Answers
The operations of functions results in another function which are shown as below.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
There are two functions given.
f(x) = x² + 7
g(x) = 2x + 1
7. Addition of functions
(f + g)(x) = f(x) + g(x)
= x² + 7 + 2x + 1
= x² + 2x + 8
8. Subtraction of functions
(f - g)(x) = f(x) - g(x)
= (x² + 7) - (2x + 1)
= x² - 2x + 6
9. (g - f)(x) = g(x) - f(x)
= (2x + 1) - (x² + 7)
= -x² + 2x - 6
10. Multiplication of Functions
(f . g)(x) = f(x) . g(x)
= (x² + 7) . (2x + 1)
= 2x³ + 14x + x² + 7
= 2x³ + x² + 14x + 7
11. Division of functions
[tex]\frac{f}{g}[/tex](x) = [tex]\frac{f(x)}{g(x)}[/tex]
= (x² + 7) / (2x + 1)
12. [tex]\frac{g}{f}[/tex](x) = [tex]\frac{g(x)}{f(x)}[/tex]
= (2x + 1) / (x² + 7)
Hence the operations of the functions are done.
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Related Questions
True or False: An Obtuse angle is between 91 and 179 degrees
Answers
Answer:
True
Step-by-step explanation:
An obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees. An obtuse angle is also called a reflex angle. A reflex angle is formed when the arms of an angle point in opposite directions. The degree of an obtuse angle is between 91 and 179 degrees. Therefore, it's true.
Hope it helps! :)
Answer:
True
Step-by-step explanation:
An obtuse angle measures more than 90 degrees and 180 degrees. So 179 is greater than 90 degrees and less than 180 degrees.
Pls help me with this question, the answer is not 278.63 square units
Answers
Answer:
375 square units
Step-by-step explanation:
Area = (1/2) h (a+b)
=1/2 × 10 (49+26)
= 5 × 75
= 375 square units
hope it helps you <3
if the radius is 10 ft,what will be the area of the circle?
Answers
The area of the circle having a radius of 10 ft will be 100π.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
Given that the radius of the circle is 10 ft. The area of the circle is calculated by the formula written as below,
Area of the circle = πr²
Substitute the value of the radius in the formula and calculate the area of the circle.
Area of the circle = πr²
Area of the circle = π x ( 10 ) ²
Area of the circle = 100π square ft
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Suppose the standard deviation of the sampling distribution of the sample mean for random samples of size 50 is 0.3 inches. If the mean length of the fish is 8 inches, use the normal distribution to compute the probability that a random sample of 50 fish will have a mean length less than 7.5 inches. Suppose the distribution of fish lengths in this lake was not normal but had the same mean and standard deviation. Would it still be appropriate to use the normal distribution to compute the probability in part (ii)? Justify your answer.
Answers
Each sampling distribution becomes more leptokurtic as sample sizes increase due to a reduction in its variety. The sampling distribution's range is smaller than the initial population's range.
Why is standard deviation used?The degree of variation of the data from the mean is referred to as "standard deviation" (or ""). When the standard deviation is low, the data tend to cluster around the mean; when it is large, the data are more spread.Your data set's average level of variability is represented by the standard deviation. It reveals the average distance between each score and the mean.the distribution of data follows a bell curve or is normal. 68% of the scores or data values, or 1 SD, nearly occupy the region of a bell curve starting at position 13 on the y axis.To learn more about standard deviation, refer to:
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facotrs of an expression based on your result from part (a) what are the factors of the polynomial x^3-5x^2-12x 36
Answers
The factors of the polynomial x³ - 5x² - 12x + 36 are (x-5) and -12(x+3).
What is the Factorisation of Polynomial?
The factors are the polynomials that are multiplied to produce the original polynomial.
The polynomial x³ - 5x² - 12x + 36 can be factored by grouping. We can factor a common factor of x out of the first two terms and the last two terms.
x³ - 5x² - 12x + 36= x(x² - 5x) -12x(1) +36(1)
= x(x-5)(x+1) -12(x+3)
So, the factors of the polynomial x³ - 5x² - 12x + 36 are (x-5)(x+1) and -12(x+3).
