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
Determine if the expression 9y^5+ y − 3y^3is a polynomial or not. If it is a
polynomial, state the type and degree of the polynomial.
Find the surface ara of the square pyramid. Enter your answer in the box
Answer:
341 cm²
Step-by-step explanation:
The base is 11 x 11 = 121
Then there is 4 side that are triangles, 11 x 10 ÷ 2 = 55 -----> 55 x 4 = 220
220 + 121 = 341
Mrs. Byrne’s class went raspberry picking. The data below show the weights of the cartons of raspberries the students picked.
The athletic department manager purchased a total of 52 footballs and soccer balls. Each football cost $23.53, and each soccer ball cost $19.86. If the manager spent a total of $1,120.80, how many soccer balls did the manager purchase?
Answer:
The manager purchased 28 soccer balls.
Step-by-step explanation:
Since the information states that the athletic department manager purchased a total of 52 balls, you can say that the result of adding up the number of footballs and soccer balls purchased is 52, which can be expressed as:
x+y=52, where:
x is the number of footballs purchased
y is the number of soccer balls purchased
Also, as the statement indicates the price of each type of ball and the total cost, you can say that adding up the results of multiplying the price of each ball for the quantity purchased is equal to the total amount spent, which is:
23.53x+19.86y=1,120.80
Now, you have 2 equations:
x+y=52 (1)
23.53x+19.86y=1,120.80 (2)
To be able to find the value of x and y, first you can isolate x in (1):
x=52-y (3)
Then, you can replace (3) in (2) and solve for y:
23.53(52-y)+19.86y=1,120.80
1,223.56-23.53y+19.86y=1,120.80
1,223.56-1,120.80=23.53y-19.86y
102.76=3.67y
y=102.76/3.67
y=28
Finally, you can replace the value of y in (3) to find the value of x:
x=52-28
y=24
According to this, the answer is that the manager purchased 28 soccer balls.
Use PEMDAS to evaluate the expression 7 x 6 + 8 − 16 ÷ 4.
Answer:
7x^6 + 4
Step-by-step explanation:
I NEED HELP Quadratics and Their Solutions
Two wires are attached 6 feet up a tree and 3 feet from the base of the tree. About how much TOTAL wire was used?
Answer:
9 cm²
Step-by-step explanation:
Two wires are attached 6 feet up a tree and 3 feet from the base of the tree. About how much TOTAL wire was used?
We solve the above question, using the Area of a Triangle
Area = 1/2 × Base × Height
Area = 1/2 × 3 × 6
Area = 9 cm²
Therefore, the total wore that was used was 9cm² of wire
Isaac owes \$8,100$8,100 on his credit card. The bank charges an annual interest rate of 21.9%, compounded monthly. If Isaac wants to pay off his credit card using equal monthly payments over the next 16 months, what would the monthly payment be, to the nearest dollar?
Answer:
[tex]M=\$605.58[/tex]
Step-by-step explanation:
From the question we are told that:
Issac's Debit [tex]P=\$8100[/tex]
Annual interest rate [tex]r=21.9\%[/tex]
Number of payments [tex]n=16[/tex]
Generally the equation for Monthly payment is mathematically given by
[tex]M=\frac{Pr}{1-(1+r)^-^n}[/tex]
[tex]M=\frac{1800*0.0219}{1-(1+0.0219)^-^{16}}[/tex]
[tex]M=\$605.58[/tex]
Therefore Payment for each month is given as
[tex]M=\$605.58[/tex]
A recipe calls for 1/2 of a teaspoon of sugar for every 15 cookies. If you are going to make 75 cookies for a party, how many teaspoon of sugar will you use.
Answer:
2.5 teaspoons
Step-by-step explanation:
75/15 = 5
1/2 · 5 = 2.5
Answer:
2.5 teaspoons of sugar
Step-by-step explanation:
[tex]\frac{15}{0.5} =\frac{75}{y}[/tex]
Cross multiply.
