When the inverse of a function is itself a function it is called self-inverse.
A mathematical phrase, rule, or law 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.
This relationship is commonly symbolized as y = f(x)—which is said “f of x”—and y and x are related such that for every x, there is a unique value of y.
A self-inverse function ‘reverses itself’ to produce the original input.
A function f is self-inverse if it has the property that f(f(x))=x for every x in the domain of f. In other words, f(x)=f−1(x).
For example, 1x and 3−x are self-inverse.
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Use the function f(x) = 4x2 + 8x − 5 to answer the questions.
Part A: Completely factor f(x).
Part B: What are the x-intercepts of the graph of f(x)? Show your work.
Part C: Describe the end behavior of the graph of f(x). Explain.
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph.
a) The quadratic function is factored as follows: f(x) = 4(x - 0.5)(x + 2.5).
b) The x-intercepts of the quadratic function are given as follows: x = -2.5 and x = 0.5.
c) The end behavior of the quadratic function is given as follows: as x -> ± ∞, f(x) -> ∞.
d) The graph is constructed at the end of the answer, considering the x-intercepts, the y-intercept, the end behavior and the vertex.
How to graph the quadratic function?The quadratic function for this problem is defined as follows:
f(x) = 4x² + 8x - 5.
Hence the coefficients are given as follows:
a = 4, b = 8, c = -5.
The discriminant is given as follows:
D = 8² - 4 x 4 x (-5)
D = 144.
Hence the x-intercepts are given as follows:
x = (-8 + square root (144))/8 = 0.5.x = (-8 - square root (144))/8 = -2.5.Considering the intercepts and the leading coefficient of a = 4, the function is factored as follows:
f(x) = 4(x - 0.5)(x + 2.5).
As the leading coefficient is positive, the parabola is concave up, meaning that the end behavior is that the function increases to infinity both at the left tail and at the right tail.
The y-intercept is given as follows:
f(0) = 4(0)² + 8(0) - 5
f(0) = -5.
The coordinates of the vertex are given as follows:
x = -b/2a = -8/8 = -1.y = -D/4a = -144/16 = -9.More can be learned about quadratic functions at https://brainly.com/question/24737967
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using factorization middle school way ☹️
On solving the provided question, we can say that - by the prime factors we have x^2 + 1 +2x = X= -1, -1
what is prime factor?Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.
here we have the equation,
[tex]x^2 + 1 + 2x\\[/tex]
(x+1)(x+1)
x = -1, -1
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Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years
If Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years then he has to pay 3009.6 back.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years.
A=P(1+rt)
Where, A is final amount, P is principal amount, r is rate of interest, t is time period.
P=3000, r=0.16%=0.16/100=0.0016, t=2
A=3000(1+(0.0016)2)
=3000(1+0.0032)
=3000(1.0032)
=3009.6
Hence, Canon needs to pay back 3009.6
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At Central Middle School the 108 students who take the AMC 8 meet in theevening to talk about problems and eat an average of two cookies apiece.Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe,1 which makes a pan of 15 cookies, lists this items: 1- cups of flour, 2 eggs, 323 tablespoons butter, cups sugar, and 1 package of chocolate drops. They will 4 make only full recipes, not partial recipes.Walter can buy eggs by the half-dozen. How many half-dozens should he buy to make enough cookies? (Some eggs and some cookies may be left over.)(A) 1(B) 2(C) 5(D) 7 (E) 15
5 half-dozens he should buy to make enough cookies.
What is an average?
Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. scored 85 on tests on average. The term "mean" can refer to the simple average or a figure that lies halfway between two extremes.
Here, we have
If 108 students eat 2 cookies on average, there will need to be 108× 2 = 216 cookies.
There are 15 cookies per pan, meaning there need to be {216}/{15} = 14.4 pans.
However, since half-recipes are forbidden, we need to round up and make{216}/{15} = 15 pans.
