Answers
Given:
[tex]\ln(y-8)=-2x+\ln C[/tex]
To find:
y as a function of x.
Solution:
We have,
[tex]\ln(y-8)=-2x+\ln C[/tex]
It can be written as
[tex]\ln(y-8)=\ln e^{-2x}+\ln C[/tex] [tex][\because \ln e^x=x][/tex]
[tex]\ln(y-8)=\ln (Ce^{-2x})[/tex] [tex][\because \ln (ab)=\ln a+\ln b][/tex]
On comparing both sides, we get
[tex]y-8=Ce^{-2x}[/tex]
Adding 8 on both sides, we get
[tex]y=Ce^{-2x}+8[/tex]
Therefore, the equation function is [tex]y=Ce^{-2x}+8[/tex].
Related Questions
What do Kelsey and Cody have to do (like most consumers) to meet the terms of this promotion?
Answers
Answer:
What.
Step-by-step explanation:
WHAT.!?
There were 239 people at a Travis Scott concert, Admission to the drive-in concert was $15 for adults and $5.50 for children. The total cost was $2758.50.
Answers
Answer:
IM A HUGE TRAVIS SCOTT FAN I SNUCK IN ONE OF HIS CONCERTS
Step-by-step explanation:
Class A has 30 pupils and class B has 30 pupils.
Both classes sit the same maths test.
The mean score for class A is 55.
The mean score for class B is 65.
What is the mean score in the maths test across both classes?
Answers
Answer:
30
Step-by-step explanation:
b/c mean is average by another word
55 + 65 = 120
120\2 = 60
what is 9 squared times 8 squared
Answers
Answer:
5184
Step-by-step explanation:
9 squared is 81 (9 x 9)
8 squared is 64 (8 x 8)
64 x 81 is 5184
A right triangle is graphed on a coordinate plane. Find the length of the hypotenuse. Round your answer to the nearest tenth.
Answers
Answer:
7.6
Step-by-step explanation:
From the graph, we know the lengths of two legs.
a = 3
b = 7
Knowing this, we can use the Pythagorean Theorem to solve for c, the hypotenuse. (remember, a^2 + b^2 = c^2)
c = √a2 + √b2
= √(7)2 + √(3)2
= √49 + √9
= √58
= 7.6
Answer:7.6
Step-by-step explanation:
write the equation for this line in slope intercept form
Answers
Answer:
y = [tex]\frac{3}{2}[/tex]x + 2
Step-by-step explanation:
Slope-intercept form is y = mx + b with m as the slope and b as the y-intercept.
The y-intercept is the point where the line intersects the y- axis.
y = mx + 2
The equation to find slope is [tex]\frac{y1-y2}{x1-x2}[/tex] Two points from the line: (0,2) (4,8)
[tex]\frac{8-2}{4-0}[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex]
y = [tex]\frac{3}{2}[/tex]x + 2
Use the definition of congruence to decide whether the two figures are congruent
Someone help please
Answers
Answer:
These two figures are not congruent.
Step-by-step explanation:
The definition of congruence is, "In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.", now knowing this we next take a look at the figures.
Coordinates (A, E) do not match up with the bottom figures (P, T). The next coordinates (E, D) also don't match up with coordinates (T, S). Coordinates (A, B) and (P, Q) don't match up together either. (B, O), (Q, R), (O, D), or (R, S) also do not match up if you look closely at them. Now you can conclude that although these two figures may look alike at first glance, their points are put in different places showing that they aren't the same in shape and size; meaning they are not congruent.
Two figures are congruent if their dimensions are equal
ABCDE = PQRST therefore, ABCDE ≅ PQRST, by the definition of congruency
Reason:
The coordinates of pentagon ABCDE are;
A(-2, 8), E(4, 8), D(6, 2), C(-2, 2), B(-4, 6)
The coordinates of pentagon PQRST are;
P(-3, 0), T(3, 0), S(5, -6), R(-3, -6), Q(-5, -2)
By performing the vector translation of [tex]\dbinom {1}{8}[/tex], to PQRST, we have;
P(-3 + 1, 0 + 8) = (-2, 8) = Coordinates of A
T(3 + 1, 0 + 8) = (4, 8) = Coordinates of E
S(5 + 1, -6 + 8) = (6, 2) = = Coordinates of D
R(-3 + 1, -6 + 8) = (-2, 2) = = Coordinates of C
Q(-5 + 1, -2 + 8) = (-4, 6) = = Coordinates of B
Given that a translation is a rigid transformation and that by performing a translation transformation of [tex]\dbinom {1}{8}[/tex], on PQRST gives ABCDE, we have that the dimensions of the pentagon ABCDE = The dimensions of the pentagon PQRST, we have;
ABCDE = PQRST
Therefore;
ABCDE ≅ PQRST, by the definition of congruency
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What is the range of the function f(x) = -2x + 5 when the domain is {-5, 5}.