We can also factorize this polynomial by using polynomial division.
we can divide x² - 5x by x, remainder will be -5x and we can divide -12x+36 by x+3, remainder will be 0
x³ - 5x² - 12x + 36 = (x(x-5) -12(x+3))
Hence, the factors of the polynomial x³ - 5x² - 12x + 36 are (x-5) and -12(x+3).
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[tex]\frac{c^{2}-d^{2} }{d^{2}+cd-2c^{2} }[/tex]
Answers
The value of the expression (c² - d²) / (d² + cd - 2c²) in the simplified form will be negative (c + d) / (d + 2c).
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ (c² - d²) / (d² + cd - 2c²)
Factorize the numerator and denominator, then we have
⇒ (c² - d²) / (d² + cd - 2c²)
⇒ (c² + cd - cd - d²) / (d² + 2cd - cd - 2c²)
⇒ [c(c + d) - d(c + d)] / [d(d + 2c) - c(d + 2c)]
⇒ [(c + d)(c - d)] / [(d - c)(d + 2c)]
⇒ - [(c + d)(d - c)] / [(d - c)(d + 2c)]
⇒ - (c + d) / (d + 2c)
The value of the expression (c² - d²) / (d² + cd - 2c²) in the simplified form will be negative (c + d) / (d + 2c).
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Please answer it asap, it's missing
Answers
Answer:
Step-by-step explanation:
To find the value of f(g(-2)), we first need to substitute g(-2) for x in the equation for f(x).
g(-2) = (-2) + 7 = 5
So, f(g(-2)) = f(5)
Now we can substitute 5 for x in the equation for f(x) to find the final value:
f(x) = 3x² - 7x + 15
f(5) = 3(5)² - 7(5) + 15
f(5) = 75 - 35 + 15
f(5) = 55
So, f(g(-2)) = 55
Answer:5
Step-by-step explanation:55
What is the slope of the function, represented by the table of values below?
Answers
slope = (y2 - y1)/(x2 - x1) = (13 - 5)/(-2-0) = 8/-2 = -4
Answer:
-4
Step-by-step explanation:
identify the transformation of the following functions from the parent function f(x)= 1/x
Answers
The parent function is the simplest form of the type of function in the graph is g(x) = 1/x
What is graph ?
In mathematics, a graph is a collection of points, called vertices, and lines, called edges, that connect the vertices. Graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, and more. Graphs are one of the most fundamental concepts in mathematics, and they are used to model many real-world problems and situations.
The transformation from the first equation to the second one can be found by finding a, h and k for each equation.
y = a / x-h + k
Find a, h and k for
g(x)= 1/x
a = 1
h=0
k = 0
The horizontal shift depends on the value of h and The horizontal shift is described as :
f(x) = f(x+h) The graph is shifted to the left h units
f(x) = f(x-h) The graph is shifted to the right h units.
Horizontal shift depends on the value of k and The horizontal shift is described as :
f(x) = f(x+k) The graph is shifted to up k units
f(x) = f(x-k) The graph is shifted down k units.
Vertical shift : none.
The sign of a describes the reflection across the x-axis. −a means the graph is reflected across the x-axis.
Reflection about the x-axis: None
To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.
Parent Function: g(x) = 1/x
Horizontal Shift: None
Vertical Shift: None
Reflection about the x-axis: None
Hence, The parent function is the simplest form of the type of function g(x) = 1/x .
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assume 85% of people actually show up for thier flight on time. because of this, airlines tend to overbook flights. a random sample of 220 booked passengers is taken and whether or not they showed up on time is recorded for each of them.
Answers
The sample proportion based on the question that we have here is 0.85
What is sample proportion?
The sample proportion (p) indicates the percentage of people in a sample who exhibit a particular quality or attribute. Divide the number of individuals (or items) who have the desired attribute by the overall sample size to obtain the sample proportion.
P=X/N, where X represents the number of successes and N represents the sample size, yields the sample proportion.
Hence from the question, we see that 85% of the passengers booked for flights actually show up. hence the proportion is 0.85.
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HELP ME OUT PLEASE!!!!!!
Answers
The range of the function y = -2x² + 12x - 13 will be [5, -∞). Then the correct option is A.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The domain means all the possible values of x and the range means all the possible values of y.
