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
Josh is driving from his house to his grandmother's house. If 1/3 gallon of gasoline will get Josh 1/9 of the way to his grandmother's, how many gallons of gasoline does Josh need for the entire trip?
Answer:
3 Gallons
Step-by-step explanation:
Answer:
3 gallons
Step-by-step explanation:
Given: 1/3 gallon needed for 1/9 of the whole trip
To find: How many gallons of gasoline Josh needs for the entire trip
Solve: Firstly, we need to find out the entire trip as a fraction
1/1
If 1/9 = 1/3, then 1/1 = 1/9 ÷ 1/3 = 0.33
No, multiply that by 1/1
1/1 × 0.33 = 0.33
Then, convert 0.33 to a whole number
Hence, Josh needs 3 gallons for the entire trip
Please help grade depends on it
Answer:
C
Step-by-step explanation:
17/10 is correct
DID I GET THIS RIGHT PLEASE HELP ITS DUE IN 10 MINUTES ( DONT GIVE ME A LINK PLEASE)
Answer:
yes that is
Step-by-step explanation:
Plsss helppp ASAP
Extra 500 point
And brainliest
Answer:
500 pts :DDDD
Step-by-step explanation:
1 ) y = mx + b
hmmm 2 is wrong
2) y = -a[tex]x^{2}[/tex]+bx+c
I'm unsure about 3 also hmm
3) y = a[tex]x^{y}[/tex]
Use the graph that shows the solution to f(x) = 9(2).
What is the solution to f(x) = g(x)?
Select each correct answer
Answer:
Step-by-step explanation:
hello :
the first graph : 1 and -1 at second ; 2
Find the value of $x$ . Round your answer to the nearest tenth.
A right-angled triangle facing downward, shortest side labeled x, second side labeled 15 and angle on the second side is labeled 27 degrees.
$x\approx$
Tan(angle) = Opposite / adjacent
Tan(27) = x/15
x = 15 * tan(27)
x = 7.6
AJ borrowed $4,000 for 5 years at 6% simple interest rate. How much interest did he pay?
Answer:
800 dollars
Step-by-step explanation:
Only number 7. I’ll give 5 stars, (which of the following relations represent functions? Select all that apply)
Find the equation of the line with Slope = -4 and passing through (-1,8). Write your equation in the form
y = mx + b
Does anyone mine helping me?
Answer:
y= -4x+4
Step-by-step explanation:
y=mx+b
where x=-1, y=8, and m=-4
8=(-4)(-1)+b
8=4+b
4=b
Thus, y= -4x+4
x^2/3=12
Plz I need help with this ASAP, it’s solving quadratic functions by square roots by the way
Answer:
this is easy. all you have to do is multiply the denominator (3) by the outside number (12) to get 36. this leaves the equation being x^2 = 36. now you just find the square route of 36 (which is 6).
Step-by-step explanation:
x^2/3 = 12
12 x 3 = 36
x^2 = 36
/36 = 6
x = 6
Step-by-step explanation:
explanation is on the picture
In 0.46, in which place is the 6?
Answer:
hundredths
Step-by-step explanation:
the 4 is in the tenth place therfore the 6 is in the hundredth place because it is 46/100
What type of triangle is ABC?
Give reasons for your answer.
Answer:
I'll say that it is a scalene triangle because all of the sides of the triangle have different lengths.
Angle CAB is congruent to angle ACD because they are alternate interior angles (note the parallel lines AB and DE). So this makes angle CAB to be 50 degrees.
For similar reasoning, angle BCE = angle ABC = 80 degrees.
Focus on the angles that are centered at point C. Those three angles form a straight line so they add to 180 degrees.
(angle ACD) + (angle ACB) + (angle BCE) = 180
(50) + (angle ACB) + (80) = 180
(angle ACB) + 130 = 180
angle ACB = 180-130
angle ACB = 50 degrees
Ultimately, this leads to triangle ABC having the interior angles of A = 50, B = 80 and C = 50.