Answers
Answer:
{-5,15}
Step-by-step explanation:
because this function is constantly decreasing, we can get our range by looking at the endpoints:
f(-5) = 15
f(5) = -5
the midpoint of AB is M (4,0). if the coordinates of A are (3, 1), what are the coordinates of B?
Answers
The coordinates of point B are (5, -1) if the midpoint of AB is M(4, 0) and the coordinates of A are (3, 1).
Let the coordinates of point B are (x, y).
According to the give question.
The midpoint of AB is M(4, 0).
The coordinates of A are (3, 1).
Therefore, the coordinates of points B are given by
(4, 0) = ( (3 + x)/2, (1 + y)/2)
⇒ (3 + x)/2 = 4, and (1 + y)/2 = 0
⇒ 3 + x = 8 and 1 + y = 0
⇒ x = 8 - 3 and y = -1
⇒ x = 5 and y = -1
Hence, the coordinates of point B are (5, -1) if the midpoint of AB is M(4, 0) and the coordinates of A are (3, 1).
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Which ordered pair is a solution of the equation y=5x? (-2, 10) (-5, 25) (-3, 15) (-2, 10)
Answers
One of the solutions of the given equation y = 5x is (2,10)
The solution of an equation means if we substitute the value of this solution into the equation, it will produce the correct equality from the left side to the right side.
If the solution has 2 variables, for example x and y, and the solution is (a,b) means that if we replace x with a and y with b, the equality is correct.
The given equation is: y = 5x
For option (-2,10), substitute x = -2 and y = 10 into the equation:
10 = 5 . (-2)
10 = -10 (False)
Hence (-2,10) is not a solution.
For option (-5, 25), substitute x = -5 and y = 25 into the equation:
25 = 5 . (-5)
25 = -25 (False)
Hence (-5, 25) is not a solution.
For option (-3, 15), substitute x = -3 and y = 15 into the equation:
15 = 5 . (-3)
15 = -15 (False)
Hence (-3, 15) is not a solution.
There is no options in the problem that gives the correct equality. Looks like there is a typo.
Example of a solution of the given equation is (2,10), since if we substitute x = 2 and y = 10 into the equation:
10 = 5 . (2)
10 = 10 (True)
Hence (2, 10) is a solution.
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25. If mVYX = 276° and m angle UVX = (4x - 5),
find the value of x.
Can someone help me please
Answers
Answer:
22.25 or 22
Step-by-step explanation:
360-276+=84
4x-5=84
4x=89
x=22.25 or 22
Answer:
answer is 11. Got this pic from the internet btw.
Step-by-step explanation:
If you were to search this question up, which I’m sure you did, you would find that in the images portion, there’s an image where it shows the same question but with multiple choice answers. Among these choices is 11.
Please help! need this As soon as possible!
Answers
Answer:
question 1 answer:
nth term is =7n+6
9th term means n=9
So the 9th term is =7*9+6=63+6= 69.
question 2 answer: 2−4+3
mark me the brainliest please
:)
Explanation:
Q2:
(x - 1)(x - 3)
= x^2 - 3x - x + 3
= x^2 - 4x + 3
Q19:
x/3 + 10 = x+2
x + 30 = 3x + 6
x - 3x = 6 - 30
-2x = -24
x = 12
Please help me. I will fail...I will mark you brainiest.
The function [tex]f(x)=15(0.85)^x[/tex]models the height, in feet, of a bouncing ball after x seconds.
What is the initial height of the bouncing ball?
What is the percent rate of change?
What is the height of the bouncing ball after 5 seconds? Express your answers as a decimal rounded to the nearest hundredth.
Answers
Answer:
1) 17.6 2) 1760% 3) 12.6
Step-by-step explanation:
give me brainlist
The initial height of the bouncing ball is 15 feet, The percent rate of change is -15% and after 5 s, the height of the ball is 6.66 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the function:
f(x) = 15(0.85)ˣ
a) The initial height of the bouncing ball is 15 feet
b) The percent rate of change = 0.85 - 1 = -0.15 = -15%
c) After 5 s, x = 5:
f(5) = 15(0.85)⁵ = 6.66 feet
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Help please asap!! I will mark you as brainliest :)
Answers

A shirt is originally $40, but today it is on sale for 35% off.
If sales tax is 8%, what is the total price for the shirt?
Answers
Answer:
$23.92
Step-by-step explanation:
35% of 40 is 14. 40-14=26. 8% of 26 is 2.08. 26-2.08=23.92
Simplify. Your answer should only contain only positive exponents.
Answers
Answer:
A
Step-by-step explanation:
find the answer- 8.19÷1.3
Answers
Answer:
-6.3
Step-by-step explanation:
You can do it on calculator.
“Pueblo” is the Spanish word for ___________ a. town. c. flock of sheep. b. stone ruins. d. oven to bake bread. Please select the best answer from the choices provided A B C D
Answers
The answer is A: Town
The base of an isosceles triangle is 4 units longer than the
sides. The perimeter of the triangle is 23.6 units. Which
system of equations can be used to find the length b of the
base and the length s of the sides?
