and the range. The letter f(x), where x is the input variable and f(x) is the output variable, is a common way to represent a function. The output variable is specified by the function's rule, but the input variable can accept any value from the function's domain.
For the given graph of the function:
a. f(0) represents the bonds after 0 years. That is the immediate value of bond in dollars at 0 year.
b. f(4.5) represents the value of the bond 4.5 years later.
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ou and i each have a fair coin. i flip n times, and you flip n 1 times. you win if i get fewer heads than you. what is the probability that you win the game?
Answers
Answer: 3
Step-by-ste3p explanation:
A city has a population of 370,000 people. Suppose that each year the population grows by 4. 75%. What will the population be after 11
years?
Answers
The population of the city will be approximately 597,543 people after 11 years.
We can solve this problem using the formula for exponential growth:
[tex]N = P(1 + r)^t[/tex]
where:
N = final population
P = initial population
r = annual growth rate (as a decimal)
t = number of years
In this case, we have:
P = 370,000
r = 0.0475 (since the annual growth rate is 4.75%)
t = 11
Substituting these values into the formula, we get:
[tex]N = 370,000(1 + 0.0475)^{11}[/tex]
Using a calculator, we can simplify this expression to:
N = 597,542.64
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what are coordinate planes explain:
Answers
Answer:
a two-dimension surface formed by two number lines.
S.
5.
You may be surprised to learn that prime
numbers are used for sending information
securely over the internet. The internet uses
computers, so they do this by multiplying two
huge prime numbers. It is hard work. Here is
a challenge for you. The number 51 is the
product of two prime numbers. What are the
two prime numbers?
Answers
The prime factors or the prime numbers whose product is 51 are 3 and 17.
What is the operation of prime numbers?
The operation of prime numbers refers to the various mathematical operations that can be performed using prime numbers. Prime numbers are positive integers that have exactly two divisors, 1 and the number itself. Some of the important operations involving prime numbers include:
Prime factorizationGCD and LCMModular arithmeticPrimality testingCryptographyNow,
If you meant to ask for the prime factors of 51, then they are 3 and 17.
because 51 is divisible by 3 because 5+1=6
and after dividing 51/3=17 which is also a prime number.
Hence,
the prime factors of 51 are 3 and 17.
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the perimeter of a rectangle is 175 feet. the short sides are each feet long, but the lengths of the long sides are . a) which equation represents this situation? correct b) write in terms of . incorrect
Answers
this is incorrect because the length of the long sides cannot be expressed in terms of just y. We need additional information about the dimensions of the rectangle to determine the length of the long sides.
a) The equation that represents this situation is:
2x + 2y = 175
where x is the length of the short sides (in feet) and y is the length of the long sides (in feet).
b) The equation in terms of y is:
2(6) + 2y = 175
which simplifies to:
12 + 2y = 175
2y = 163
y = 81.5
However, this is incorrect because the length of the long sides cannot be expressed in terms of just y. We need additional information about the dimensions of the rectangle to determine the length of the long sides.
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a rectangular container 12 cm long, 8 cm wide, and 36 cm high was one - third full. when some syrup from a bottle was poured into the container, it got half full. find the volume of the syrup poured from the bottle into the container in millimeters
Answers
when some syrup from a bottle was poured into the container, it got half full. The volume of the syrup poured from the bottle into the container in millimeters is 576,000 cubic millimeters.
Since for solving the problem we need to find the volume of the container in millimeters. We are given the length, breadth, and height which are 12 cm,8 cm, and 36 cm.Now the volume of the container is:
V = l x w x h = 12 cm x 8 cm x 36 cm = 3,456 cubic cm. Now we convert the above result into millimeters by multiplying by 1,000, so we get V= 3456 x 1000= 34560000 cubic mm
Now to find the volume of the syrup that was poured into the container, we know that the container was one-third full before the syrup was added and half full after the syrup was added.onsidering x to be the volume of the syrup poured from the bottle into a container and n to be the volume of the syrup in the container after it was added:
1/3(V) + x = 1/2(V), where v is the volume of the container in millimeters, so we substitute the calculated value of the volume we get :
=>1/3(V) + x = 1/2(V)
=>x = 1/2(V) - 1/3(V)
=> x = 1/6(V) = 1/6(3,456,000) = 576,000 cubic mm
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What is the equation of this graph?
A.) y=-x²-2x-8
B.) y=x²-2x-8
C.) y=3x²-12x-8
D.) y=-3x²-12x-8
Answers
The equation of the quadratic function that passes through these points is:
[tex]y = -3x^2 - 12x - 8.[/tex]
What is quadratic equation?