15 × y = 0.5 × 75
15y = 37.5
15y ÷ 15 = 37.5 ÷ 15
y = 2.5
Which function has the same range as
f(x)= -2sqrt (x-3)+8
Answer:
Answer: : g(x)=-sqrt(x+3)+8
Step-by-step explanation:
The function has the same range is the third one:
g(x)=-sqrt(x+3)+8
The range of this function is:
x+3>=0
sqrt(x+3)>=sqrt(0)
sqrt(x+3)>=0
Multiplying the equation by -1:
-1[ sqrt(x+3)>=0]
- sqrt(x+3)<=0
Adding 8 both sides of the equation:
- sqrt(x+3)+8<=0+8
- sqrt(x+3)+8<=8
g(x)<=8
Then Range g(x)= (-Infinite, 8]
Answer: Third option: g(x)=-sqrt(x+3)+8
Find the Area of the trapezoid.
A. 56
B. 28
C. 49
D. 35
Answer: b
Step-by-step explanation:
If it snows tomorrow, the probability is 05 that John will practice his trombone. If it does not snow tomorrow, there is only a 0.6 chance that John will practice. Suppose the chance of snow tomorrow is 70%. What is the probability that John will practice his trombone?
Answer:
54 percent
Step-by-step explanation:
The final probability is a weighted average of the going to play probabilities determined for each weather scenario:
P(John performs cello; provided that it rains) * P(it rains) + P(it rains) + P(it rains) + P(it rains) + P(it rains) +
If it doesn't rain, P(John plays cello) * P(it doesn't rain) =
0.54 = 0.6 * 0.7 + 0.4 * 0.3
The likelihood is 54 percent.
wha the MIDPOINT of (-6, 8) and (6, -7)
Answer:
here you are:
the midpoint for (-6,8) and (6,-7) is (0, 1/2)
Step-by-step explanation:
the midpoint for (-6,8) and (6,-7) is (0, 1/2)
If 10x+6y=7 is a true equation, what would be the value of 6(10x+6y)?
Answer:
42
Step-by-step explanation:
We know that 10x + 6y = 7, and so
6(10x + 6y) = 6(7) = 42
Please help...My answer is close but not close enough..
No links :)
Answer:
76
Step-by-step explanation:
(5x3)+(5x3)=30
15-6=9
5x9=45
45+30=75
Since 76 is the closest to 75 it's 76
In the figure below, m∠ABC = 57 degrees and m∠DAB =116 degrees. What is m∠ABC?
Answer:
∠ACB = 59°
Step-by-step explanation:
∠BAC = 180 - 116 = 64°
∠ACB = 180 - 64 - 57 = 59°
factor completely;
3x^2+4x-7
Answer:
(3x-7) (x+1)
Step-by-step explanation:
3x^2 - 4x - 7
First split the middle term
3x^2 + 3x - 7x - 7
Make into two separate expressions
(3x^2 + 3x) (-7x-7)
Take out what you can
3x (x+1) -7 (x+1)
Now you have your answers
(3x-7) (x+1)
What is 1\10 x 1.2 >>>>>>>>>>>>>>>>>>>>>>>>
Answer:
1/10 x 1.2 is 0.12
Step-by-step explanation:
so yeeeeeeee
Factorise using the sum and product method with all the steps!
British curriculum
No links or websites please !
Answer:
(2x+3)(x-5)
Step-by-step explanation:
Given the expression 2x²-7x-15
Factorize
2x²-10x+3x-15 =0
2x(x-5)+3(x-5)
(2x+3)(x-5)
Hence the factored form of the expression is (2x+3)(x-5)
HI thts way tooo much to answer but ye
I NEED HELP WITH THIS IVE RETAKEN IT LIKE 4 TIMES PLS HELP
Answer:
(a)=40 (b)=60
Step-by-step explanation:
(a)=
So first 70 +70 = 140 then 180-140 = 40
(b)
So first 180/3 = 60 all angles =60
Translate the sentence into an inequality. Ten times the sum of a number and 21 is at most 16. Use the variable y for the unknown number.
Answer:
10y+ 21 ≥ 16
Step-by-step explanation:
Determine if each pair of triangles is congruent. If so, write the congruence
statement and explain how you know the triangles are congruent.