1 pan requires 2 eggs, so 15 pans require 2×15 = 30 eggs.
Since there are 6 eggs in a half dozen,
we need 30/6 = 5 half-dozens of eggs.
Hence, 5 half-dozens he should buy to make enough cookies.
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The top-notch middle school had athletes from all the grades playing on a sports team. 6th grade 7th grade 8th grade basketball 2 4 7 baseball 1 6 5 soccer 7 4 4 football 8 15 10 explain what the ratio 5:73 represents. the ratio 5:73 represents the ratio of 8th grade baseball players to total athletes. the ratio 5:73 represents the ratio of 7th grade football players to total athletes. the ratio 5:73 represents the ratio of total athletes to 7th grade football players. the ratio 5:73 represents the ratio of 6th grade athletes to total athletes.
The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
What is ratio?In mathematics, a ratio is a comparison of two or more numbers that demonstrates how large one number is relative to the other. The divisor or number that is dividing is known as the consequent, while the dividend or number being divided is known as the antecedent. A ratio divides two numbers to compare them.
Given that the Total number of athletes are 2+4+7+1+6+5+7+4+4+8+15+10
= 73
Ratio of 5:73 represent the athletes in a particular grade with specific games to total number of athletes in the school.
There are on one event is where 5 athletes are, that is 8th grade baseball players.
So the correct answer is The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
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A triangle has vertices at (1, 3), (2, -3), and ( -1, -1). What is the approximate perimeter of the triangle?
Answer choices
15
10
14
16
Answer:14
Step-by-step explanation:You can use distance formula to find the length of each side, and then add them together to approximate the perimeter.
pls i need to know what the answer is!!!
The solution of the equation 3(2m - 1) ≤ 4m + 7 is option A m ≤ 5.
What are inequalities?A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. An inequality symbol denotes that the expressions on each side are not equal.
The given inequality is 3(2m - 1) ≤ 4m + 7
Remove the brackets by multiplying 3 with each term inside it:
6m - 3 ≤ 4m + 7
Subtract 4m from both sides of the equation.
6m - 3 - 4m ≤ 4m + 7 - 4m
2m -3 ≤ 7
Add 3 to both sides of the equation.
2m - 3 + 3 ≤ 7 + 3
2m ≤ 10
Divide both sides of the equation with 2.
2m/2 ≤ 10/2
m ≤ 5
Hence the solution of the equation is m ≤ 5, that is option A.
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Simplifying algebraic expressions
The simplified form of the algebraic expression [tex]2c-7c[/tex] is [tex]-15[/tex]
The given algebraic expression is [tex]2c-7c[/tex] and we need to use [tex]c=3[/tex]
Let's substitute the value of [tex]c[/tex] in the given algebraic expression, that is
[tex]=2(3)-7(3)\\=6-21\\=-15[/tex]
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Answer:
-15----------------------
Given expression
2c - 7cSimplify it:
2c - 7c = (2 - 7)c = - 5cFind its value by plugging in the value of c:
- 5c = - 5*3 = - 15The first 5 terms of a certain sequence are 6. 12, 24, 48, and 96.
Which two statements about this sequence are true?
This is a geometric sequence.
This is an arithmetic sequence.
The function f(n)2(6)"
The function f(7) = 6(2)"
The function f(n) = 6 -6(n
represetits this sequence, where is a positive whole
represents this sequence, where is a positive whole r
1) represents this sequence, where n is a positive wh
Answer:
see explanation
Step-by-step explanation:
there is a common ratio between consecutive terms, that is
12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 96 ÷ 48 = 2
this indicates the sequence is geometric
the nth term of a geometric sequence is
f(n) = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 6 and r = 2 , then
f(n) = 6 [tex](2)^{n-1}[/tex]
2/3 of the students in a class passed their math test. If 16 of students passed the test, how many students are in the class
Answer:
24 students are in the class
Step-by-step explanation:
Let x represent the total number of students in the class. We have the equation:
(2/3)x = 16
x = 24 students
So, there are 24 students in the class.
