Answers
The numeric value of the expression for this problem is given as follows:
[tex]\sqrt{2} + 1[/tex]
How to simplify the expression?The expression for this problem is defined as follows:
[tex]\frac{4 - 3\sqrt{2}}{(\sqrt[4]{2} - \sqrt[4]{8})^2}[/tex]
Applying the square of the subtraction in the denominator, we have that:
[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = \sqrt[4]{4} - 2\sqrt[4]{2}\sqrt[4]{8} + \sqrt[4]{64}[/tex]
[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = 4^{\frac{1}{4}} - 2\sqrt[4]{16} + \sqrt[4]{4^3}[/tex]
[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = (2^2)^{\frac{1}{4}} - 2 \times 2 + 3[/tex]
[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = \sqrt{2} - 1[/tex]
Hence the simplified expression is given as follows:
[tex]\frac{4 - 3\sqrt{2}}{\sqrt{2} - 1}[/tex]
Rationalizing the denominator, we have that:
[tex]\frac{4 - 3\sqrt{2}}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}[/tex]
Applying the subtraction of perfect square, the denominator simplifies to one, hence the value of the expression is given by the numerator as follows:
[tex](4 - 3\sqrt{2})(\sqrt{2} + 1) = 4\sqrt{2} + 4 - 3 \times 2 - 3\sqrt{2}[/tex]
[tex][tex](4 - 3\sqrt{2})(\sqrt{2} + 1) = \sqrt{2} + 1[/tex]
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Related Questions
a particle follows the path where x and y are in feet. if the particle starts from rest when , and accelerates along the path at 0.5 ft/s2, determine the radius of curvature, , the velocity,, the normal acceleration, , and the magnitude of the acceleration, , after it travels 30 feet along the path to the point (2.806, 142). (1410 ft, 5.48 ft/s, 0.0213 ft/s2, 0.500 ft/s2)
Answers
The radius of curvature is 1410 ft, the velocity is 5.48 ft/s, the normal acceleration is 0.0213 ft/s2, and the magnitude of the acceleration is 0.500 ft/s2 after the particle travels 30 ft along the path to (2.806, 142).
The radius of curvature, r, can be calculated using the formula r = v2/a, where v is the velocity and a is the normal acceleration. The velocity is calculated by integrating the acceleration with respect to time. The normal acceleration is calculated by taking the derivative of the velocity with respect to time. The magnitude of the acceleration is the same as the acceleration given in the problem.
1. Calculate the velocity, v, by integrating the acceleration (0.5 ft/s2) with respect to time:
v = 0.5 * t = 0.5 * 30 s = 15 ft/s
2. Calculate the normal acceleration, a, by taking the derivative of the velocity with respect to time:
a = dv/dt = 0.5 ft/s2
3. Calculate the radius of curvature, r, using the formula r = v2/a:
r = 15 ft/s2/0.5 ft/s2 = 30 ft = 1410 ft
4. The magnitude of the acceleration is the same as the acceleration given in the problem, 0.5 ft/s2.
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Pls help this is the only one plss
Answers
Answer:
1.247 then 1.244 and finally 1.234
Step-by-step explanation:
If the first or second numbers match up, look at the third number to tell the greatest number
Erick and Mia live the same distance from the park and decide to meet at the park one afternoon. The graphs show
their distances from home over the same 30-minute period as they walked to the park. Each section of each graph
represents 10 minutes.
Distance from Home
Erick
Time
Distance from Home
Mia
Time
Which of the following statements is true?
It took Mia 10 minutes to walk to the park
Mia left home immediately to head to the park
Erick and Mia arrived at the park at different times
It took Frick only 10 minutes to walk to the park
Answers
Erick and Mia both live the same distance from the park and decided to meet there one afternoon.
Which of the following statements is true?The graphs show their distances from home over a 30-minute period as they both walked to the park. Each section of each graph represents 10 minutes. From the graphs, it appears that Mia left home immediately to head to the park, while Erick took a few minutes before leaving.This is evidenced by the fact that Mia's graph shows that she was already walking for 10 minutes, while Erick's graph shows that his distance from home had not changed after 10 minutes.Additionally, since Mia's graph is further along than Erick's, this suggests that Mia arrived at the park before Erick. Therefore, it is true that Mia left home immediately to head to the park, and it took her 10 minutes to walk there.However, it took Erick more than 10 minutes to walk to the park, and the two arrived at the park at different times.That it took Mia 10 minutes to walk to the park. Although Erick and Mia left home at the same time, they may have chosen different routes, or one of them may have stopped along the way, so they arrived at the park at different times. It is not stated that it took Erick only 10 minutes to walk to the park.To learn more about The distance refer to:
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Consider a function f defined as follows: f(x)=(x-3)^2, x belongs to [1,2]. Is f invertible in the domain [1,2]? If yes, find the inverse of the function.
