if f(x) =7x+5/3-x, then show that fof power -1(x) is an identity function
If f(X)= 7x +5/3 - x =6x +5/3
y= 6x +5/3
6x= y-5/3
f^-1(y)=x=(y-5/3)/6
So we can write
f(f^-1(y))= f((y-5/3)/6) = 6 (y-5/3)/6 +5/3= y-5/3+5/3= y
The same result can be obtained for f^-1(f(x))=x
If the function is f(x)= 7x +5/(3-x) then it is not invertible since it is not injective (pictures)
a wire 10cm long is cut into two pieces, one of length x and the other of length 10-x. Each piece is bent into the shape of square. find the value of x that minimizes the total rea of the two squres
Answer:
The value of x that minimizes the total area of the two squares is x = 5.
Step-by-step explanation:
A wire 10 centimeters long is cut into two pieces, with one piece measuring x centimeters and the other (10 - x) centimeters.
Each piece is bend into the shape of a square, and we want to find the value of x that minimizes the total area of the two squares.
If x is bend into a square with four equivalent sides, then each side measure:
[tex]\displaystyle A = \frac{x}{4}[/tex]
Likewise, each side of the second square will measure:
[tex]\displaystyle A = \frac{10-x}{4}[/tex]
The area of a square is its side squared. Hence, the area of both squares will be given by:
[tex]\displaystyle T = \left( \frac{x}{4}\right) ^2 + \left(\frac{10-x}{4}\right)^2[/tex]
Simplify:
[tex]\displaystyle \begin{aligned} T &= \frac{x^2}{16} + \frac{x^2 - 20x + 100}{16} \\ \\ &=\frac{2x^2-20x+100}{16}\\ \\ &= \frac{1}{8}x^2-\frac{5}{4}x+\frac{25}{4} \end{aligned}[/tex]
Since this is a quadratic with a positive leading coefficient, the minimum value will occur at the vertex point.
Recall that the x-coordinate of the vertex is given by:
[tex]\displaystyle x = -\frac{b}{2a}[/tex]
In this case, a = 1/8 and b = - 5/4. Hence:
[tex]\displaystyle x = -\frac{\left(-\dfrac{5}{4}\right)}{2\left(\dfrac{1}{8}\right)} = 5[/tex]
In conclusion, the value of x that minimizes the total area of the two squares is x = 5.
How many pumps will it take to fill the giant soccer ball.
ayuda urgente con paso a paso porfavor
3. Una ciudad contrata un escultor para diseñar la escultura “El lápiz”. El diseño
que presenta para la escultura tiene forma y medidas que se muestran en la
imagen, donde la distancia del centro de la base del prisma a cada uno de sus
lados es de 3,4 m y su perímetro es de 24 m. La altura total de la escultura es 5
m. ¿Cuánto volumen de material es necesario para construir la escultura?
El volumen de material requerido para la construcción de la escultura es:
[tex]V_{tot}=122,26\: m^{3}[/tex]
Esta escultura esta compuesta de dos volúmenes, un prisma de base hexagonal y una pirámide de base hexagonal. Calculemos el volumen de cada figura por separado, para luego sumarlos.
Prisma
La ecuacion del área de un hexágono está dada por:
[tex]A_{hex}=\frac{P*a}{2}[/tex]
Donde:
P es el perimetro del hexágono (P = 24 m)a es la distancia del centro a uno de sus lados, apotema. (a = 3,4 m).Entonces el área será:
[tex]A_{hex}=\frac{24*3,4}{2}[/tex]
[tex]A_{hex}=40,8\: m^{2}[/tex]
Ahara, el volumen de un prisma de base hexagonal está dada por:
[tex]V_{prisma}=A_{hex}*h[/tex]
h es la altura del prisma, en nuestro caso h = 2 m.
Entonces:
[tex]V_{prisma}=40,8*2[/tex]
[tex]V_{prisma}=81,6\: m^{3}[/tex]
Pirámide
El volumen de una pirámide de base hexagonal está dado por:
[tex]V_{piramide}=\frac{A_{hex}*H}{3}[/tex]
Donde:
H es la altura de la pirámide.A(hex) es el área del hexágonoNosotros tenemos la apotema del volumen 4,53 m, por lo tanto podremos calcular H usadon el teorema de pitagoras.
