Answers
Answer:
x = 0 or 1/2
Step-by-step explanation:
Solving an exponential equation of this nature with different bases and coefficients is always a bit of an ad hoc affair. Here, we can divide by the right side expression and make a substitution that turns it into a quadratic.
__
[tex]3\cdot16^x+2\cdot81^x=5\cdot36^x\\\\0.6\left(\dfrac{4}{9}\right)^x+0.4\left(\dfrac{9}{4}\right)^x=1\\\\\textsf{Let $z=\left(\dfrac{4}{9}\right)^x$}\\\\0.6z+\dfrac{0.4}{z}=1\qquad\text{after substitution}\\\\3z^2-5z +2 = 0\qquad\text{multiply by $5z$ and put in standard form}\\\\(3z-2)(z-1)=0\qquad\text{factor}\\\\z=\dfrac{2}{3}\quad\text{or}\quad z=1\\\\x=\dfrac{\log(z)}{\log(4/9)}=\boxed{\dfrac{1}{2}\quad\text{or}\quad 0}[/tex]
_____
Additional comment
A graphing calculator often solves these very nicely, especially when the equation is put into the form f(x) = 0.
Related Questions
the graph shows the number of servings in different amounts of frozen yogurt listed on a carton. Enter an equation that gives the number of servings y in x pints. Use only decimal form, if necessary.
Answers
Answer:y=2.5x
Step-by-step explanation:
We have been given a graph that shows numbers of servings (y) in different amounts (x) of frozen yogurt listed on a carton.
To write an equation that gives the number of servings y in x pints, we will have to find the slope (rate of change) of our given linear function.
Since we know that rate of change of a function can be found by vertical change of the function divided by horizontal change of the function.
m= Slope (rate of change).
=Difference between two y-coordinates.
=Difference between corresponding x-coordinates of the y-coordinates.
Upon substituting coordinates of two points (0,0) and (4,10) in slope formula we will get,
The slope of our given line is 2.5.
Now we will write equation of our given line is slope-intercept form. The equation of a line in slope-intercept form is: , where m=slope and b = y-intercept (initial value).
Upon substituting m=2.5 and coordinates of point (4,10) in slope-intercept form of equation we will get,
Upon substituting m=2.5 and b=0 in slope-intercept form of equation we will get,
Therefore, the equation will give the number of servings y in x pints.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Write the quadratic equation in factored form. Be sure to write the entire equation.
x 2 - 5x - 24 = 0
Answers
Answer:
x=x2-24/5
2 −24
Step-by-step explanation:
x2−5x−24=0
Add 5x to both sides. Anything plus zero gives itself.
x
2
−24=5x
Add 24 to both sides.
x
2
=5x+24
Charlene has a monthly salary of $3,410. with her present budget, charlene has a net income that is 7% of her monthly salary. charlene is going to reduce her net income by $125 each month and put this money towards paying down her debt. what will charlene’s new net income be? a. $113.70 b. $176.70 c. $229.95 d. $238.70
Answers
Charlene has a monthly salary of $3,410. with her present budget, the corrected net income is $113.70
What is income tax?Income tax is a tax applied on individuals or entities concerning income or profit earned by them.
Charlene has a monthly salary = $3,410.
Charlene has a net income that is 7% of her monthly salary.
The computation of the new net income is shown below
= Monthly salary × net income percentage - reduced amount of net income per month
= $3,410 × 7% - $125
= $113.70
Hence, the corrected net income is $113.70
Learn more about income ;
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I need help on way more then just thisT-T-math-
Answers
Answer:
Your answer is B) 3.6 cm.
Step-by-step explanation:
10 mm = 1 cm. To convert 36 mm to cm all you have to do is divide by 10.
36/10 = 3.6
So, 36 mm = 3.6 cm.
In the future, if you were to convert cm to mm, just multiply by 10.
This is because 10mm = 1cm
So 36mm = 3.6cm
Find the area and perimeter of each figure
Answers
Answer:
A is Area= 100 and perimeter=40
B is Area=112.5 and perimeter=15
C is Area=144 and perimeter=48
Step-by-step explanation:
No explanation needed
HELP! WILL GIVE BRAINLEST! What is the approximate degree measure of an angle of 4.59 rad?
Answers
Answer:
263 degrees......... ........
Step-by-step explanation:
263 is the answer.
If you borrow $700 for 5 years at
an annual interest rate of 7%, how
much will you pay altogether?
Answers
Answer:
its 945 or 982
Step-by-step explanation:
8. Identify the constant of proportionality between the perimeter of the square below and its side length.
Answers
Answer:
yes
Step-by-step explanation:
I believe the yes is yes
Pls helppppppp.