(Need a detailed explanation showing the function is invertible, then determining the inverse.)
Answers
The function f(x) = (x - 3)² is invertible on the interval [1,2], as each output is related only with a single input.
The inverse of the function is given as follows:
[tex]f^{-1}(x) = -\sqrt{x} - 3[/tex]
How to obtain the inverse function?The function for this problem is defined as follows:
f(x) = (x - 3)²
The x-coordinate of the vertex of the quadratic function is given as follows:
x = 3.
Hence the function is invertible on the domain [1,2], which is entirely on one side of the vertex, and thus each output is related only with a single input.
The inverse function is obtained exchanging the variables x and y, and then isolating y, thus:
x = (y - 3)²
[tex]y - 3 = -\sqrt{x}[/tex]
[tex]y = -\sqrt{x} - 3[/tex]
[tex]f^{-1}(x) = -\sqrt{x} - 3[/tex]
The negative symbol is because the function is on the left side of the vertex.
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Write a recursive formula for the following arithmetic sequence.
16,13,10,7
a1=
a(n)= blank for n >_ 2
Answers
Answer:
a1 = 16
a(n) = a(n-1) -3 for n ≥ 2
Step-by-step explanation:
You want a recursive formula for the arithmetic sequence 16, 13, 10, 7, ....
Arithmetic sequenceThe given sequence has a first term of 16. The common difference is ...
13 -16 = -3
Each successive term is found by adding this difference to the one before. That describes the relation expressed by the recursive formula.
[tex]\begin{cases}a_1=16\\a_n=a_{n-1}-3&\text{for $n\ge2$}\end{cases}[/tex]
If (-2, b) is a point on the graph of 2x + 3y = 2, what is b?
Answers
Consequently, b must have a value of -3.The following points should be located on the cartesian plane: (0,a), (a,0), (-a, 0), (0,-a)..
What is b?How to calculate a line's equation given two points:Make use of the slope formula to determine the slope.
To find the y-intercept (b), use one of the points and the slope.
The slope-intercept form of a line is y = mx + b, and you may obtain the equation for the line by plugging in the values for m and b once you have those values.
On the graph of 2x + 3y = - 5, 2,b) is located.
To estimate
The amount b
Given that (2,b) is located on the graph of 2x + 3y = 5,
hence, we do
( 2 × 2 ) + ( 3 × b ) = - 5
⇒ 4 + 3b = - 5
⇒ 3b = - 9
⇒b = - 3
Consequently, b must have a value of -3.
The following points should be located on the cartesian plane: (0,a), (a,0), (-a, 0), (0,-a)...
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In the article Sweets for the Sweets On Study Island
The information about the acids that are created from the sugar in sweets and bacteria from teeth comes from
A. Smile Magazine .
B. Science and Service Magazine.
C. Jaws.
D. The journal of the American Medical Association.
Answers
Correct option is C, The information about the acids that are created from the sugar in sweets and bacteria from teeth comes from Jaws.
What Candy Is Not So Bad for Your Teeth?gum, lollipops, and hard sweets without additional sugar.
Gum with a high Xylitol content, like Icebreaker Ice Cubes, makes you salivate more, which helps kill dangerous bacteria. Hard sweets and sugar-free lollipops can also stimulate the salivary glands.
Black chocolate offers more antioxidants than milk chocolate and less sugar.
As long as it is eaten in moderation and leaves your teeth bushed, the occasional candy piece is acceptable.
The greatest strategy to stop sugar's harmful effects on teeth is to always pay close attention. We advise you to limit your sugar intake, regularly brush away the bacteria-filled plaque on your teeth, and consume nutritional meals to maintain strong teeth.
Combining routine dental exams with fluoride treatments from our dental team will give you and your family the best chance of preventing tooth decay.
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in 2012 the population of california was 38,041,430, and the population living in the united states but outside california was 275,872,610. during the year, it is estimated that 748,252 persons moved from california to elsewhere in the united states, while 493,641 persons moved to california from elsewhere in the united states.
