The distance from point A to point B is approximately 998 feet (rounded to the nearest foot).
Let's denote the distance from point A to the lighthouse as "x", and the distance from point B to the lighthouse as "y". Also, let's denote the height of the lighthouse as "h". Then we have the following diagram:
Lighthouse
|\
| \
| \ h
| \
|θ2 \
|____\
x y
A B
From the diagram, we can see that:
tan(6°) = h/x (equation 1)
and
tan(4°) = h/y (equation 2)
We need to find the value of "d", the distance from point A to point B. We can use the following equation:
d^2 = x^2 + y^2 (equation 3)
We can solve equation 1 for h:
h = x tan(6°)
Substitute this into equation 2:
x tan(6°) / y = tan(4°)
Solve for y:
y = x tan(6°) / tan(4°)
Substitute this into equation 3:
d^2 = x^2 + (x tan(6°) / tan(4°))^2
Simplify:
d^2 = x^2 (1 + tan^2(6°) / tan^2(4°))
Solve for d:
d = x sqrt(1 + tan^2(6°) / tan^2(4°))
Substitute the given values:
d = 996 sqrt(1 + tan^2(6°) / tan^2(4°))
Using a calculator, we get:
tan(6°) / tan(4°) = 0.1051
So,
d = 996 sqrt(1 + 0.1051^2) ≈ 998.38 feet
Therefore, the distance from point A to point B is approximately 998 feet (rounded to the nearest foot).
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How to convert us dollar to thai baht?
Convert USD to THB, multiply amount of USD by the current exchange rate between USD and THB, which can be found on financial news or currency exchange websites, to get the equivalent amount in THB.
To convert US dollars (USD) to Thai baht (THB), you need to use the current exchange rate between the two currencies. Here are the steps to convert USD to THB:
Find the current exchange rate between USD and THB. This information can be found on financial news websites, currency exchange websites, or by contacting a bank or currency exchange service.
Multiply the amount of US dollars you want to convert by the current exchange rate to get the equivalent amount in Thai baht. For example, if the current exchange rate is 1 USD = 31.50 THB and you want to convert 100 USD to THB, the calculation would be:
100 USD x 31.50 THB/USD = 3,150 THB
Therefore, 100 USD is equal to 3,150 THB.
Note: The exchange rate between USD and THB can fluctuate over time, so make sure to use the current exchange rate for the most accurate conversion.
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9 = -7w + 12w – 6
Solve steps explaining pls
Answer:
Step-by-step explanation:
9 = - 7w + 12w - 6
by transposing,
9 + 6 = -7w + 12w
15 = 5w
w = 15 / 5
w = 3
Hope this helps
plz mark as brainliest!!!!!!
Answer:
\(w=3\)
Step-by-step explanation:
\(9 = -7w + 12w -6\)
Start by combining like terms (\(-7w+12w\)):
\(9=5w-6\)
Add \(6\) to both sides of the equation:
\(15=5w\)
Divide both sides of the equation by the coefficient of \(w\), which is \(5\):
\(3=w\)
_
Check your work by substituting the solved value of \(w\) (\(3\)), into the initial equation:
\(9 = -7(3) + 12(3) -6\)
Multiply:
\(9=-21+36-6\)
Combine like terms:
\(9=9\)
Since both sides of the equation are equal, our answer is correct!
Can someone help me PLZ! I keep posting the same question and no ones helping me :(((((((((((( its dues in 20 mins!!
Solve the system of equations below. Write your answer as an ordered pair. Start by multiplying the first equation by 2.
2x + 2y = 12
5x + 4y = 28
Answer:
x=4
y=2
Step-by-step explanation:
2*4+2*2=12
8+4=12
5*4+4*2=28
20+8=28
Have a good day ;-),
and can I please have brainliest? Thanks!
The Answer is 4,2
x=4 y=2
Solve for x. -2(-4x - 1) = x + 3 = -30
Train A covers 240 miles in the same time train B covers 180 miles. If the average speed of train A is 20mph more than that of train B, then what is the average speed of train B ?
Average speed of train B is 60 mph.
To find average speed of train B:
Let average speed of train B = x mph.
Based on information provided to us it is said average speed of train A is 20 mph more than B.
Average speed of train A = (x + 20) mph.
Speed = Distance/ Time
The time taken by both trains will be the same since they cover their respective distances in the same time.