Because we have exactly two interior angles that are the same measure, this must mean triangle ABC is isosceles. The congruent angles are opposite the congruent sides, meaning that AB = BC.
What is the solution to 85<-5x+5?
A. x < 16
B. x > 16
C. x < -16
D. x > -16
Answer:C. x < -16
Step-by-step explanation:
Find the volume of the cylinder
Either enter an exact answer in terms of t or use 3.14 for t
10
4 units
Answer:
502.4 cubic unit
Step-by-step explanation:
Given data
The parameter for the cylinder is as follows
Height h= 10units
Radius r= 4 units
We know that the expression for the volume of a cylinder is
V= πr^2h
substitute
V= 3.14*4^2*10
V= 3.14*16*10
V= 502.4 cubic unit
Hence the volume is 502.4 cubic unit
Urgent help … If you know,Please help me ☹️☹️☹️
Graph a line that is perpendicular to the given line. Determine the slope of the given
line and the one you graphed in simplest form. Click and drag on the graph to draw a
line.
Answer:
y=2/3
Step-by-step explanation:
Find two points on the line and find the slope.
1,-3 -1,1
y1-y2/x1-x2
-3-1/1--1
-3/2
Then find the reciprocal of this slope by flipping the numerator and the denominator, changing the sign from positive to negative and visa versa.
Please help me !!!!!
Answer:
B. A dilation with a scale factor of 0.5
Step-by-step explanation:
A. is wrong because it is congruent transformation because reflections keep the angles and side lengths of the figure the same.
B. is right because it is NOT congruent because a dilation of any scale factor other than 1 results in a similar figure, because the side lengths are proprtional but not equivalent
C. is wrong because translations keep the angles and side lengths of the figure the same.
D. is wrong because a scale factor of 1 changes nothing about the figure.
1744 plus 9752 plus 9556
Answer: 21052
Step-by-step explanation:
Answer:
21052
Step-by-step explanation:
1. SUNDAES Carmine bought 5 ice cream sundaes for his friends. If each sundae costs $4.95, how much did he
spend? Justify your answer by using the Distributive Property.
Answer:
24.75
Step-by-step explanation:
you want to multiply 4.95×5 and you will get the answer $24.75.
Use the equation below to find y, if m =6, x = 3, and b = 5.
y = mx + b
x^2+2x+9=(x+1)^2+n What is n?
Answer:
I believe that the answer is 'n=8'.
“Type your answer in the box below without units” HELPPPPP
Answer
each loaf cost $2 all you had to do was divided 24 and 12 and you get $2
Step-by-step explanation:
ill mark u BRAINLIEST pls help me with this.
Determine the equation of the line that passes through (2,-3) and (1,-6). Explain how you got your answer.
Answer:
y = 3x - 9
Step-by-step explanation:
Let's start by finding the slope of the line:
The formula for slope is [tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex].
Plug in the numbers and solve:
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
[tex]m = \frac{-3 - (-6)}{2 - 1}[/tex]
[tex]m = \frac{3}{1}[/tex]
[tex]m = 3[/tex]
The slope of the line is 3.
The slope intercept form of a line is y = mx + b, where m is the slope and b is the y coordinate of the y-intercept.
Plugging in the number we got for the slope, the equation becomes:
y = 3x + b
Let's solve for b by plugging in an ordered pair for y and x:
y = 3x + b
-3 = 3(2) + b
-3 = 6 + b
b = -9
The y-coordinate of the line is (0, -9).
Now, plugging in the number into our equation, we get:
y = 3x + (-9)
y = 3x - 9
And that's the equation of the line!
You and your brother had a cookie bake-off! You made a dozen cookies each with a circumference of 10 inches and your brother made a dozen cookie bars with a perimeter of 10 inches. Who used more cookie dough? Assume the cookies are the same thickness.