Answers
The migration matrix that has been found is
[0.98033 0.00179
0.01967 0.99821 ] by matrix method.
The 2012 populations of California and the US minus California are 38,041,430 and 275,872,610, respectively, according to the exercise statement. Let's represent these quantities by the variables c and u. What we want are two vectors m1 and m2 such that
cm 1+um 2 = [ 2013 population of California
2013 population of US minus California ]
m1 = [ 0.98033 0.01967 ] and m2 = [ 0.00179 0.99821]
Now that we have the two vectors for equation ,we use the fact that a vector equation of the form
au + bv = w
is equivalent to a matrix equation of the form
[ u v ] [a b] = w
to get our migration matrix for this system.
[0.98033 0.00179
0.01967 0.99821 ]
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The complete question is :
In 2012 the population of California was 38,041,430, and the population living in the United States but outside California was 275,872,610. During the year, it is estimated that 748,252 persons moved from California to elsewhere in the United States, while 493,641 persons moved to California from elsewhere in the United States. Set up the migration matrix for this situation, using five decimal places for the migration rates into and out of California. Let your work show how you produced the migration matrix.
multiply 101 base two by 11 base two
Answers
Answer:
1 1 1 1 to base two
Step-by-step explanation:
1 0 1 base two
× 1 1 base two
+ 1 0 1
1 0 1
=1 1 1 1 base two
harley was tested 10 times and 9 of those times he choose the correct cup. 1. identify the observational unit and the variable in
Answers
The observational unit is Harley and the variable is 0, 1, 2, ..., 10.
When gathering statistical data, information is gathered and statistics are compiled on an observation unit, which is also known as a statistical unit occasionally. An observation is the value of a certain variable at a specific time.
The observational unit in this scenario is Harley and the variable is the number of times Harley chose the correct cup out of 10 trials. The variable can take on the values of 0, 1, 2, ..., 10, where 0 represents the number of incorrect choices and 10 represents the number of correct choices.
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If a0=10 and an+1=-5an then find the value of a4
Answers
The value of a4 would be equal to -666.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given that [tex]a_0=10[/tex] and [tex]a_n+1=-5a_n[/tex]
This is a recursive formula. So we can simply substitute in each value. For instance, a₂
Use the recursive definition repeatedly.
a2 = -5(6) +4 = -26
a3 = -5(-26) +4 = 134
a4 = -5(134) +4 = -666
Therefore, the value of a4 is -666
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Cuales son los primeros 10 múltiplos de 18 y 27?
Answers
Answer:0, 18, 36, 54, 72, 90, 108, 126, 144, 162
Step-by-step explanation:0 es múltiplo de 18, pues 18 x 0 = 0
18 es múltiplo de 18, pues 18 x 1 = 18
36 es múltiplo de 18, pues 18 x 2 = 36
54 es múltiplo de 18, pues 18 x 3 = 54
72 es múltiplo de 18, pues 18 x 4 = 72
90 es múltiplo de 18, pues 18 x 5 = 90
108 es múltiplo de 18, pues 18 x 6 = 108
126 es múltiplo de 18, pues 18 x 7 = 126
Answer:
Step-by-step explanation:
18: 0, 18, 36, 54, 72, 90, 108, 126, 144, 162
27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270
The graph of the linear function passes through the points (4, 24) and (6, 30).
What is the equation of the function?
y =x +?
Answers
The equation of the graph that passes through the points (4, 24) and (6, 30) is y = 3x + 12
What is the equation of line of the graph?The slope-intercept form is expresses as;
y = mx + b
Where m is slope and b is y-intercept.
The point-slope form is expressed as;
y - y₁ = m( x - x₁ )
Given that the the graph passes through the points (4, 24) and (6, 30).
First, determine the slope.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 30 - 24 )/( 6 - 4 )
Slope m = ( 6 )/( 2 )
Slope m = 3
Next, plug the slope m = 3 and point 1 ( 4,24) into the point-slope form and simplify.
y - y₁ = m( x - x₁ )
y - 24 = 3( x - 4 )
y - 24 = 3x - 12
y = 3x - 12 + 24
y = 3x + 12
Therefore, the equation of line is y = 3x + 12,
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a local ice cream shop kept track of the number of cans of cold soda it sold each day, and the temperature that day, for 2 months during the summer. the data are displayed in the scatterplot below:
Answers
As per the given scatter plot, if the outlier were removed, r would get closer to 1.