The equation is given below.
y = -2x² + 12x - 13
Convert the equation into a vertex form, then we have
y = -2x² + 12x - 13
y = -2x² + 12x - 18 + 18 - 13
y = -2(x² - 6x + 9) + 18 - 13
y = -2(x - 3)² + 5
The range of the function y = -2x² + 12x - 13 will be [5, -∞). Then the correct option is A.
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at the amusement park, janine bought a bottle of water for $2. she also bought game tickets for $0.50 each. janine spent a total of $15. which of the following equations can be used to find the number of $0.50 game tickets, g, janine bought?
1. 2g-0.50=15
2. 2g+0.50=15
3. 0.50g-2=15
4. 0.50g+2=15
Answers
Answer:
4. 0.50g+2=15
Step-by-step explanation:
(4,8) & (2,8)
find the slopee
Answers
Answer:
0/-2 or zero slope
Step-by-step explanation:
(4,8), (2,8)
x1 y1 x2 y2
y2- y1
_____
x2 - x1
↓
8-8
___= 0/ -2
2-4
the slope is 0/-2, making it equal 0 slope
the function b(r) shows the number of baskets of apples per tree an orchard farmer gets if there's r inches of rainfall during the summer then what can be formulated?
Answers
In an apple orchard, the density of planting determines how many of apples a single tree will produce. An illustration of this is Y=X².
What is meant by function?There are different kinds of means in mathematics, especially in statistics. Each mean summarises a specific set of data, frequently in order to assess the overall importance of a specific data set.A function is a relationship where each input has one and only one output and where there are many inputs.A rule, law, or mathematical formula that establishes the relationship between the independent variable and the dependent variable (the dependent variable).A function is an example of a rule because it produces one output from one input. Alex Federspiel is who took the photos. Y=X2 provides an example of this.To learn more about function, refer to:
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The perimeter of the TCL 3-Series Roku Smart TV is 112 inches. The width of the TV is 16 inches greater than its height. Find the width and the height of the TV.
Answers
Answer: Height = 20 inches, Width = 36 inches
Step-by-step explanation:
Let the height be [tex]h[/tex] and the width be [tex]h+16[/tex].
Using the formula for the perimeter of a triangle,
[tex]2(h+h+16)=112\\\\2(2h+16)=112\\\\2h+16=56\\\\2h=40\\\\h=20 \implies h+16=36[/tex]
Tommy's four dogs, Fido, Jack, Sam, and Lilly, went to the vet to be weighed. Fido weighed 27 pounds, Jack weighed 37.5 pounds, Sam weighed 53 pounds, and Lilly weighed 16 pounds.
What is the total weight of the four dogs?
A.103 pounds
B. 147.9 pounds
C.112.9 pounds
D.122.9 pounds
Answers
Answer: 133.5
Step-by-step explanation:
Add the weights together and, for some reason, you get 133.5
Answer:
133.5 pounds------------------------------------
Add the four numbers together to get the total weight:
27 + 37.5 + 53 + 16 = 133.5 poundsIt doesn't match any options, please double check if they are (or given weights) correct.
If the length of a rectangular field is 7 feet less than six times its width, and the perimeter is 140 feet.
Length of a rectangular field is_____
feet.
Answers
From the given data, using perimeter of rectangle, Length(L) = 6 × 11 - 7 of the rectangular field.
The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. P = x+x+y+y, where P is the perimeter.
Let length of the rectangular field = L
Width of rectangular field = W
Given,
length of a rectangular field is 7 feet less than six times its width
perimeter is 140 feet,
According to the question,
L = 6W - 7
Perimeter of the rectangle = 2 (L + W)
140 = 2 (6W - 7 + W)
140 = 2 (7W - 7)
70 = 7 W - 7
77 = 7 W
W = 11
L = 6 × 11 - 7
Length = 59
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The bullseye on an archery target has a radius of 3 inches. The entire target has a radius of 9 inches. To the nearest hundredth, find the area of the target outside of the bullseye. Use 3.14 for π.
Answers
Answer:
226.1 [tex]in^{2}[/tex]
Step-by-step explanation:
if x k converges to x, and yk converges to y, does xk/yk converge to x/y math?
Answers
Yes, xk/yk converges to x/y. This can be proven mathematically using the definition of a limit.
If xk converges to x and yk converges to y, then the limit of xk/yk as k approaches infinity is equal to the limit of x/y. This can be expressed algebraically as limk→∞xk/yk = limk→∞x/y, which is equal to x/y. Thus, xk/yk converges to x/y.