[tex]4,53^{2}=a^{2}+H^{2}[/tex]
[tex]4,53^{2}=3,4^{2}+H^{2}[/tex]
[tex]H=2,99\: m[/tex]
Por lo tanto el volumen de la pirámide será:
[tex]V_{piramide}=\frac{40,8*2,99}{3}[/tex]
[tex]V_{piramide}=40,66\: m^{3}[/tex]
El volumen total del material necesario será:
[tex]V_{tot}=V_{prisma}+V_{piramide}[/tex]
[tex]V_{tot}=81,6+40,7=122,26\: m^{3}[/tex]
Puedes aprender más de volúmenes aquí:
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Espero te haya sido de ayuda!
6K x 1/6
K is just k
6k · 1/6 = 6/6k = k
.......
Step-by-step explanation:
hopefully it is clear and understandable
:)
need help please cant understand this probplem
Answer:
No solution
Step-by-step explanation:
Distribute the right side of the equation.
This will make it 3/8f+1/2=3/8f - 18
And, since 3/8f plus 1/2 will never equal the same thing as 3/8f minus 18, there are no solutions
Answer and Step-by-step explanation:
First, distribute the 6 to the [tex]\frac{1}{16} f[/tex] and -3.
[tex]\frac{3}{8} f + \frac{1}{2} = \frac{6}{16} f - 18\\\\\frac{3}{8} f + \frac{1}{2} = \frac{3}{8} f - 18[/tex]
If you were to subtract [tex]\frac{3}{8} f[/tex] from both sides of the equation, you would be left with [tex]\frac{1}{2} = -18[/tex], which isn't correct.
This means that there are NO solutions to this equation, or no value of f that will make both sides of the equation equal to each other.
#teamtrees #PAW (Plant And Water)
I hope this helps!
what is 5.08 centameters converted to inchies
Answer:
It's two inches
Suppose that g(x) = f(x) + 5. Which statement best compares the graph of
g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted 5 units down.
B. The graph of g(x) is the graph of f(x) shifted 5 units up.
C. The graph of g(x) is the graph of f(x) shifted 5 units to the right.
О
D. The graph of g(x) is the graph of f(x) shifted 5 units to the left.
Answer:
B
Step-by-step explanation:
The correct statement is, the graph of g(x) is the graph of f(x) shifted 5 units up.
What is vertical shifting?In geometry, a vertical shift otherwise known as vertical translation, is a translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system. In simpler terms, it is a shift in which a plane figure moves vertically.
Given that g(x) = f(x) + 5. We need to find that which statement best compares the graph of g(x) with the graph of f(x),
So,
If f is any function of x, then the graph of the function f(x) + c, may be obtained by a vertical translation of the graph of f(x) by distance c.
For this reason, the function f(x) + c is sometimes called a vertical translate of f(x).
Hence, the correct statement is, the graph of g(x) is the graph of f(x) shifted 5 units up.
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HELP! 25 minus 6 times a number increased by 3 times the same number is -56
Write equation and solve.
Answer:
25 - (6 x y) + (3 x y) = -56, y = 3.44
Step-by-step explanation:
-56 + 25 = 31, 6y + 3y = 9y, 31 = 9y, 31 / 9 = 3.44
it's a repeating number so uh yeah
y = 3.44
A number is considered "blue" if the sum of its digits is equal to the product of its digits. Which of the following
is "blue"?
Answer:
gcfcfud g fhhfhchgdjchfhfhgfhhufxyvhcj v hxhcnchchdfhvhdnfjc
Answer:
212205
Step-by-step explanation:
Well each letter is a number of a alaphabet
How can the graph of f(x) = 1/(- x) - 9 be obtained from the graph of y = 1/x
Answer:
hsjjsjsjjsjjdjjsnnsjsj
if f(x)=9-4x^2 Find
a) f(-2)
b) f(-3) f(3)
c) x such that f(x) = 0
Answer:
see explanation
Step-by-step explanation:
(a)
To evaluate f(- 2) substitute x = - 2 into f(x) , that is
f(- 2) = 9 - 4(- 2)² = 9 - 4(4) = 9 - 16 = - 7
(b)
Similarly substitute x = - 3 and x = 3 into f(x)
f(- 3) = 9 - 4(- 3)² = 9 - 4(9) = 9 - 36 = - 27
f(3) = 9 - 4(3)² = 9 - 4(9) = 9 - 36 = - 27
(c)
let f(x) = 0 , then
9 - 4x² = 0 ( add 4x² to both sides )
9 = 4x² ( divide both sides by 4 )
[tex]\frac{9}{4}[/tex] = x² ( take the square root of both sides )
± [tex]\sqrt{\frac{9}{4} }[/tex] = x
± [tex]\frac{\sqrt{9} }{\sqrt{4} }[/tex] = x
± [tex]\frac{3}{2}[/tex] = x
That is x = - [tex]\frac{3}{2}[/tex] or x = [tex]\frac{3}{2}[/tex]
45. Real Estate Appreciation Bob Michaels purchased a
house 8 years ago for $42,000. This year it was appraised at
$67,500.