Answer:
Your brother (I think i'm right)
Step-by-step explanation:
Perimeter is bigger than circumferance if same "length"
Help me find part A and B
Answer:
Step-by-step explanation:
From the given question,
a). m∠WAX = 60°
If m(arc WX) = 100°
Then by theorem,
Angle formed between the chords in a circle, measures the half of the sum of intercepted arcs.
m(∠WAX) = [tex]\frac{1}{2}(\text{arc WX + arcYZ})[/tex]
60° = [tex]\frac{1}{2}(100+\text{arcYZ})[/tex]
120 = 100 + arc YZ
120 - 100 = arc YZ
m(arc YZ) = 20°
b). m(arc WX + arc YZ) = 2(60°)
m(arc WX + arc YZ) = 120°
what is the answer to this question? Please give me the short answer and long answer.
Answer:
Each triangle weighs 3 grams.
Step-by-step explanation:
On the left side, there are 6 squares (12 grams) 3 circles (9 more grams), and 2 triangles (2x grams).
On the right side, there are 3 squares (6 grams) 2 circles (6 grams), and 5 triangles (5x grams).
This makes the equation 21 + 2x = 12 + 5x.
Let's find x.
21 + 2x = 12 + 5x
Subtract 5x from both sides.
21 - 3x = 12
subtract 21 from both sides.
-3x = -9
Divide by -3.
x = 3.
Each triangle weighs 3 grams. Let's prove this.
21 + 2x = 12 + 5x
21 + 2(3) = 12 + 5(3)
21 + 6 = 12 + 15
27 = 27
Members of alachua district choir were given the choice between romanticism or gothic style singing which style they preferred sing for the state competition
Here is the complete question.
Members of the Alachua district choir were asked when given the choice between romanticism gothic style singing, which style they preferred to sing for state competition. The data was broken down by gender:
48 males preferred Romanticism
63 males preferred Gothic
59 females preferred Romanticism
62 females preferred Gothic
Part A: Fill in and complete the following contingency table. Circle the largest joint frequency and put a box around the smallest marginal frequency.
Romanticism Gothic Total
Males
Females
Total
Part B: Which style was preferred as the state competition piece and by what percentage?
Part C: Which subject was preferred the most by Males?
Part D: What frequency does 125/232 represent?
Answer:
The answer is below
Step-by-step explanation:
Part A:
Romanticism, Gothic, Total
Males 48, 63, 111
Females 59, 62, 121
Total 107, 125, 232
Part B: The preferred style is Gothic by a percentage of
P = 125 ÷ 232
Hence, we have P = 54%
Part C: Based on the table provided, the subject aspired the most by males was Gothic since 63 males chose it over 48 chose Romanticism.
Part D: The frequency 125/232 depicts the total of people that preferred Gothic over the total of people in both categories.
show all steps solving 6x^2+x=5
Answer:
explain abit about it
please l don't understand
Evaluate the function for an input value of 3. f (x) = -4x^2 – 3x – 5
Answer:
-50Step-by-step explanation:
Function given:
f(x) = -4x² – 3x – 5Evaluate the function for an input value of 3
Input value is x = 3, output value is:
f(3) = -4(3²) – 3(3) – 5 = -4(9) - 9 - 5 = -36 - 14 = -50f(3) = -50f(3)
-4(3)²-3(3)-5-4(9)-9-5-36-14-50Jason has a bag of 30 pencils. Each pencil is 18 centimeters long. What is the combined length of the pencils in meters?
Add and subtract fraction word problem
Answer:
9/10
Step-by-step explanation:
Answer:
3 glasses of milk will give you 9/10 of the recommended amount of calcium per day!
Step-by-step explanation:
Firstly, Let's identify the amount per day as show by the problem that is 3/10.
In simple terms, the question requires us to find the amount of calcium 3 glasses would provide.
Well, if one glass provides 3/10.
To find the value of three glasses, we need to multiply!
[tex]\frac{3}{10}*3\\\frac{3}{10}*\frac{3}{1}[/tex]
The amount of calcium three days would provide is [tex]9/10[/tex].
Hope it helps! :)