The term scatter plot in math is used to plot data points on a horizontal and a vertical axis in the attempt to show how much one variable is affected by another
Here we have given that a local ice cream shop kept track of the number of cans of cold soda it sold each day and the temperature that day, for two months during the summer by using the scatter plot.
Here we have also know that X-axis is temperature measured in degrees Fahrenheit with a range from about 55 to 100 degrees and the value of Y-axis is the number of cans of soda sold with a range from about 165 to 195 cans.
While we take into consideration that a reasonable value of the correlation coefficient r for these data is 1.2.
Where as if the temperature were measured in degrees Celsius (C = 5/9 * (F - 32)), then the value of r would change accordingly.
Thus makes that the correlation coefficient would increase and be closer to 1.
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Solve the following equation
1.6
3.9
0=
Answers
The solution to the equation is 6.24
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
o/3.9=1.6
Express the variable as x for proper identification
So, we have the following representation
x/3.9=1.6
Multiply both sides of the equation by 3.9
This gives
x = 3.9 * 1.6
Evaluate
x = 6.24
Hence, the solution is 6.24
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Complete question
Solve the following equation
o/3.9=1.6
Given, y <-x+aandy>x+bIn the xy-plane, if (0, 0) is a solution to the system of inequalities above, which of thefollowing relationship between a and b must be true?A a>bB b>aC |a|> |b|D a = -b
Answers
For the given system of inequalities y < -x + a and y > x + b in the xy-plane , the solution represents the relation between a and b is given by :
Option A. a > b.
In the xy -plane given system of inequalities are :
y < -x + a
y > x + b
⇒ x + b < y < -x + a
⇒ x + b < -x + a
⇒ 2x < a - b
Now ( 0, 0 ) is the solution of the given system of inequalities represents :
2(0) < a - b
⇒ a - b > 0
⇒ a > b
Therefore, the relationship between the 'a' and 'b' for the given system of inequalities is given by :
Option A. a > b
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7/12 simplified
i need this as quick as possible
Answers
Answer: 7/12 can't be simplified anymore. Have a nice day ;)
What is the length of the transverse axis?
Answers
The transverse axis has a length of 5 units.
What is transverse axis and find its length?A transverse axis is a line that divides a conic section (such as an ellipse or hyperbola) into two symmetric parts. In the case of an ellipse, the transverse axis is the major axis, and it runs perpendicular to the minor axis.
To find the length of the transverse axis, we can use the equation (x − 1)²/a² + (y + 3)²/b² = 1, where a and b are the lengths of the major and minor axes, respectively.
The given equation is :
(x−h)²/a² + (y−k)²/b² = 1
Where h and k are the coordinates of the center of the ellipse.
Now we can substitute the given values in the equation
(x−1)²/25 + (y+3)²/9 = 1
To find the length of the transverse axis, we can take square root of the major axis value, a² = 25
√25 = 5
So the length of the transverse axis is 5 units.
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. Max needs 104 cups of flour to make a batch
of pizza dough for the pizzeria. He only has
4 cups of flour. How much more flour does
he need to make the dough? (STEP BY STEP. FOR THE LAST TIME.)
Answers
To make the dough, he'll need 5 3/4 cups of floor.
What is fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. In mathematics, a fraction is used to represent a portion or part of a whole. It symbolizes the equal parts of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, and the bottom number is known as the denominator.
Here,
10 1/4 cups of flour needed to make a batch=41/4 cups
4 1/2 cups of floor is there=9/2 cups
flour does he need to make the dough,
=41/4-9/2
=(41-18)/4
=23/4
=5 3/4 cups
He needs 5 3/4 cups of floor to make the dough.
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\item prove that if $f$ is a continuous function defined on an open subset $u$ of $\cc$, then sets of the form $\{z \in u: |f(z)|
Answers
The set of all points in an open subset of the complex plane, such that the absolute value of a given continuous function is equal to a given number.
The set of all points in an open subset of the complex plane, such that the absolute value of a given continuous function is equal to a given number, is a set of points that can be found by taking the given continuous function and evaluating it at each point in the open subset of the complex plane. This set of points can be expressed as a set of the form [tex]$\{z \in u: |f(z)|=c\}$[/tex] where u is the open subset of the complex plane and f is the given continuous function. The absolute value of the function must be equal to some number c in order for the point to be included in the set. This set of points is useful for understanding the behavior and properties of the given continuous function on the open subset of the complex plane.