For train A:
Speed of train A = (x + 20) mph
Distance covered by train A = 240 miles
Time taken by train A = Distance / Speed = 240 / (x + 20) hours
For train B:
Speed of train B = x mph
Distance covered by train B = 180 miles
Time taken by train B = Distance / Speed = 180 / x hours
Since the time taken by both trains is the same, we can set up an equation:
240 / (x + 20) = 180 / x
240x = 180(x + 20)
240x = 180x + 3600
240x - 180x = 3600
60x = 3600
x = 3600 / 60
x = 60
Therefore, the average speed of train B is 60 mph.
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if 26 children were to be born in a hospital on a given day, how many combinations of 6 boys and 20 girls would exist? 230,230 4 x 10^26 500,000 15 Z
The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.
]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.
In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.
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find the gcf and the distributive property to each sum.19,22
Answer:
50 is sum of gcf its couldn't of 19 is 20
7. Two search parties start at the courthouse where a missing girl was last seen, Party A travels 4 blocks
north and 8 blocks east. Party B travels 5 blocks west and 3 blocks south. How many blocks south and
how many blocks west is Search Party B from A?
Answer:
Step-by-step explanation:
Consider the following sequence of numbers \( 11,8,9,4,2,5,3,12,6,10,7 \) a) Sort the list using selection sort. Show the state of the list after each call to the swap procedure. b) Sort the list usin
a) To sort the given list using selection sort, we repeatedly find the smallest element from the unsorted part of the list and swap it with the first element of the unsorted part.
Here is the step-by-step process: Original list: 11, 8, 9, 4, 2, 5, 3, 12, 6, 10, 7
Step 1: Find the smallest element and swap it with the first element:
Swap 2 and 11: 2, 8, 9, 4, 11, 5, 3, 12, 6, 10, 7
Step 2: Find the smallest element from the remaining unsorted part and swap it with the second element:
Swap 3 and 8: 2, 3, 9, 4, 11, 5, 8, 12, 6, 10, 7
Step 3: Continue the process until the list is sorted:
Swap 4 and 9: 2, 3, 4, 9, 11, 5, 8, 12, 6, 10, 7
Swap 5 and 11: 2, 3, 4, 5, 11, 9, 8, 12, 6, 10, 7
Swap 6 and 11: 2, 3, 4, 5, 6, 9, 8, 12, 11, 10, 7
Swap 7 and 9: 2, 3, 4, 5, 6, 7, 8, 12, 11, 10, 9
Swap 8 and 12: 2, 3, 4, 5, 6, 7, 8, 9, 11, 10, 12
Swap 9 and 11: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
The sorted list using selection sort is: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
b) To sort the list using insertion sort, we start with the second element and repeatedly insert it into its correct position among the already sorted elements. Here is the step-by-step process:
Original list: 11, 8, 9, 4, 2, 5, 3, 12, 6, 10, 7
Step 1: Starting with the second element, insert it into the correct position:
8, 11, 9, 4, 2, 5, 3, 12, 6, 10, 7
Step 2: Insert the third element into the correct position:
8, 9, 11, 4, 2, 5, 3, 12, 6, 10, 7
Step 3: Continue the process until the list is sorted:
4, 8, 9, 11, 2, 5, 3, 12, 6, 10, 7
2, 4, 8, 9, 11, 5, 3, 12, 6, 10, 7
2, 4, 5, 8, 9, 11, 3, 12, 6, 10
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Giving brainlist to whoever answers
Answer: should be x> -18
Step-by-step explanation: hope this helps
Answer:
x > -18
Step-by-step explanation:
8 > 2 - x/3
Multiply the equation by 3.
24 > 6 - x
Flip around to make working with it easier.
6 - x < 24
Subtract 6 from both sides.
-x < 18
Divide by -1. When dividing by a negative in an inequality, flip the sign.
x > -18.
The mean SAT score in mathematics is 554. The standard deviation of these scores is 39. A special preparation course claims that the mean SAT score, HI, of its graduates is greater than 554. An independent researcher tests this by taking a random sample of 60 students who completed the course; the mean SAT score in mathematics for the sample was 567. At the 0.01 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 5542 Assume that the population standard deviation of the scores of course graduates is also 39. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H. μ a р H.: 0 H: 0 х S ê 0. DO (b) Determine the type of test statistic to use. (Choose one) ロ=口 OSO 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) O . $ ?