Answers
Step-by-step explanation:
2s + b = 23.6
s + 4 = b
s = b - 4
2b - 8 + b = 23.6
3b = 31.6
b = 31.6 / 3 = 10.53333333(etc.) which is approx. 10.53
s = 6.53
Answer:
1gm = 1000mg so 0.1gm = 1000mg
first, convert the weight to kg
160lb * 1kg/2.2lb = 72.7kg
next, the dose
72.7kg * 100mg/kg = 7270mg
Step-by-step explanation:
2.25x + 15 = 9.5x + 0.5
Answers
Answer:
x=2
Step-by-step explanation:
Step-by-step explanation:
2.25x+15=9.5x+0.5
15-0.5=9.5x-2.25x
14.5=7.25x
x=14.5
7.25
x=2
hope it helps.
The cook prepares 12 hard-boiled eggs, 36 scrambled
eggs, and 7 poached eggs. Write the ratio of hard-
boiled to scrambled eggs as a fraction.
Answers
Answer: 12/36 and simplified would be 1/3
Step-by-step explanation:
12 - hard boiled eggs
——
36 - scrambled
Divide them by 12 and you get a simplified fraction
In the scale used on a blueprint, 1/5 inches represents 3 feet. On the blueprint, what is the length of a room with an actual length of 30 feet?
(You have to convert the fraction to a decimal first)
A. 6 in
B. 2 in
C. 1/2 in
D. 2 1/2 in
Answers
9514 1404 393
Answer:
B. 2 in
Step-by-step explanation:
The lengths are proportional, so you have ...
blueprint length / room length = (1/5 in)/(3 ft) = (x in)/(30 ft)
Multiplying by 30 ft gives ...
x in = (1/5 in)(30/3) = 10/5 in = 2 in . . . . . note that units of ft cancel
The blueprint length of the room is 2 inches.
__
Comment on "convert the fraction"
As a general rule, you can work math problems with the numbers in any convenient form: fractions, decimals, scientific notation, percentages. Your calculator or your mental arithmetic methods may prefer one form over another, but conversion isn't always necessary.
What is the equation of the line that passes
through the points (-7, -10) and (-6, -8)?
Answers
6(5g-7h+4)
6(5g−7h+4)
Answers
Answer:
Step-by-step explanation:
30g-42h+24
30g-42h+24
Write the equation of the line in slope-intercept form, y=mx+b.
(4, -4) m= 1/2
Answers
Answer: y=0.5x+6
Step-by-step explanation:
each time x moves 1 the point moves 0.5 vertically so
4, -4
3, -4.5
2, -5
1, -5.5
0, 6
Answer:
y=0.5x+6
Step-by-step explanation:
what is the factor X squared plus 4X plus 3 equals 15
Answers
Answer:
(x-2) (x+6)
Step-by-step explanation:
If it is written like this:
[tex]x^{2} +4x + 3 = 15[/tex]
To focus on the equation on the left rewrite the equation equal to the value of zero.
(x-2) (x +6) = 0
The answer is (x-2) (x+6)
Parvinder wants to save $500 for a trip. Which inequality shows the least amount she must save each month for 6 months to accomplish this?
A 6x 500 B 6x > 500 C 6x => 500 D x => 500 + 6
Answers
Answer:
The correct answer is C. 6x = 500.
Step-by-step explanation:
In this expression, the "x" represents how many dollars he needs to save every month. Or in other words, the amount of money he earns a month multiplied by the amount of months should equal 500 in order for Parvinder to be able to go on his trip.
Therefore, the correct answer is C. 6x = 500.
Hope this helps! :D
What is 2x + 9 times 7x if x equals -75
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I am bo*red someone talk to me
Answers
Answer:
-4875
Step-by-step explanation:
and hello
How many 5-digit numbers can you form using the digits 8 and 9?
Answers
Answer:
As repetition is not allowed,
For first digit selection, we have 8 choices.
for second digit selection 7 choices.
Similarly, 6 choices for 3rd digit, 5 choices for 4th digit and 4 choices for 5th digit.
Hence, total choices 8*7*6*5*4 = 6720
Step-by-step explanation:
A sloth travels about 7 feet every minute. Generate the set of ordered pairs for the ratio relationship between the total distance traveled y and the number of minutes x for a total of 1, 2, 3, and 4 minutes.
(1,
), (2,
), (3,
), (4,
)
Part B
Answers
the 4 ordered pairs for the given proportional relation are (1, 7), (2, 14), (3, 21), (4, 28).
How to find the set of ordered pairs?
Here we know that the sloth travels about 7 feet every minute, then we can define the speed as:
S = 7 ft/min
Now remember the relation:
distance = speed*time
Then the proportional relation is:
D = 7*t
The ordered pairs are of the form (t, D)
if t = 1.
D = 7*1 = 7
if t = 2
D = 7*2 = 14
if t = 3
D = 7*3 = 21
if t = 4
D = 7*4 = 28
Then the 4 ordered pairs are (1, 7), (2, 14), (3, 21), (4, 28).
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