Answer:
24 students
Step-by-step explanation:
16/2=8
8*3=24
suppose you and three friends are each dealt 13 cards from a shuffled deck, and you observe that you were dealt a single ace; what is then the probably that your three friends also each have an ace
The probability of each of your three friends having an ace is 32%.
The probability of each of your three friends having an ace is calculated using the Binomial Probability Formula. The formula is P(x) = nCr * p^x * (1-p)^(n-x). Here, n = 13 (number of cards dealt to each person) , r = 1 (number of aces you want to calculate the probability of), p = 4/52 (probability of getting an ace from a deck of 52 cards) and x = 1 (number of aces each of your three friends have).
Therefore, the probability of each of your three friends having an ace is P(x) = 13C1 * (4/52)^1 * (48/52)^(13-1) = 0.32.
This means that the probability of each of your three friends having an ace is 32%.
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NEED HELP ASAP - Algebra 2
Every complex number has the form a+bi with a and b as real numbers. Is it possible to create a complex number in which b=0? If so, create two examples to show your hypothesis is true. If not, explain why it is not possible.
Your response must be at least 50 words.
No, It is not possible to have a complex number in the form of a + bi when b = 0.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Complex number.
It is in the form of a + ib.
Where a and b are real numbers.
Now,
If b = 0 then we can not have a complex number.
Example:
a + bi
a = 1 and b = 0
1 + 0i = 1 which is not a complex number.
In order to have a complex number a can be any real number and 0 but b can not be a zero.
Thus,
It is not possible to have a complex number in the form of a + bi when
b = 0.
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The distance between a 16 feet long chord and the center of a circle is 15 feet. Compute the diameter of the circle
The diameter of the circle is 30 feet
To compute the diameter of the circle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the diameter of the circle, and the other two sides are the radius and the distance between the chord and the center of the circle.
So, we can write the equation:
diameter^2 = radius^2 + (distance between chord and center)^2
We know the radius is half the diameter, so we can substitute that in:
diameter^2 = (diameter/2)^2 + (15)^2
And we can solve for the diameter:
diameter^2 = diameter^2/4 + 225
diameter^2 = diameter^2/4 + 225
4diameter^2 = diameter^2 + 900
3diameter^2 = 900
diameter^2 = 900/3
diameter = sqrt(900/3)
So the diameter of the circle is 30 feet.
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please give a step by step explanation please
The radius of a sphere whose surface area is 324*pi cm² is:
R = 9 cm.
What is the radius of the sphere in the image?We know that the surface of a sphere of radius R is given by:
S = 4*pi*R^2
Where pi = 3.14
Here we know that a sphere has a surface of 324*pi cm², then we can write the equation:
S = 324*pi cm² = 4*pi*R^2
We can divide both sides by pi, so we get:
324 cm^2 = 4*R^2
Now we can solve that equation for R, we will get:
R^2= (324 cm^2)/4 = 81cm^2
R = √(81 cm^2)
R = 9cm
The radius of the sphere is 9cm.
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What is the value of S unit?
Triangle ABD is a right-angled triangle. The value of s which is the hypotenuse of the triangle ABD is 17 units.
What is triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.
Here,
Given information:
From the given figure, the following information can be extracted:
Triangle ABD is a right-angled triangle.
Base AB is 8 units, Height BD is 15 units.
s is the hypotenuse of the triangle ABD.
Use the Pythagoras theorem to solve for the value of s or AD,
AD²=AB²+BD²
s²=8²+15²
s²=289
s=17 units
Therefore, the value of s which is the hypotenuse of the triangle ABD is 17 units.
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Y=6 and x=-1 parallel or perpendicular line
Answer:
perpendicular
Step-by-step explanation:
5.07 - 2.148
????????????