(d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we support the preparation course's claim that the population mean SAT score of its graduates is greater than 554? Yes No
We have the following details
mean = 554
n = 60
bar x = 567
alpha = 0.01
How to solve for the hypothesisA. h0. u = 554
H1. u > 554
B. Given that the standard deviation is known what we have to make use of is the independent z test
test statistics calculation
567-554/(39/√60)
= 2.582
d. at alpha = 0.01 and test statistics = 2.582, the value of the p value = 0.0049
0.0049 < 0.01. So we have to reject the null hypothesis.
e. Yes We have to accept that we support the preparation course's claim that the population mean SAT score of its graduates is greater than 554
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(a) If u = f(x, y) and x = r cos 8.y = r sin 8, then show that du 2 2 (²)² = (²+)² + ( (du) 2 ex. 4-2 (b) Evaluate fx dx dy over the region bounded by y = x² and y = x³. (10) (10) (20)
The expression \(du^2 = (dx)^2 + (dy)^2\) in polar coordinates can be derived using the given transformations u = f(x, y), x = r cos θ, and y = r sin θ.
In the given problem, we have u = f(x, y) and the transformations x = r cos θ and y = r sin θ, where r and θ represent the polar coordinates. We need to find the expression for \(du^2\).
Using the chain rule, we can express the differentials dx and dy in terms of dr and dθ:
dx = dr cos θ - r sin θ dθ,
dy = dr sin θ + r cos θ dθ.
Substituting these into the expression \(du^2 = (dx)^2 + (dy)^2\), we get:
\(\[du^2 = \left(dr \cos \theta - r \sin \theta d\theta\right)^2 + \left(dr \sin \theta + r \cos \theta d\theta\right)^2\]\).
Expanding and simplifying the above expression, we obtain:
\(\[ du^2 = (dr)^2 + r^2 (d\theta)^2 \]\).
This is the desired expression for \(du^2\) in polar coordinates.
Moving on to the second part of the question, we are asked to evaluate ∫∫fx dx dy over the region bounded by y = x² and y = x³.
Converting the integral into polar coordinates, we need to determine the limits of integration. From the given equations y = x² and y = x³, we can find the intersections by solving x² = x³, which gives x = 0 and x = 1.
In polar coordinates, x = r cos θ and y = r sin θ. We need to find the values of r and θ that correspond to the points of intersection.
For x = 0, we have r cos θ = 0, which implies θ = π/2 or θ = 3π/2.
For x = 1, we have r cos θ = 1, which implies r = 1/cos θ.
Therefore, the limits of integration for r are from 0 to 1/cos θ, and for θ, they are from π/2 to 3π/2.
Finally, we can evaluate the integral ∫∫fx dx dy by converting it to polar coordinates and applying the limits of integration found above.
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Find h.
10 in.
h = [?] in.
5.
4 in.
PLEASE ILL DO ANYTHING
Answer:\(h=\sqrt{96}in.\)
Step-by-step explanation:
.
Find an equation for the line that passes through the points (-1 -2) and (5, 2).
Answer:
y = 2/3x - 4/3
Step-by-step explanation:
m = y2 - y1/x2 - x1
m = 2 - (-2)/5 - (-1)
m = 4/6 = 2/3
y - y1 = m(x - x1)
y - (-2) = 2/3(x - (-1))
y = 2/3x - 4/3
A glass contains alcohol and water in the ratio 1:4. A second glass has the same quantity of liquid but this time the ratio of alcohol to water is 2:3. Each glass is emptied into a third glass. what is the ratio of alcohol to water for the final mixture?
Answer:
easy is 4
Step-by-step explanation:
who wanna join mt clash of clans clan?
What is the value of x?
Answer: 101
Step-by-step explanation:
180 - 76 - 48 = 56
180 - 56 - 23 = 101
Over a short interval near time t=0 the coordinate of an antomobile in meters is given by x(1)=30t2−15t3, where t is in seconds. At the end of 1.0 s the automobile is: A) Accelerating B) Moving at constant velocity C) Deaccelerating D) Atrest E) Need additional information. 5. A muon (an elementary particle) enters a region with a speed of 8.00×105 m/s and then is slowed at the rate of 3.20×1014 m/s2. How far does the muion take to stop? A) 0.100 km B) 2.00×108 m C) 0.1 m D) 0.10 m E) 0.100 m
Over a short interval near time t=0, the coordinate of an automobile is given by x(1) = 30t² − 15t³. At the end of 1.0 s the automobile is deaccelerating (option C). The muon takes 0.100 m to stop (option E).