I don’t understand
Answers
Check the picture below.
so the deck is a 72x52 rectangular area, and the pool is simply two semicircles with a rectangle, as you see in the picture, we can put both semi-circles and make one circle with their area, so both together are really the area of a circle whose diameter is 29, and thus its radius is half that or 14.5.
Now, the area Belvedere is going to seal is really the "shaded" or bricked area, if we take the area of the whole deck, including the pool, and then get the area of the pool and subtract it from that of the deck's, what's leftover, is the area that wasn't subtracted, namely the "shaded" area.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\stackrel{deck's}{rectangle}}{(72)(52)}~~ - ~~\stackrel{\stackrel{pool's}{rectangle}}{(40)(29)}~~ - ~~\stackrel{\stackrel{pool's}{circle}}{\pi (14.5)^2}}\implies 3744~~ - ~~1160~~ - ~~210.25\pi \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{using~\pi =3.14}{\approx 1923.8}~\hfill[/tex]
Which expression is equivalent to 2(3w)?
Answers
Answer:
6w
Step-by-step explanation:
Multiply the constant by the coefficient.
2 times 3 is 6 and since there's a w beside 3, you'd have 6w.
Point W is located at (-2,3) on a coordinate plane. Point W is reflected over the x-axis to create Point W. Point W is then reflected over the y-axis to create point W. What ordered pair describes the location of point W?
Answers
Answer: W is now at (2,-3)
Step-by-step explanation: flip by the x-axis to turn (-2,3) to (-2,-3) then flip it on the y-axis to turn (-2,-3) to (2,-3).
What is the number between 80 and 90 that has seven as a factor
Answers
Answer:
the answer is 84
Five friends plan to split a restaurant bill evenly. The total cost of the meal is $89.75, and they want to leave a 20% top. What amount should each friend pay?
Answers
Answer:
$21.54
Step-by-step explanation:
89.75 x .2 = 17.95
17.95+89.75=107.70
107.70/5=21.54
A (___________________) includes information
about how well you manage money.
A credit card
B checking account
C work-study program
D credit history
Answers
Answer: d credit history
Step-by-step explanations :
please help, thanks if you do
Answers
Answer:
Step-by-step explanation:
f(x) = (-2)^x
x = 3 from the left
f(3) = (-2) ^3
f(3) = (-2) * (-2) * (-2)
f(3) = - 8
You have to realize that you are working with an exponential equation (that is x is a power, not a variable. A variable equation would be written as y = 3x
=
Given a = 8, b = 12, and c= 14, use the Law
of Cosines to solve the triangle for the value
of B. Round answer to two decimal places.
Answers
Answer:
please where is the diagram
Which equation represents an exponential function?
3
x
4
3
x
4
3 x to the 4th power
3
(
4
)
x
3
(
4
)
x
3 times 4 to the x th power
3
x
−
4
3
x
−
4
3 x to the negative 4 power
3
x
3
x
3 x
Answers
Answer:
pls why did you decide to type vertically, you could have typed it horizontally for clearer understanding, thanks.
Step-by-step explanation:
by my analysis
the answer should be the first option
3x to the 4th power
mathematically 3x^4.
Don't spam!
correct solution and answer= Brainliest answer
Answers
So
[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\\ \rm\Rrightarrow sin45=\dfrac{P}{6}[/tex]
[tex]\\ \rm\Rrightarrow\dfrac{1}{\sqrt{2}}=\dfrac {P}{6}[/tex]
[tex]\\ \rm\Rrightarrow P=\dfrac{6}{\sqrt{2}}[/tex]
[tex]\\ \rm\Rrightarrow P=3\sqrt{2}[/tex]
50 points pls help!!!!!!
Make sure you are right I will have to retake this if you are wrong
if the terminal point of Ø is (0,1), what is tan Ø?
undefined
1
1/2
0
Answers
Answer:
undefined
Step-by-step explanation:
Since, the terminal point of is (x,y), thus
[tex]tan[/tex] Ø [tex]\frac{y}{x}[/tex]
x-coordinate is 1 and the y-coordinate is 0. Using [tex]tan0=\frac{y}{x}[/tex] we get:
[tex]tan[/tex] ∅ [tex]=\frac{1}{0}[/tex]
[tex]tan[/tex] ∅ [tex]=0[/tex]
Therefore, tan Ø is undefined.
Or we can just do 1/0 which is undefined
~Lenvy~
help i don't understand
Answers
What is 4.78 as a percent
Answers
To convert from decimal to percent, just multiply the decimal value by 100. In this example we have: 4.78 × 100 = 478%
A customer at a video game store pays $420 for 6 games and 2 controllers. A second customer pays $180 less than the first customer for 2 games and 4 controllers. The price of each game is the same, and the price of each controller is the same. Which system of equations can be used to find the price, in dollars, of each game, g, and each controller, c
Answers
The linear system with two variables is used to find the price. The price of each game is $60 and the price of each controller is $30.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
A customer at a video game store pays $420 for 6 games and 2 controllers.