A quadratic equation is a polynomial equation of the second degree, which means it contains one variable with an exponent of 2. The general form of a quadratic equation is:
[tex]ax^2 + bx + c = 0[/tex]
Using polynomial interpolation with these 5 points, we can find a quadratic polynomial that passes through all the points. Let the equation of the polynomial be [tex]y = ax^2 + bx + c[/tex].
Using the point (0, -8), we get:
[tex]-8 = a(0)^2 + b(0) + c[/tex]
c = -8
Using the point (-1, 1), we get:
[tex]1 = a(-1)^2 + b(-1) - 8[/tex]
a - b = 9
Using the point (-3, 1), we get:
[tex]1 = a(-3)^2 + b(-3) - 8[/tex]
9a - 3b = 27
Using the point (-4, -8), we get:
[tex]-8 = a(-4)^2 + b(-4) - 8[/tex]
16a - 4b = 0
Using the point (-2, 4), we get:
[tex]4 = a(-2)^2 + b(-2) - 8[/tex]
4a - 2b = 12
Solving this system of equations, we get:
a = -3
b = -12
c = -8
Therefore, the equation of the quadratic function that passes through these points is:
[tex]y = -3x^2 - 12x - 8.[/tex]
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Decide if each of the following is a minor arc, major arc, or semicircle by circling the correct answer .
Answers
Answer:
Step-by-step explanation:
minor, semi, minor, major (in that order)
minor is smaller than a semi-circle while major is larger than a semi-circle.
(g+5)(g-4) expand and simplify
Answers
Aron needs 5/7 of a yard of fabric to cover a chair ad 2/3 of a yard of the fabric to cover a footstool. How much more fabric is required for the chair than the footstool?
Answers
Answer:
Step-by-step explanation:
To find out how much more fabric is required for the chair than the footstool, we need to subtract the amount of fabric required for the footstool from the amount of fabric required for the chair.
The amount of fabric required for the chair is 5/7 of a yard.
The amount of fabric required for the footstool is 2/3 of a yard.
So to find the difference, we need to subtract:
5/7 - 2/3
To do this, we need to find a common denominator, which is 21 in this case. We get:
(15/21) - (14/21) = 1/21
Therefore, Aron needs 1/21 more yard of fabric to cover the chair than the footstool.
The graphs below have the same shape. What is the equation of the red
graph?
f(x) = 4 – x²
g(x) = ?
O A. g(x) = (7 - x)2
O B. g(x) = 1 - x2
O C. g(x) = 7 - x2
D. g(x) = (1 - x)2
Answers
Answer:
C
Step-by-step explanation:
The red graph is obtained by shifting the graph of f(x) = 4 - x² upwards by some amount. We can see that the highest point on the red graph occurs at x = 0, where the value is 4.
To shift the graph of f(x) upwards by 3 units, we can add 3 to the entire function:
f(x) + 3 = 4 - x² + 3
= 7 - x²
So the equation of the red graph is:
g(x) = 7 - x²
Therefore, the correct answer is option C: g(x) = 7 - x².
how do you solve this to get the answer
Answers
Answer:
The answer is
-7/8 + 3/10
Step-by-step explanation:
See the picture
Hope you understand :)
in exercise physiology, a person's maximum heart rate, in beats per minute, is found by subtracting his age in years from 220. so, if a represents your age in years, then your maximum heart rate is:
Answers
Step-by-step explanation:
If your age is ' a ' then your max heart rate = 220 - a
Help needed LIKE RN!! URGENT!!
Answers
The surface area of the cylinder is approximately 127.17 cm².
What is the surface area of the cylinder?Surface area of cylinder is the total space covered by the flat surfaces of the bases of the cylinder and its curved surface. The formula for the surface area of a cylinder is: 2πr² + 2πrh.
To solve this problem, we first need to find the radius of the cylinder. The diameter of the cylinder is 3 cm, so the radius is half of that:
r = 3/2
= 1.5 cm
We need to substitute the values we know into the formula for surface area:
= 2π(1.5)² + 2π(1.5)(12)
= 2π(2.25) + 2π(18)
= 4.5π + 36π
= 40.5π
We will now approximate the value of π to get the numerical answer, so, our Surface Area will be:
= 40.5π
= 40.5 * π
= 40.5 * 3.14
≈ 127.17 cm²
Answered question "A cylinder is 12 cm tall and has a diameter of 3 cm. What is the surface area?"
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if the dental director wanted to analyze the data collected from the cpi, which type of descriptive statistics should be used to measure central tendencies?
