Answer:
The answer is "It must be shown that both [tex]j(k(x))\ and \ k(j(x))=x[/tex]"
Step-by-step explanation:
Given:
[tex]j(x) = 11.6 e^{x} \\\\k(x) =\ln\frac{x}{11.6}[/tex]
To show that both are equal functions, and show that both[tex]j(k(x))\ and\ k(j(x)) =x,[/tex]
For [tex]j(k(x));[/tex]
[tex]j(k(x)) = j[(\ln \frac{x}{11.6})]\\\\j[(\ln (\frac{x}{11.6})] = 11.6e^{\ln (\frac{x}{11.6})}\\\\j[(\ln \frac{x}{11.6})] = 11.6(\frac{x}{11.6})\\\\[/tex](The natural logarithm is canceled by exponential function)
[tex]j[(\ln \frac{x}{11.6})] = 11.6 \times\frac{x}{11.6}\\\\j[(\ln \frac{x}{11.6})] = x\\\\j[k(x)] = x\\\\for\ \ k[j(x)]:\\\\k[j(x)] = k[11.6e^x]\\\\k[11.6e^x] = \ln (\frac{11.6e^x}{11.6})\\\\k[11.6e^x] = \ln(e^x)[/tex]
Its natural logarithm leaving x will nullify expanding universe.
[tex]k[11.6e^x] = x\\\\k[j(x)] = x[/tex]
In the question, it is seen that[tex]j[k(x)] = k[j(x)] = x[/tex], shows that the functions [tex]j(x) = 11.6 e^{x} \ and \ k(x) = \ln \frac{x}{11.6}[/tex] is inverse functions.
Answer:
C
Step-by-step explanation:
Ed2021
Evaluate |─8| + |2|.
Answer:
10
Step-by-step explanation:
|-8| = 8
Answer:
10
Step-by-step explanation:
The absolute value is never negative and is shown by the vertical line.
|-8|=8 and |2|=2.
8+2=10
Based on the statment, below which statement could be used to prove <1=<2?
vertical angles are congruent
supplementary angles are congruent
complementary angles are congruent
two angles that form a linear pair are congruent
Answer:
Vertical angles are congruent
Which of the following is not a function ?
A B C D
PLEASE HELP FAST
Answer:
C
Step-by-step explanation:
Hey can you help me fast!!
a) The pass marks in an examination is 40%. Rajani secured 295 marks and
failed by 25 marks. Find the full marks of the examination
Answer:
320 marks = 40 percent therefore the total marks for the exam= 320+320+160=800 marks.
Step-by-step explanation:
let the full marks be " x "
Rajani has scored 295 marks , if she would had scored 25 more marks then she would had passed the examination,
So, passing marks :
=》295 + 25
=》320
passing percentage ( P% ) :
=》
[tex]40 = \dfrac{passing \: \: marks}{total \: \: marks} \times 100[/tex]
=》
[tex]40 = \dfrac{320}{x} \times 100[/tex]
=》
[tex]x = \dfrac{320 \times 100}{40} [/tex]
=》
[tex]x = 8 \times 100[/tex]
=》
[tex]x = 800[/tex]
So, passing marks = 800 marks
P(x)=x^3-3x^2-4x+12; x+2
Using factor theorem
Answer:
The groups have no common factor and can not be added up to form a multiplication.
Solve the following system using substitution:
x - 4y = -1
-3x +8y = -2
Answer: ( 4, 5/4)
Step-by-step explanation: x = 4, y = 5/4
What is the perimeter of a square with a length of 13cm and a base of 13cm???
Please Help I Need This By Tomorrow!
Determine the center and radius of the following circle equation:
x² + y2 + 20x – 14y + 133 = 0
Centre ( - 10 , 7 )
Radius -> 4 unit
help please ill give brainliest answer
Answer:
ΔLMN ≅ ΔLQP by (SAA)
Step-by-step explanation:
It is given that line (NM) is congruent to the line (PQ), meaning they have the same measure. This is signified by the small red line on each of these sides.