Given that x(1) = 30t² − 15t³
The velocity of the automobile is given by:
v = dx/dtv = 60t − 45t²
When the time t = 1.0 s, we have: v = 60(1.0) − 45(1.0)²= 15 m/s
Since the velocity is positive, the automobile is moving to the right (i.e. accelerating).
However, since the velocity is decreasing, the automobile is deaccelerating. To determine the acceleration, we take the derivative of the velocity with respect to time:
a = dv/dta = 60 − 90t
When t = 1.0 s, a = 60 − 90(1.0)= −30 m/s²
Since the acceleration is negative, the automobile is deaccelerating (option C).
5. The initial velocity, u = 8.00×10⁵ m/s
The acceleration, a = -3.20×10¹⁴ m/s² (since the muon is slowed down)
Final velocity, v = 0
We want to find the distance traveled, s.
To find the distance traveled, we use:
s = (v² − u²)/2a
Here, u = 8.00×10⁵ m/s,
v = 0, and
a = -3.20×10¹⁴ m/s²
So,s = (0 − (8.00×10⁵)²)/2(−3.20×10¹⁴)= 0.100 m
Therefore, the muon takes 0.100 m to stop (option E).
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An Amtrak official obtains data on a particular day concerning the length of time (in minutes) that the metroliners leaving New York take to reach Philadelphia, with the following results:
93 89 91 87 91 89
Find the sample variance.
a. 3.6
b. 5.6
c. 6.8
d. 7.6
e. 4.4
The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.
The sample variance is a measure of how much the individual data points in a sample vary from the mean.
It is calculated by finding the average of the squared differences between each data point and the mean.
To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:
Calculate the mean (average) of the data set:
Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90
Subtract the mean from each data point and square the result:
(93 - 90)^2 = 9
(89 - 90)^2 = 1
(91 - 90)^2 = 1
(87 - 90)^2 = 9
(91 - 90)^2 = 1
(89 - 90)^2 = 1
Calculate the sum of the squared differences:
9 + 1 + 1 + 9 + 1 + 1 = 22
Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):
Variance = 22 / 5 = 4.4
It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.
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The population of some bacteria increases by 15% every day. If the original
population was 6000 bacteria, calculate the size of the population after 10 days
Answer:
To solve this problem, we can use the formula for exponential growth:
N = N0 * (1 + r)^t
Where:
N0 = the initial population size
N = the population size after t time periods
r = the growth rate per time period
t = the number of time periods
In this case, we know that the initial population (N0) is 6000, the growth rate (r) is 15% per day, and we want to find the population size (N) after 10 days (t = 10).
First, we need to convert the growth rate from a percentage to a decimal:
r = 15% / 100% = 0.15
Now we can plug in the values and solve for N:
N = 6000 * (1 + 0.15)^10
N = 6000 * 3.439
N ≈ 20,634
Therefore, the population of bacteria after 10 days would be approximately 20,634.
johnny the gambler tosses 6 fair six-sided dice numbered 1 through 6. in order to win the jackpot, he needs a 5 or 6 on exactly 3 of the dice. what are johnny's chances to win?
The probability of Johnny winning is \(20 *(\frac{2^3}{3^6} )\).
Given data;
Johnny throws six equal dice with six sides and the numbers 1 through 6 on them. He needs a 5 or 6 on precisely 3 of the dice to take home the prize. What are Johnny's odds of winning?
The probability of 5 or 6 = 2/6
= 1/3
The probability of not 5 or 6 = 4/6
= 2/3
The total probability of getting in exactly 3 chances;
⇒ ⁶C₃ * (1/3)³ * (2/3)³
⇒ \(20 *(\frac{2^3}{3^6} )\)
Hence, the chances for Johnny to win are \(20 *(\frac{2^3}{3^6} )\).
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WILL MARK BRAINLIEST!! PLEASE HELP ASAP.