Answer:
Step-by-step explanation: 2.922
Answer: 2.922
Step-by-step explanation: (Look at the attachment for the best experience, or idea) So, as you can see in the attachment below, we first need to line up the decimal points with one another. They subtract in line with the other decimals and borrow. As we know, our answer is 2.922.
Please give me a step by step explanation
Answer:
[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]
Step-by-step explanation:
The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].
[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]
We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].
Now add these equations together to get our equation.
[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]
Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].
=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]
willl mark you brainlieestttt
Answer:
C
Step-by-step explanation:
Answer:
- 7√10
Step-by-step explanation:
Step 1 : Take √10 common
2√10 - 5√10 - 4√10
= √10 ( 2 - 5 - 4 )
Step 2 : Subtract the numbers separately.
2 - 5 - 4
= 2 - 9
= - 7
Step 3 : Multiply √10 and - 7
√10 * - 7 = - 7√10
convert y=2(x-5)(x+2) into standard form
Answer:
Step-by-step explanation:
y=2x-5+2
then you do minus 2 on both sides
Hope this helped!
question is in the photo, please provide explanation as well
What is an example of a no solution equation?
The equation 5x + 5 = 5x - 5 has no solution because the left side of the equation (10) cannot equal the right side of the equation (-5).
No solution equation:
5x + 5 = 5x - 5
To solve this equation, we must first isolate the variable. To do this, we can subtract 5x from both sides of the equation.
5x + 5 = 5x - 5
Subtract 5x from both sides:
5 + 5 = - 5
Simplify:
10 = -5
At this point, we can see that this equation has no solution because the left side of the equation (10) cannot equal the right side of the equation (-5).
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Is x-intercept a number or a point?
The point at a graph where the graph cuts the x-axis is known as the x-intercept. Therefore, the x-intercept is a point.
A graph is made up of four quadrants in which two are positive and two are negative quadrant.
There are two types of axis which are x-axis and y-axis two negative and two positive.
The y-intercept is the point where the graph cuts the y-axis .Graph Theory is the study of graphs which comes under discrete mathematics.
It is defined as a mathematical structure that connects a group of points to express a specific function.
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What is the length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in?
The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the square of the length of the other two sides (a and b).
In this case, a = b = 9 in, so:
c2 = 92 + 92
c2 = 81 + 81
c2 = 162
c = √162
c = 12.73 in
The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in, calculated using the Pythagorean theorem.The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in.
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Question 3: Use the graph to fill in the blank with the correct number. f(3) =
10A
5
•
0
5
•
-5.
-10%
Your answer
Answer:
f(3) = 2
Step-by-step explanation:
See the attached graph. f(3) = ____ is asking us to find the value of the function, f, at the point x = 3. At x = 3, the value of y is 2.
when processing an invoice what account is debited
a. cash
b. accounts payable
c. accounts receivable
d. the answer depends on the transaction
Answer:
D
Step-by-step explanation:
Because the account that gets debited depends on the specific transaction
7.3 significant figure
Answer:
7.0
Step-by-step explanation:
from the first figure which is not a 0
7.3-7.0(1 significant figure)
Find the product using any method. (Please help me on this!)
Answer:
The answer is (4x² - 36x + 81)
Step-by-step explanation:
Given(2x - 9)²Property Used(a - b)² = a² - 2ab + b²So,
(2x - 9)² = (2x)² - 2(2x)(9) + (9)²
(2x - 9)² = 4x² - 36x + 81
Thus, The product of (2x - 9)² is (4x² - 36x + 81)
Use the distributive property to simplify the expression
6(8x+5)
Step-by-step explanation:
6(8x+5)
Use the distributive property to multiply 6 by 8x+5.
48x+30
Hope it Helps!
a solid metal sphere of volume 1280cubic centimeters
is melted down and recast into 20 equal solid cubes.fund length of the side of each cube
a solid m or a solid m fear of volume