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the manager of a car dealership records the colors of automobiles on a used car lot identify the type of data collected a. quantitative data b.Qualitative c. can be qualitative or quantitative
Answers
The records about colors of automobiles on a car lot is a type of qualitative data.
Qualitative data consists of descriptions and characteristics that are difficult to quantify but easy to perceive in the human senses, such as smell, food, gender, country, and color. Observations, individual interviews, focus groups, and other similar procedures are used to get this information. Categorical data is another name for qualitative data in statistics; it refers to information that may be sorted into groups based on the characteristics of a given entity or event. Qualitative data are also known as categorical data since they may be sorted into categories.
When trying to determine the exact frequency of certain features or attributes, qualitative data is a very useful tool. It gives the statistician or the researcher the ability to generate parameters that can be used to examine larger data sets.
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Simplify and write the trigonometric expression as a single squared trig function, with no fractions:
Tanx cscx =
Answers
The simplification of the trigonometric function tan x csc x is; sec x
How to simplify trigonometric functions?The six trigonometric functions are defined as;
sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Now, we know that;
cot x = cos x/sin x
sec x = 1/cos x = (cos x)⁻¹
csc x = 1/sin x = (sin x)⁻¹
tan x = sin x/cos x
Thus;
tan x csc x = (sin x/cos x) * (1/sin x)
= 1/cos x = (cos x)⁻¹
= sec x
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Evaluate \dfrac{e}{4}+2f-3
4
e
+2f−3start fraction, e, divided by, 4, end fraction, plus, 2, f, minus, 3 when e=12e=12e, equals, 12 and f=\dfrac12f=
2
1
Answers
The value of the expression when e = 12 and f = 1/2 is 1
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
e/4 + 2f - 3
Also, from the question, we have the following values:
e = 12 and f = 1/2
substitute the known values in the above equation, so, we have the following representation
e/4 + 2f - 3 = 12/4 + 2 * 1/2 - 3
Evaluate the expression
e/4 + 2f - 3 = 1
Hence, the solution is 1
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mrs. heart asked 100 randomly selected adult americans if they thought that women should be allowed to go into combat situations. here are the results, classified by the gender of the subject. Male= Yes : 18, N0: 32 Famale = Yes: 34, No: 16 What is the probability that a randomly selected subject in the study is Male or answered "No"? A 0.18 B) 0.66 C 0.78 D 0.84
Answers
The probability that a randomly selected subject in this is Male or answered 'No' is A: 0.18.
The probability that a randomly selected subject in the study is Male or answered "No" is the sum of the probability that the subject is Male and the probability that the subject answered "No", which is a measure of the overlap between these two events.
To find the probability that a subject is Male, we take the number of Male subjects (50) and divide it by the total number of subjects (100):
P(Male) = 50/100 = 0.5
To find the probability that a subject answered "No", we take the number of subjects who answered "No" (48) and divide it by the total number of subjects (100):
P(No) = 48/100 = 0.48
We can use the formula P(A or B) = P(A) + P(B) - P(A and B) to find the probability that a randomly selected subject is Male or answered "No"
P(Male or No) = P(Male) + P(No) - P(Male and No)
We know that 18 out of 50 Male subjects answered No and 16 out of 50 Female subjects answered no, so the probability that a Male subject answered No is 18/50 = 0.36, and the probability that a Female subject answered No is 16/50 = 0.32
P(Male and No) = P(Male) * P(No|Male) = 0.5 * 0.36 = 0.18
P(Female and No) = P(Female) * P(No|Female) = 0
Hence, the probability that a randomly chosen subject in this is male or answered 'no' is A: 0.18.
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would you expect your answer in (1) to be accurate? explain. hint: show that maximum distance is less than 10%.
Answers
The accurate of the function is calculated using the fomula O(n).
Function in math is known as an equation that has only one answer for y for every x and it assigns exactly one output to each input of a specified type.
Here we have given that maximum distance is less than 10%.
As we all know that the basic approach is to check only consecutive pairs of x and y.
Here we have given that for every element x or y, then we have to check the index of the previous occurrence of x or y and if the previous occurring element is not similar to current element update the minimum distance.
Here we have a question arises what if an x is preceded by another x and that is preceded by a y for that situation we have to know how to get the minimum distance between pairs.