A second customer pays $180 less than the first customer for 2 games and 4 controllers.
The price of each game is the same, and the price of each controller is the same.
Let x be the price of games and y be the price of the controller. Then the equations will be
6x + 2y = 420 ...1
2x + 4y = 240 ...2
By solving the equations 1 and 2, then we have
x = 60 and y = 30
More about the linear system link is given below.
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What is the mean of the data set?
{2, 5, 1, 7, 6, 4, 3}
Enter your answer in the box.
Answers
Your answer is 4.
Explanation:--
The Mean of the Data set is ---
2+5+1+7+6+4+3
7
= 4.
Hence, Mean of the data set is 4.
Answer:
To find the mean, you must add all the numbers and divide it by the amount of numbers in the set.
2 + 5 + 1 + 7 + 6 + 4 + 3
= 28
28 divided by 7 = 4
The answer is 4
Step-by-step explanation:
The arithmetic mean is the simple average, or sum of a series of numbers divided by the count of that series of numbers.
In the world of finance, the arithmetic mean is not usually an appropriate method for calculating an average, especially when a single outlier can skew the mean by a large amount.
Other averages used more commonly in finance include the geometric and harmonic mean.
3/4(x+8)=9 In the equation shown, what is the value of xx that makes the equation true?
Answers
Answer:
x = 4
Step-by-step explanation:
here's my work :D
Answer:
x = 4
Step-by-step explanation:
3/4(x + 8) = 9 <== convert the fraction to a decimal
0.75(x + 8) = 9 <== distribute
0.75x + 6 = 9 <== subtract 6 from both sides
- 6 - 6
0.75x = 3 <== divide both sides by 0.75 to isolate the variable
/0.75 /0.75
x = 4
Hope this helps!
A county in north carolina spans 532 square miles. the population density of deer in the county is 11 deer per square mile. how many deer live in the county? round to the nearest whole number, if necessary. 48 deer 68 deer 5,852 deer 5,992 deer
Answers
Answer:
C
Step-by-step explanation:
The total population of Deer's in the given span area is 5852 Deer's.
What is population density?Population density is defined as the total number of humans presence
per unit square miles. Mathematically, we can write -
Population density = (Total human population)/(Total span area)
Given is that a county in north Carolina spans 532 square miles. the population density of deer in the county is 11 deer per square mile
We can write the total population of Deer's in the given span area as -
Population = Deer's population density x total area span
Population = 11 x 532
Population = 5852
Therefore, the total population of Deer's in the given span area is 5852 Deer's.
To solve more questions on Population density, visit the link-
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Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.)
ln z(z − 1)^8, z > 1
Answers
Answer:
[tex]\ln z + 8\ln (z-1)[/tex]
Step-by-step explanation:
[tex]\ln z(z-1)^8[/tex]
Using the product rule: [tex]\ln(xy)=\ln x + \ln y[/tex]
[tex]\implies \ln z + \ln (z-1)^8[/tex]
Using the power rule: [tex]\ln x^n=n \ln x[/tex]
[tex]\implies \ln z + 8\ln (z-1)[/tex]
[tex]\\ \rm\Rrightarrow lnz(z-1)^8[/tex]
[tex]\\ \rm\Rrightarrow lnz+ln(z-1)^8[/tex]
lna^b=blna[tex]\\ \rm\Rrightarrow lnz+8ln(z-1)[/tex]
What is the missing angle?
Answers
3x + 27 =180
-27
3x = 153
÷3
x = 51
a=142
(vertically opposite angles are equal)
Reflex angles adds up to 360
360 - (142x2) = 76
76/2 = 38
t & c = 38
Hope this helps!
Answer:
Here you go :) if you need anything tell me!
A puppy and a kitten are 180 meters apart when they see each other. If the puppy can run at a speed of 25 meters per second, and the kitten runs at a speed of 20 meters per second. How soon will they meet if they simultaneously start running toward each other?
Answers
Answer:
it will take 4 seconds
it takes the puppy 25 seconds and the cat 20 seconds
20+25= 45
180 divide by 45 = 4 seconds your answer is 4 seconds
your welcome!
pls help, its due today. !!!
Answers
Answer:
its dark blue
Step-by-step explanation:
Q17.
Jim wants to buy 10 rolls of wallpaper
He sees these prices.
Wallpaper
Single roll £12. 50
Pack of 3 rolls
£34. 50
Pack of 5 rolls
€58. 75
What is the cheapest price for 10 rolls?
Answers
Step-by-step explanation: 10 Single roll $125
Pack of 3 roll, one will be $11.5 and 10 will be $115
Pack of 5 roll, one will be $11.75 and 10 will be $117.5