Moreover, it is also given that angle (MNL) is congruent to angle (QPL), this is shown by the red arc around these angles.
Finally one can figure out that angle (NLM) is congruent to angle (PLQ) by the vertical angles theorem. The verticle angles theorem states that when two lines intersect, the opposite angles are congruent.
Thus the two triangles are congruent by side-angle-angle postulate, abbreviated as (SAA).
I need help on this math problem
Answer:
x+66+55=180(being sum of the angle of triangle=180degree
x=180-121
therefore, x=59
plz give me thanks
Answer:
All triangles have angles that add up 180 degrees.
So Angle x = 180 - 55 -66
which equals 59 degrees.
Step-by-step explanation:
The swimming pool shown is a right prism with concave hexagonal bases.... pls help
3 bottom sections:
10 x 20 = 200
5x 20 = 100
10 x 20 = 200
Bottom area = 200 + 200 + 100 = 500 square feet.
Short side: 3 x 20 = 60
Deep end wall : 6 x 20 = 120
Side wall : (24 x6) - (10x3) - (1/2 x 4x3) = 144-30-6 = 108
2 side walls: 108 x 2 = 216
Total area : 500 + 216 + 60 + 120 = 896 square feet
Divide total area by area of 1 gallon:
896/400 = 2.24 gallons
It will take 2.24 gallons of paint
to make a sports drink for a football team, jaylen filled 9/10 of a large cooler with water. then he filled the remaning space with 6 cups of sports drink concentrate.
How many gallons of sports drink did Jaylen make?
Hello!
Assuming that we are using U.S. terms, there are sixteen cups in a gallon.
We can assume that there are six cups per tenth of the cooler. Our first job is to multiply 6 times 10 to get the amount of cups of sports drink.
6 · 10 = 60.
Now we need to find out how many gallons of sports drinks there are. To find how many cups go into a gallon, we divided 60 by 16.
60 ÷ 16 = 3.75
So, for our final answer,
Jaylen made 3.75 gallons of sports drink. (3 [tex]\frac{3}{4}[/tex])
waffletowne
an athlete did one round around a circle of radius 42m.what is the total distance covered by him
Answer:
2 * pi * 42 meters
Step-by-step explanation:
One round means a parameter of the circle
One of the legs of a right triangle measures 8 cm and the other leg measures 12 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer: 14.4
Step-by-step explanation:
5. 3(x - 1) = 23 – 5(x + 2)
Answer:
x = 2
Step-by-step explanation:
3(x - 1) = 23 - 5(x + 2) ← distribute parenthesis on both sides
3x - 3 = 23 - 5x - 10
3x - 3 = 13 - 5x ( add 5x to both sides )
8x - 3 = 13 ( add 3 to both sides )
8x = 16 ( divide both sides by 8 )
x = 2
Answer:
x=2
Step-by-step explanation:
Serena's rabbit weighs 3 1/2 pounds. Jarod's rabbit weighs 3 times as much as Serena's rabbit. How much does Jarod's rabbit weigh?
whats the number of outcomes?
Answer:
Chocolate andstrawberrySomeone answer this please
Answer:
-23/6=y
Step-by-step explanation:
3x-6y=11
3*-4-6y=11
-12-6y=11
y=-23/6
Please help me with this question it contains angles and measurements
Answer:
m∠ONP = 43*
m∠LNO = 137*
m∠MNP = 137*
Step-by-step explanation:
Each line segment is a straight line meaning they are each worth 180°, so if you take 43° from 180° you're eft with 137° which is what ∠LNO and ∠MNP are equal to. ∠ONP is 43° since it is a vertical angle to ∠MNL which is also 43°.
HELP PLEASE ANSWER I NEED HELP
Answer:
x=30
Step-by-step explanation:
x/5-16=-10
x/5=-10+16
x/5=6
x=6×5
x=30
Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation.
y = negative 2 x squared + 7 x + 4
a.