(a) A linear equation V = mt + b, 0
the value V of the house for 15 years after it was pur-
chased. Determine m and b.
(b) Graph the equation and trace to estimate in how many years
after purchase this house will be worth $72,500.
(c) Write and solve an equation algebraically to determine
how many years after purchase this house will be worth
$74,000.
(d) Determine how many years after purchase this house will
be worth $80,250.
19
Answer:
a)
Since t is between 0 and 15, and the house was purchased 8 years ago, we have two pairs of values:
t = 0, V(0) = 42000t = 8, V(8) = 67500Find the slope, m:
m = (67500 - 42000)/8 = 3187.50The value of b is 42000, since at t = 0, V = 42000
So the equation is:
V = 3187.50t + 42000b)
The graph is attached.
When V = 72500, t = 9.6 (approximately)
c)
When V = 74000
74000 = 3187.5t + 420003187.5t = 32000t = 32000/3187.5t ≈ 10 years (rounded down)d)
When V = 80250
80250 = 3187.5t + 420003187.5t = 80250 - 420003187.5t = 38250t = 38250/3187.5t = 12 yearsRachel’s free-throw average for basketball is 60%. How many times do you think she will make a free-throw in her next 50 tries?
Answer:
Rachel will make 30 free-throws!
Step-by-step explanation:
Hello!
I came up with this solution with some easy mental math! If you weren't aware, 60% of 50 is a whole number! Meaning that 60% of 50 is 30. You could even double 50 to make it 100, everyone knows that dealing with percentages with the number 100 make them a whole lot easier!
Back to what I was saying, if you used 100, you would also have to take 60% of 100, which is 60. And then have to divide 60 by 2 because you doubled the 50! Giving you 30 free-throws, which is the correct answer!
Hope this helped! Let me know if you have any further questions! :)
X : X E Z,-5< X < 2 in tabular form would be?
Step-by-step explanation:
X={-4,-3,-2,-1,0,1}
Write integers which are greater than -5 but less than 2.
Note:if you need to ask any question please let me know.
PLEASE HELP PLEASE PLEASE PLEASE
Answer:
Machine A is 5, machine B is 6, and machine c is 3. Therefore C is the fastest.
Step-by-step explanation:
What is the total number of common tangents that can be drawn to the circles?
A. 1
B. 0
C. 2
D. 3
Answer:
B. 0
Step-by-step explanation:
The circles do not intersect, tangents require intersection
Answer:
B.) 0
Step-by-step explanation:
I got it correct on founders edtell
the point (-1,0.5) lies on the graph of f^-1(x)=2^x based on this information, which point lies on the graph of f(x)=log2x
Answer:
(-1,0.5)...
the inverse "f^-1" of an exponential function is BY DEFINITION the "Log" function
Step-by-step explanation:
Is (2,3),(4,7),(1,-3),(5,7),(-2,8) a function? Please help
Answer:
Yes, this is a function.
Step-by-step explanation:
Every input has its own unique output (no x number goes to more than one y number).
can any one solve this problem
Answer:
sorry i can't
please mark me as brainlest
10. State the divisibility rules for 4 and 8 and check if the number 684572 is divisible by 4 and 8.
Answer:
yes the number is divisible by 4 in which we get 171143 without any decimal but if we try to divide it by 8 then we get
85571.5 with decimal include
2x(5-x)+3x^2
shown work please
[tex]\\ \rm\Rrightarrow 2x(5-x)+3x^2[/tex]
[tex]\\ \rm\Rrightarrow 10x-2x^2+3x^2[/tex]
[tex]\\ \rm\Rrightarrow 10x+(-2+3)x^2[/tex]
[tex]\\ \rm\Rrightarrow 10x+x^2[/tex]
[tex]\\ \rm\Rrightarrow x^2+10[/tex]
Examples of geometric transformations can be found throughout the real world. Think about some places where you might use or see transformations. Give at least three examples for each type of transformation. Make use of the Internet, books, magazines, newspapers, and everyday life experiences to come up with your examples.
Transformation Real-World Example
translation 1.