Answers
To measure central tendencies in the data collected from the Consumer Price Index (CPI), the dental director should use measures of central tendency, such as the mean, median, and mode.
The mean is the average of a set of numbers and is calculated by adding all the numbers together and then dividing by the total number of numbers. The median is the middle number when the numbers are placed in order from least to greatest. The mode is the number that appears most often in a set of numbers.
Using these measures of central tendency will allow the dental director to gain a better understanding of the CPI data, as they will be able to identify the center point of the data and also see how frequently particular values appear. This can help in making informed decisions about policies and other changes.
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write the equation of a circle with center at (-1/2,1/4) and r= [3]
Answers
The equation of the circle is 16 x^2 + 16x +16 y^2- 4y -45 =0
Here the center of circle is at (1/2, 1/4 ) and radius is √ 3
The equation of a circle with center (h , k) and radius r is given by
(x - h)^2 + ( y - k)^2 = r^2
Here it is given that the center of circle (-1/2 , 1/4) = (h, k) and radius r= √ 3
Therefore the equation of required circle is
(x - (-1/2) )^2 + (y-1/4)^2= √ 3^2
=> x^2 + 1/4 + x + y^2 +1/16 - 4y= 3
=> 16x^2 + 4 +16x+ 16 y^2 -4y +1= 48
=>16 x^2 + 16x +16 y^2- 4y -45 =0
therefore the required equation of circle is
16 x^2 + 16x +16 y^2- 4y -45 =0
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The voltage in an electrical circuit is multiplied by itself each time it is reduced. The voltage is 27/125 of a volt and it has been reduced three times. What is the voltage in exponential form?
Answers
Answer: x 3= 27/125
Step-by-step explanation:
The figure shows intersecting lines k and m. What is the measure of angle a?
Type the number in the box.
86°
a
degrees
Answers
According to the information provided, k and m are crossing lines with an angle of 86°. We know this because k and m are straight lines.
The angles add up to 180 degrees.
Then we receive,
[tex]a + 86 =180[/tex]
Or, a = 180 -86
Or, a = 94°.
As a result, an is 94°.
The angle an is 94 degrees.
Supplementary angle are formed when two angles add to 180 degrees. When additional angles are added together, they form a straight angle, or 180 degrees. In these other words, if indeed the sum of angles 1 and 2 equals 180 degrees, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" to one another in this context.
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Help em fin the answer
Answers
Answer:
1 ft per 4 seconds
120 seconds
72 seconds
Step-by-step explanation:
A grocer can buy oranges for $1.65 per pound.
1. Write an equation relating c, the cost; and p, the pounds of oranges.
2. An orange order cost $260.10. How many pounds did the grocer order? (Round to the nearest whole number)
Answers
Answer:
157 pounds I'm pretty sure the equation would be 1.65c=p
Step-by-step explanation:
p is 1 because no given varible since p=1 pound 1.65 would equal p they 157 pounds bc 260.10/1.65 gives you 157 rounded
Aria puts 0. 75 liters of apple juice and 0. 5 liter of cranberry juice in a pitcher that holds 2 liters of liquid. She fills the rest of the pitcher with orange juice. What fraction of the mixture is orange juice?
Answers
Answer:
Step-by-step explanation:
Your equation is 0.75L + 0.5L + x = 2L
x = Orange juice
0.75L + 0.5L = 1.25L
2L - 1.25L = 0.75L
[tex]\frac{0.75L}{2L}[/tex] is your fraction
[tex]\frac{75}{200}[/tex] simplified is [tex]\frac{3}{8}[/tex]
I hope this helped,
130.25.122.63mario's pizzeria bakes olive pieces in the outer crust of its 20-inch (diameter) pizza. there is at least one olive piece per inch of crust. how many olive pieces will you get in one slice of pizza? assume the pizza is cut into eight slices.
Answers
By using circumference of circle, we find that In one slice of pizza you will get about 8 olive pieces from Mario's Pizzeria.
The circumference of circle of a 20-inch diameter pizza can be calculated as follows:
Circumference = π × diameter
Circumference = 3.14 × 20
Circumference = 62.8 inches
If there is at least one olive piece per inch of crust, then there will be 62.8 olive pieces on the outer crust of the entire pizza.
If the pizza is cut into eight slices, each slice will have 1/8th of the total circumference of the pizza. Therefore, each slice will have:
62.8 inches ÷ 8 slices = 7.85 inches of outer crust
Since there is at least one olive piece per inch of crust, each slice will have approximately 8 olive pieces on the outer crust.
Therefore, you can expect to get about 8 olive pieces in one slice of pizza from Mario's Pizzeria.
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