1. If a scooter travels 36 miles on just 3 gallons of gas, how far will it travel on 16 gallons of gas?
2. A babysitter earns $28.50 for 2 hours of work. If she gets paid $99.75, then how many hours did she work?
3. A moose travels 4.5 kilometers in 5 hours. How far will it travel in 60 hours?
4. If 3 cm. of silver chain costs $9.60, then how much chain will $22.40 buy?
5. If a train ticket costs $145.50 to travel 50 miles, how far will $552.90 allow you to travel?
6. If $239.85 buys 369 liters of oil, then how much oil will $1.95 buy?
7. If you travel 220 miles in 66 hours, how far will you travel in just 3 hours?
8. If a gallon of aviation fuel costs $17.50, then how much will 8.2 gallons cost?
9. A snail crawls 7 cm in 2 minutes. At this rate, how far will it travel in 13 minutes?
10. If 17 kg of fertilizer covers 4 acres, how many kg will be needed to cover 244 acres?
11. How much will 4.4 gallons cost if 1 gallon costs $2.85?
12. Lunchmeat costs $2.50 for 5 oz. How much lunch meat will $32.50 buy?
(PLEASE EXPLAIN HOW YOU GOT THE ANSWER PLSS)
Answer:
you bad
Step-by-step explanation:
ferfrfvrgb rg bg bb
a researcher squeezed a bulb as many times as possible in 30 seconds. the procedure was performed a total of ten times in succession. which choice would you identify to be the most likely prediction for the number of squeezes in the 11th trial?
The most likely prediction for the number of squeezes in the 11th trial is that it will be approximately the same as the number of squeezes in the previous trials.
This is because the researcher is likely to experience fatigue over the course of the trials, so the number of squeezes should not significantly increase after the tenth trial.
Fatigue is a normal physiological response to physical activity and can affect performance, resulting in decreased strength, power, and endurance. The researcher is likely to become increasingly tired and less able to squeeze the bulb during each successive trial, so the 11th trial should not show any significant increases in the number of squeezes compared to the previous trials.
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What are the intercepts of the function? The x-intercepts are
Answer:
-1,0 and -11,0 because you already factored and solved.
biblical tithing basically means you will give ______ percent of your income to the lord. 20 5 10 25
Biblical tithing basically means you will give 10 percent of your income to the lord.The word tithe refers to "tenth" or "tenth part," so biblical tithing implies offering one-tenth of one's income to the church.
Biblical tithing is the method of giving the first fruits of one's labor to the Lord. Tithing originated from the Old Testament in which people would offer 10% of their harvest to the Lord.Tithing is a way of giving back to God as well as to others, according to the Bible.
As a result, Christians are required to tithe a tenth of their earnings. While this might appear to be a significant amount of money, if Christians can trust God with their finances, they can discover that he blesses them in ways they never imagined. In the New Testament, there is no specific requirement to tithe, but Christians are urged to give generously to the church and those in need.
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There are 90 penguins in a zoo. There are two types - Humboldt and Emperor.
52 are female, of these 6 are Emperor penguins.
There are 5 male Emperor penguins.
Use this information to complete the frequency tree.
PLEASE ANSWER I WILL GIVE BRAINLIEST!!!
Answer:
still need it?..........
Please help figure this out
Answer:
1st. Common Difference of 3
2nd. Not Arithmetic
3rd. Not Arithmetic
Step-by-step explanation:
The 1st one, you can add to get the next number, but the other ones you have to multiply.
Write 6x10 to the power of 2 in standard notation.
What are the answers for each?
Answer:
7% of 33= 2.1
2% of 640= 12.8
15% of 470=70.5
7/9 of 51= 119/3
.52 of 62= 32.24
Answer:
1) 2.31
2) 12.8
3) 72
4) 44.625
5) 32.24
Step-by-step explanation:
7% of a number is simply 0.07*the number.
7/8 is just .875*the number
Hope it helps <3
a hexadecimal number is a number written in the base 16 number system.
t
f
True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.
In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.
The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.
For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.
Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.
Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.
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Solve each of the following. Round your answer to 3 places after the decimal, if necessary. (a) 3 10 4 20 (b) 2log(x-4) + 7 = 11
a) The answer is 110.
b) The solution to the equation is x = 104.
(a) To solve the expression 3 * 10 + 4 * 20, we can perform the multiplication and addition in order of operations:
3 * 10 = 30
4 * 20 = 80
Then, we add the results together:
30 + 80 = 110
So, the answer is 110.
(b) To solve the equation 2log(x-4) + 7 = 11, we can isolate the logarithmic term and solve for x:
2log(x-4) = 11 - 7
2log(x-4) = 4
Divide both sides by 2:
log(x-4) = 4/2
log(x-4) = 2
Now, we can rewrite the equation in exponential form:
10^2 = x - 4
Simplify the exponential expression: 100 = x - 4
Add 4 to both sides:
100 + 4 = x
104 = x
So, the solution to the equation is x = 104.
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