2.
3.
reflection 1.
2.
3.
rotation 1.
2.
3.
dilation or stretch 1.
2.
3.
Answer:
Translation:
1. Movement of furniture
2. Airplane positioning within a taxiway
3. The position of the mouse cursor on your computer
Reflection:
1. A mirror
2. A double-door exit at school
3. Chairs facing each other at school
Rotation:
1. The Earth's rotation
2. Hands on a clock
3. A carousel
Dilation/Stretch:
1. A balloon expanding
2. A balloon deflating
3. Biological growth
Transformation involves changing the position and/or size of a shape. Some real world examples of transformation are:
Translation: Mouse cursor
Reflection: Mirror
Rotation: The clock
Dilation: Magnifying lenses
Translation
When an object is moved away from its original position, then the object has been translated. Real world examples include:
Walking on a straight pathRepositioning the mouse cursorMoving the token of a ludo gameReflection
When an object is flipped from its original position, then the object has been reflected. Real world examples include:
The mirrorIdentical twinsDouble-edged swordRotation
When an object is turned around a center, then the object has been rotated. Real world examples include:
The wall clockPlanets rotation around the sunTurning of wheelsDilation
When the size of an object is changed in equivalent proportions, then the object has been dilated. Real world examples include:
Magnifying lensPrototypes of architectural designsMapsSee attachment for examples of each transformation
Read more about transformations at:
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Solve the compound inequality.
3 > 2x or x - 4 > 2
x <
or x >
Answer:
so our x is <
less than
explanation: 3>2x= 1.5<x
x- 4>2 =6<x
Pls help me I would appreciate it :]
Step-by-step explanation:
3(5)+5÷4
15+5÷4
20÷4
5 Answer
Answer:
16.25
Step-by-step explanation:
Let x = 5. Substitute the value for the variable.
3(5) + 5 ÷ 4
15 + 5 ÷ 4
15 + 1.25
16.25
A farm has fruit trees planted in rows. There are 6 fruit trees in the first row, and each additional row has 3
more fruit trees than the row before it. If there are 18 rows of fruit trees, how many fruit trees are there on
the farm?
O 324
O 426
O 456
O 567
Answer:
567
Step-by-step explanation:
It is going to be arithmetical sequence, a1=6
d=3, n=18
Sn= (2a1+d(n-1))/2*n= (2*6+3*17)/2*18= 63*9=567
The arrangement of fruits trees in the farm is modeled after an arithmetic progression, thus, there are 567 fruit trees in the farm.
What is the number fruit tress in the farm?The number of fruits trees in the farm represents an arithmetic progression as each row of trees in the farm increases by 3 more than the one after it.
The number of trees is calculated using the arithmetic formula as follows:
[tex]S_n = \frac{2a + d(n - 1)}{2}× n[/tex]
where
a = 6, n = 18; d = 3Substituting the values
[tex]S_n = \frac{2 \times 6 + 3(18 - 1)}{2}× 18 = 567[/tex]
Therefore, there are 567 fruit trees in the farm.
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A simple pulley with the give radius 4 in used to lift heavy objects is positioned 10 feet above ground level. Given that the pully rotates 720 degrees determine the height yo which the object is lifted.
9514 1404 393
Answer:
50.3 inches
Step-by-step explanation:
720 degrees is 2 full turns, or twice the circumference of the pulley. The circumference is given by ...
C = 2πr
C = 2π(4 in) = 8π in
Then 2 times that is ...
height lifted = 2(8π in) = 16π in ≈ 50.3 in
The object was lifted about 50.3 inches.
What is 1/2(x+14) because i am having trouble solving it and no calculator has been able to help me also.
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\frac{1}{2}x+7[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Simplifying the equation...}}\\\\\frac{1}{2}(x+14)\\------------\\\rightarrow \frac{1}{2}*x = \frac{1}{2}x\\\\\rightarrow\frac{1}{2}*14=7\\\\\rightarrow \frac{1}{2}(x+14)= \boxed{\frac{1}{2}x+7}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
A cookie company expanded its standard package of 36 cookies to include 4 extra cookies of a brand new flavor. If all of the cookies from an expanded package were put in a container and one were selected at random, what is the probability that it will be a cookie of the new flavor?
Answer:
1/9 probability
Step-by-step explanation:
The total cookies are 36 and the new flavors are 4, if you simplify 4/36, it equals 1/9
Can someone please help me on this, I do not understand
Answer:
Think u have to find out what the x means and go from there