To calculate this, we can take a sequence of xk an yk values, and divide every xk by its corresponding yk. For example, if xk = {2, 4, 8, 16, 32} and yk = {1, 2, 4, 8, 16}, then the sequence xk/yk = {2/1, 4/2, 8/4, 16/8, 32/16} = {2, 2, 2, 2, 2}. This sequence converges to 2, which is equal to x/y. Therefore, xk/yk converges to x/y.
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PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!
Answers
The function that best models the number of game consoles sold in millions since 2009 is g(x) = (25.5)(0.6)ˣ.
The correct option is B.
What is Exponential Growth?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.
y = a(1+r)ˣ,
where a is the initial population and r is the rate in decimals and sx is the time period.
Given:
The graph shows the number of game consoles sold in millions since 2009.
Let the function is,
g(x) = abˣ.
And graph passes through two points (0, 25.5) and (1, 15.3).
So,
when x = 0 then g(x) = 25.5.
That means, a = 25.5
And, when x = 1 then g(x) = 15.3.
That means,
15.3 = (25.5)b.
b = 0.6
Therefore, the function is g(x) = (25.5)(0.6)ˣ.
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A rule for a histogram that decides into which class intervals subjects are placed if their value is on the boundary between two intervals.
Answers
A rule for a histogram that decides into endpoint convention class intervals subjects is placed if their value is on the boundary between two intervals.
Endpoints are defined as physical devices that connect to and exchange information with a computer network.
There are some examples of endpoints:
They are mobile devices, desktop computers, virtual machines, embedded devices, and servers.
Internet-of-Things devices like cameras, lighting, refrigerators, security systems, smart speakers, and thermostats are also examples of endpoints.
When a device connects to a network, the flow of information between, for instance, a laptop and a network, is much like a conversation between two people over the phone.
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If you need to take out a $80,000 student loan 2 years before duating, which loan option will result in the owest overall cost to you: a subsidized loan with 7.4% Interest for 10 years, a federal unsubsidized loan with 9% interest for 10 years, or a private loan with 5.0% interest and a term of 15 years? How much would you ave over the other options? All payments are deferred for 6 months after graduation and the interest is apitalized. Part: 0/5 Part 1 of 5 (a) Find the total cost of the subsidized loan. The total cost of the subsidized loan is S decimal places, if necessary. 10 Round your answer to two
Answers
Answer:
$139,200
Step-by-step explanation:
To find the total cost of the subsidized loan, we need to calculate the total amount of interest that will be added to the loan over the 10-year repayment period. We can use the formula for simple interest:
I = Prt
Where:
I = Interest
P = Principal (the original loan amount)
r = Interest rate (expressed as a decimal)
t = Time (in years)
In this case:
I = 80,000 * 0.074 * 10 = 59,200
The total cost of the loan would be the sum of the principal and the interest:
80,000 + 59,200 = $139,200
So the total cost of the subsidized loan is $139,200.
Abe can mow a lawn in 3 hours. After he has been working for 1/3 hour, Bob helps, and working together, it takes 1 and 2/3 hours more to finish the job. How long would it take Bob to mow the lawn by himself?
Please show work.
Answers
Bob would take 5 hours to mow the law by himself.
Let us consider, the area of the lawn to be mowed to be x inch².
It is given that the law can be mowed by Abe alone in 3 hours.
We know that,
Rate of work = Work/Time
⇒ rate of work of Abe = area to be mowed(work)/time taken
= (x/3) inch²/hour
Now,
Abe has been working alone for 1/3 hour
⇒work done by Abe alone = rate of work of Abe x time
= (x/3) inch²/hour x 1/3 hour
= x/9 inch²
Remaining work = x - x/9 = 8x/9 inch²
Let, the rate of work of Bob be y inch²/hour.
It is given that the time taken by Abe and Bob to complete the remaining work together is 1 and 2/3 hours, i.e, 5/3 hours.
Therefore,
The rate of work of Abe and Bob when working together
= work ÷ time
=(8x/9) ÷ (5/3)
=8x/15 inch²/hour
⇒ Rate of work of Abe + Rate of work of Bob = 8x/15
⇒ x/3 + y = 8x/15
⇒ y = (8x/15) - (x/3)
⇒ y = 3x/15 = x/5 inch²/hour
Thus, the time taken by Bob to mow the law by himself
= work ÷ rate of work
= x inch² ÷ (x/5) inch²/hour
= 5 hours
So, it would take 5 hours for Bob to mow the lawn alone.