Hereby analyzing closely it can be seen that every x followed by a y or vice versa can only be the closest pair so ignore all other pairs.
Complete question:
Write the function to calculate the accuracy? show that maximum distance is less than 10%.
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Miss Flores has three candy bars that she is going to give to the four students who do their best work at Saturday school how much candy bar will each student receive
Answers
For function f(x) = 3x-2
and g(x)=x², workout
fg(x)
Answers
For the function f( x) = 3x- 2 and g( x) = x2, the workout fg( x) is 3x2- 2.
What is function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are inclusively appertained to as the function's sphere and codomain, independently. originally, functions represented the idealized relationship between two changing amounts.
A formula, rule, or legislation that specifies how one variable( the independent variable) and another variable are related( the dependent variable).
Four orders of functions live functions with return values and arguments.
This function accepts arguments and gives back a result.
functions that take arguments but have no return values.
functions with return values and no arguments.
functions that have no arguments or return values.
we are given two function f( x) and g( x);
f( x) = 3x- 2 and
g( x) = x2
So, for fg( x), we've to put value of g( x) into f( x);
Hence, the equation will be;
fg( x) = 3x2- 2.
thus, for the function f( x) = 3x- 2 and g( x) = x2, the fg( x) is 3x2- 2.
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Which unit rate corresponds to the proportional relationship shown in the graph?
Drag and drop the answer into the box to match the graph with its unit rate.
A graph with a line running through coordinates left parenthesis 0 comma 0 right parenthesis and coordinates left parenthesis 12 comma 16 right parenthesis.
Answers
1.33 cm/s
Step-by-step explanation:
The line is going from point (0;0) to point (12;16), the proportional relationship between these points refer to the slope of the line, which can be found with this expression:
Replacing all values we have:
Therefore the relation shown in the graph is represented by 1.33 cm/s, which refers to the constant speed developed by the object.
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Answer:
1.33 cm/s
Step-by-step explanation:
Since the cylinder and the prism share the same height, what is the volume of the prism?
Diameter of cylinder base - 19.8
base area of cylinder - 307.8
volume of cylinder - 9.234
base area of the prism - 196
Answers
Answer:
The volume of the prism is 6.186
Step-by-step explanation:
1. The volume of a cylinder can be calculated using the formula V = πr^2h where r is the radius of the cylinder base, h is the height and π is a mathematical constant.
2. The diameter of the cylinder base is given as 19.8 cm and the base area of the cylinder is given as 307.8 cm^2.
3. The volume of the cylinder is given as 9.234 cm^3.
4. If the cylinder and the prism share the same height, the volume of the prism can be calculated by using the base area of the prism.
5. The base area of the prism is given as 196 cm^2.
6. The volume of the prism can be calculated by multiplying the base area with the height of the prism.
7. The volume of the prism is 196cm^2 * h = 6.186 cm^3
8. So the volume of the prism is 6.186 cm^3
let v denote the set of all differentiable real-valued functions defined on the real line. prove that v is a vector sp ace with the operations of addition and scalar multiplication defined in example 3.
Answers
The set of all differentiable real-valued functions defined on the real line. Proved that V is a vector space with the operations of addition and scalar multiplication defined as:
(f + g)(s) = f(s) + g(s)
(c f)(s) = c[f(s)].
Let V denote the set of all differentiable real-valued functions defined on the real line. Prove that V is a vector space with the operations of addition and scalar multiplication defined as:
(f + g)(s) = f(s) + g(s)
(c f)(s) = c[f(s)].
To prove vector space, we need to hold eight properties of vector space.
1) Closed
(f + g)(s) = f(s) + g(s) (given)
so, closed holds with respect to given defined operation.
2) Associative law
let defined three function, f,g,h in V,
(f+g)(s)+h(s)=f(s)+g(s)+h(s)
= f(s)+(g+h)(s)
hence associative law hold.
3) Existence of identity,
(f+o)(s)=f(s)
f(s)+o(s)=f(s)
Hence, O(s) is identity for this function,
4) Existences of Inverse,
(-f)(s) is inverse for f(s)
5) Commutative law,
(f+g)(s)=(g+h)(s)
6)( cf)(s)=c[f(s)]g
7) c(f+g)(s)=cf(s)+g(s)
8) c(fg)(s)=(cf(s))g(s)
Hence, the given function is defined Operations.
learn more about Vector space.
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