Answer:
top one, yes. by the SSS theorem
bottom one, no. The bases are not congruent
Step-by-step explanation:
can someone help me please this is a major grade
Answer:
$7.63
Step-by-step explanation:
well 6/10 is the same as 0.6 and 3/100 is the same as 0.03
so when you add the 7and 0.6 =7.6 +0.03=7.63
Answer:
7.63
Step-by-step explanation:
7 dollars - 7.00
0.6 dollar - 0.6
0.03 dollar - 0.03
(becoming)
7.00
0.6
0.03
-----------
$7.63
^line up the decimals while adding
Hopefully this helps,
-Rose
An engineer is designing a fountain that shoots out drops of water. The nozzle from which the water is launched is 3 meters above the ground. It shoots out a drop of water at a vertical velocity of 14 meters per second. Function h models the height in meters, h, of a drop of water t seconds after it is shot out from the nozzle. The function is defined by the equation h(t)=−5t2+14t+3. How many seconds until the drop of water hits the ground?
Answer:
After 3 seconds
Step-by-step explanation:
Given
[tex]h(t) = -5t^2 + 14t + 3[/tex]
Required
Time the drop will hit the ground
When the drop hits the ground,
[tex]h(t) = 0[/tex]
So, we have:
[tex]0 = -5t^2 + 14t + 3[/tex]
Rewrite as:
[tex]5t^2 - 14t - 3 = 0[/tex]
Expand
[tex]5t^2 + t - 15t - 3 = 0[/tex]
Factorize
[tex]t(5t + 1) -3(5t + 1) = 0[/tex]
Factor out 5t + 1
[tex](t -3)(5t + 1) = 0[/tex]
Split
[tex]t -3 = 0[/tex] or [tex]5t + 1 = 0[/tex]
Solve for t
[tex]t = 3[/tex] or [tex]5t = -1[/tex]
Time cannot be negative.
So:
[tex]t = 3[/tex]
Halla X
Para una practica de 11 mins q-q
A piece of fabric is for 1/6 yards long if 2 1/4 yards are cut off The Yards remain I'll see you
Answer:
2 1/12 yds remain
Step-by-step explanation:
1. You first change the denominators, so then the fractions will be alike. 2 1/4-1/6
2. Find the LCD or Least Common Denominator. 12 can go into and it is alike, so 2 3/12-2/12
3. Now we can find the answer!
So the answer is 2 1/12
Please mark me brainliest!
Luke sold 4 times as many books as Maurice. If Maurice had sold 18 more books, he would have tied Luke for first place. How many books did Luke sell?
Answer:
24
Step-by-step explanation:
I guessed and checked but 24 -18 is 6 and 6 times 4 is 24
M + 18 = 4M
18 = 4M - M
18 = 3M
M = 18/3 = 6
4M = 4(6) = 24 sold by Luke
The perimeter of a square is 12x - 8. Which of the following is the length of
one side of the square?
Answer:
3x-2
Step-by-step explanation:
12x-8/4 = 3x-2 is one side length of a square
Just answer the question in the picture. It's just math vocab! DO NOT answer for points OR SPAM LINKS!!! I will REPORT!
Answer:
A circle is a round shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
The distance from the center to the circumference of a circle
The diameter is the length of the line through the center that touches two points on the edge of the circle.
The Radius is the distance from the center outwards. The Diameter goes straight across the circle, through the center. The Circumference is the distance once around the circle.
In plane geometry, a chord is the line segment joining two points on a curve. The term is often used to describe a line segment whose ends lie on a circle.
A line segment that has the endpoints on the circle and passes through the midpoint is called the diameter. The diameter is twice the size of the radius. A line segment that has its endpoints on the circular border but does not pass through the midpoint is called a chord. A circle is the same as 360°.
A line that intersects two or more points on a curve. (From the Latin secare "to cut")
The length of the side opposite the angle divided by the length of the adjacent side.
A line that intersects a circle in exactly one point is called a tangent and the point where the intersection occurs is called the point of tangency. The tangent is always perpendicular to the radius drawn to the point of tangency. A secant is a line that intersects a circle in exactly two points.
Common tangents to two circles may be internal or external. A common internal tangent intersects the line segment connecting the centers of the two circles whereas a common external tangent does not.
Step-by-step explanation:
they are in order! tell me if i made a mistake:)
What is the approximate volume?
Answer:
B
Step-by-step explanation:
1) find the base area
base area = side^2 = 30^2 = 900 m^2
2) find the Volume
V = (base area x height)/3 = (900 x 21)/3 = 6300 m^3
Answer:
B) 6,300 m³
Step-by-step explanation:
The volume of approximate = L×W×H/3
30×30×21/3=
answer: 6,300
[tex]**************[/tex]
hope it helps...
have a great day!!