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Write the equation of the line that passes through the points (-3, 3) and (1, 2).
Answers
Use synthetic division to show that x = 5/2 is a zero of the function f(x) = 2x^3 - 5x^2 - 6x + 15
Answers
x = 5/2 is a zero of the function f(x) = 2x³ - 5x² - 6x + 15.
What is a function?
A function in mathematics from a set X to a set Y allocates precisely one element of Y to each part of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Here, we have
Given: x = 5/2 is a zero of the function f(x) = 2x³ - 5x² - 6x + 15,
f(x) = 2x³ - 5x² - 6x + 15
When we f(x) = 2x³ - 5x² - 6x + 15 by x-5/2 we get
Remainder = -10
Quotient = 2x² - 6
Divisor = x - 5/2
2x³ - 5x² - 6x + 15 = 2x² - 6 - 10/(x - 5/2)
Hence, x = 5/2 is a zero of the function f(x) = 2x³ - 5x² - 6x + 15.
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Here is a list of equations. Circle all the equations that are identities. Be prepared to
explain your reasoning.
1. a = -a
2. a² + 2ab + b² = (a + b)²
3. a² - 2ab + b² = (a - b)²
4. a²b² = (a - b)(a - b)
5. (a + b)(a²- ab + b²) = a³ - b³
6. (a - b)³=a³-b³-3ab(a + b)
7.a²(a - b)4-b²(a - b) = (a - b)²(a + b)
Answers
Answer:
2356
Step-by-step explanation:
Write an algebraic expression as indicated.
Two numbers total 123. Let x represent one of the numbers. Write an algebraic expression for the other number.
Answers
The other number can be represented as 123-x.
a clerk is wrapping two cube-shaped packages and wants to know the smallest amount of wrapping paper that can wrap each package. the edge length of the larger package is 3in. the greater than the length of the smaller package. the surface area of the larger package is 384 in^2. what is the surface area of the smaller package?
Answers
The surface of the smaller cubic package is 150 squared inches.
What is the surface area of the smaller package?Remember that for a cube of side length S, the surface area is given by:
A = 6*S^2
In this case,w we know that the surface area of the larger cube is 384 in^2, replacing that we will get:
384 in^2 = 6*S^2
S = √(384 in^2/6) = 8in
And the edge of the smaller package is 3 inches shorter, then its sidelength is:
s = 8in - 3in = 5in
Then its surface area is:
A = 6*(5in)^2 = 150 in^2
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3 ^ (12/5) * root(3 ^ b, a) = 3 ^ 2 * sqrt(3)
Answers
The value of the expression: (5 + √3)/(2- √3) = 13 +7√3
How to rationalize the surd?The given surd to be rationalized is (5 + √3)/(2- √3)
Using a²-b² = (a+b)(a-b)
You can rewrite the value 1 in many ways as 2/2, 16/16, or 1 = (5 + √3)/(2-+√3)
Multiplying by 1 but in the form 1 = (2 + √3)/(2- √3) given
(5 + √3)/(2- √3) * (2 + √3)/(2-+√3)
⇒ (5 + √3)(2+√3) / [2² - (3√2)²]
Simplifying the surd to have
(10+ (5 + √3 + 2√3 + 3)/4-1
Therefore this gives 13 + 7√3
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Correct question:
How do you simplify (5 + √3)/(2- √3)?
Need help ASAP!!! This is due by tomorrow
Answers
Answer:
a= 17
Step-by-step explanation:
Since all sides are equal length, all angles must be equal. Since all of the angles of every triangle sum to 180*, 180/3= 60*. Therefore, (4a-8)*=60*
From there, we can solve for a by adding 8 to both sides:
(4a-8)+8=60+8
4a=68
Then we can divide both sides by 4 to get
(4a)/4= 68/4
a=17
Answer:
a = 17
Step-by-step explanation:
This seems to be an equilateral triangle, so the angle is 60 degrees. 68 - 8 is 60. 4a represents 4 × a, and we know 4 × a has to be 68. 68 / 4 is 17, meaning a = 17.