( 1.75, -2.125)
c.
( 1.75, 10.125)
b.
( 1.75, 4)
d.
( -1.75, 10.125)
Given:
The equation of a parabola is:
[tex]y=-2x^2+7x+4[/tex]
To find:
The vertex of the graph of the given equation by using a graphing calculator.
Solution:
We have,
[tex]y=-2x^2+7x+4[/tex]
By using the graphing calculator, draw the graph of the given equation as shown below.
From the below graph it is clear that the function is maximum at point (1.75,10.125).
So, the vertex of the given equation is (1.75,10.125).
Therefore, the correct option is c.
I bought a 5lb bag of sugar. I used 1 2/3 for cookies and 2 3/4 for cake. How much sugar do I have left?
Answer:
7/12lb
Step-by-step explanation:
5-1 2/3-2 3/4
=5-5/3-11/4
=10/3-11/4
=40/12-33/12
=7/12lb
Answer:
[tex]\frac{7}{12}[/tex]
Step-by-step explanation:
There was an initial amount of 5 lbs.
[tex]1\frac{2}{3}+2\frac{3}{4}=4\frac{5}{12}[/tex]
4 (5/12) of the sugar was used.
[tex]5 - 4\frac{5}{12}=\boxed{\frac{7}{12}}[/tex]
(7/12) of sugar should be remaining.
Hope this helps.
Will mark brainliest
Answer: A) multiply the input by 6.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
12÷2=6
36÷6=6
48÷8=6
54÷9=6
72÷12=6
so that means you have to multiply the input by 6.
Line a is parallel to line b if the measure of <7 is 114, what is the measure of <4
Answer: 66
Step-by-step explanation:
just do this, 180-114= 66 it's not even that hard.
hope this helps.
Which is a multiple of 10?
30 25 15 0
Answer:
30 is the multiple of 10.
Answer:
30
Step-by-step explanation:
Multiples of 10 would include:
10
20
30
40
50
and so on...
The table shown below represents a function. Which of the following values could not be used to complete the table?
x
у
-10
-25
-5
5
10
15
20
-20
0-15
0-5
Answer:
20 -20 0-15 0-5
Step-by-step explanation:
The original graph
X Y-25 -10-5 105 15Hope this helps you :)
The tax rate at this restaurant is 9.5%.
Marc’s sales tax is $1.61. How much was his subtotal?
Answer:
I don't know, I'm just doing this to get points. lol
Step-by-step explanation:
haha
The radius of the base of a cone is 6 inches the height of the cone is 6 inches. Which is closest to the volume of the cone
Answer:
V = 226.19
Step-by-step explanation:
v=(Pi)(r^2)(h/3) = 3.14(6^2)(6/3) = 3.1415(36)(2) = 226.19
The closest to the volume of the cone is given by 226.19.
We have given that,
The radius of the base of a cone is 6 inches the height of the cone is 6 inches.
What is the formula of the volume cone?V=(Pi)(r^2)(h/3)
V= 3.14(6^2)(6/3)
V= 3.1415(36)(2)
V= 226.19
Therefore, The closest to the volume of the cone is given by 226.19.
To learn more about the volume of the cone visit:
https://brainly.com/question/1082469
#SPJ2
Mi tarjeta de crédito está saturada por lo que tanto recurre un préstamo que cobra el 8% mensual por la cantidad que se solicite me prestaron 3500 cuál es la cantidad de que debo pagar al prestamista en un mes para saldar la deuda
Answer:
El valor que debes pagar al prestamista en un mes para saldar la deuda es: 3780.
Step-by-step explanation:
Para encontrar el valor que debes pagar en un mes para saldar la deuda, debes calcular el 8% del valor que te prestaron y este sería el monto de los intereses. Después, debes sumarle esta cantidad al valor que te prestaron:
monto del préstamo= 3500
3500*8%=280
3500+280=3780
De acuerdo a esto, la respuesta es que el valor que debes pagar al prestamista en un mes para saldar la deuda es: 3780.