mathimatics 5 quarter 3 measuring time using 12 hours

We solved the homogeneous differential equation (x - y)dx - xdy = 0 by using the substitution u = y/x and transforming it into a separable differential equation. We then found the general solution y = (x ± √5x) / 2.

We can substitute the given homogeneous differential equation to make it a separable differential equation in order to solve it. The substitution u = y/x should be used.

In the first place, we separate u regarding x utilizing the remainder rule:

Now, we can use u and its derivative to rewrite the original equation: du/dx = (x(dy/dx) - y) / x2

(x - y)dx = xdy

(x - y)dx - xdy = 0

(x - y)dx - xdy/dx * dx = 0

(x - y)dx - x(du/dx)dx = 0

Then, we can counteract the dx terms and revise the condition:

We now have a separable differential equation: (x - y) - xdu = 0, (x - y) - xdu = 0, (x - y) - xdu = 0, and so on. We can reword it as follows:

By dividing both sides by x(1 - u), we obtain: x - xu = y x(1 - u) = y

1/(1 - u) = y/x By reintroducing u = y/x, we obtain:

1/(1 - y/x) = y/x x/(x - y) = y/x By multiplying by two, we obtain:

By rearranging the terms, we have: x2 = xy - y2

xy - y2 - x2 = 0 This is a quadratic equation in terms of y. The quadratic formula can be used to solve it:

y = (- b ± √(b^2 - 4ac))/(2a)

For this situation, a = - 1, b = x, and c = - x^2. When we use the quadratic formula to replace these values, we get:

y = (-x (x2 + 4x2)) / (-2) Simplifying the equation further:

y = (-x (5x2)) / (-2) y = (-x (5) * x) / (-2) y = (x 5x) / 2 The given homogeneous differential equation has the following general solution:

y = (x  5x)/2 In conclusion, we converted the homogeneous differential equation (x - y)dx - xdy = 0 into a separable differential equation by substituting u = y/x. The general solution, then, was y = (x  5x) / 2.

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The corresponding parts are:

The statement is given as:

△ABC was transformed using two rigid transformations.

The rigid transformations imply that:

The images of the triangle after the transformation would be equal

So, the corresponding parts are:

The results are true because rigid transformations do not change the side lengths and the angle measures of a shape

To do this, we simply make use any of the following congruent theorems:

The classmate's claim is that

Only two pairs of corresponding parts are enough to prove the congruent triangle

The above is true because of the following congruent theorems:

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Mary's average monthly expense for housing is $2,129.93.

We need to add up all her annual housing expenses and divide the total by 12 (the number of months in a year):

Total annual housing expenses = mortgage payments + real estate taxes + annual insurance premium + maintenance + utilities

Total annual housing expenses = $14,169.20 + $3,960.00 + $840.00 + $1,410.00 + $5,180.00

Total annual housing expenses = $25,559.20

Average monthly expense = Total annual housing expenses ÷ 12

Average monthly expense = $25,559.20 ÷ 12

Average monthly expense = $2,129.93

Therefore, Mary's average monthly expense for housing is $2,129.93.

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Answer:  approximately 4.7368 minutes

This decimal value is the result of computing 90/19

=====================================================

Explanation:

Let's find the LCM of 6, 9 and 15. First, list out the prime factorization of each value.

The unique prime factors are 2, 3, and 5. We have 2 show up at most once, 3 show up at most twice, and 5 show up at most once. The LCM is 2^1*3^2*5^1 = 2*9*5 = 18*5 = 90.

We'll use this LCM value to set up an example below.

---------------

Consider the tank to be 90 gallons. If we only use tap A, keep tap B closed, and don't open pipe C, then tap A fills the tank at a rate of 90/6 = 15 gallons per minute since it needs 6 minutes to completely fill the tank.

If we have tap B do all the work (keep tap A and pipe C closed), then the rate is 90/9 = 10 gallons per minute for this tap.

Keeping pipe C closed, the two taps A and B work together to have a combined rate of 15+10 = 25 gallons per minute.

Now we consider pipe C being opened. This drains the tank and can do so in 15 minutes (assume the taps A and B aren't open). If we're dealing with a full 90 gallon tank, then its rate is 90/15 = 6 gallons per minute.

The net rate is 25-6 = 19 gallons per minute. We can think of it as a tug of war where the taps A and B ultimately win out despite the fact that pipe C is draining the water. The two taps fill the tank faster than the pipe can drain the tank.

In other words, the tank ultimately gets filled up rather than drained out over the long run. That net speed is at 19 gallons per minute.

The amount of time needed is approximately 90/19 = 4.7368 minutes.

Side note: you can start with any size tank. It doesn't have to be 90 gallons. I picked on this value because it works cleanly with the original given numbers 6, 9 and 15.

Answer:

\(x=\frac{90}{19}\) = 4.73 minutes

\(\frac{1}{6}x +\frac{1}{9}x - \frac{1}{15} x = 1\)

\(\frac{135}{810}x +\frac{90 }{810}x - \frac{54}{810} x = 1\)

\(\frac{171}{810}x = 1\)

x = 4.73 minutes

Step-by-step explanation:

x=2/3

6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10

Answer:

2x-1=y,2y+3=x

Step-by-step explanation:

no explanation

Answer:

x-5

x-2

Step-by-step explanation:

Questions 1:

√(x²-10x+25)

x²-10x+25= (x-5)²

√(x-5)²= x-5

question 2:

x²-4x+4= (x-2)²

√(x-2)²= x-2

Answer:

\( y = - 3 \\ \frac{4 + y}{4y} = \frac{4 + ( - 3)}{4( - 3)} = \frac{4 - 3}{ - 12} = \frac{ - 1}{12} \)

Answer:

6.25 or 8 try those

Step-by-step explanation:

In conclusion, 9 blarsfs and 6 crobs on Shm'lort correspond to approximately 200 seconds in Earth time.

Let's start by finding the conversion rates between Shm'lort time and Earth time. From the given information, we know that 3 blarsfs and 18 crobs correspond to 1 minute on Shm'lort. This means that 1 blarsf is equivalent to 20 seconds (60 seconds / 3 blarsfs) and 1 crob is equivalent to 3.33 seconds (60 seconds / 18 crobs).

Next, we can use the conversion rates to calculate the Earth time for 9 blarsfs and 6 crobs:

9 blarsfs = 9 blarsfs * 20 seconds/blarsf = 180 seconds

6 crobs = 6 crobs * 3.33 seconds/crob = 19.98 seconds (approximately 20 seconds)

Therefore, the total Earth time elapsed for 9 blarsfs and 6 crobs on Shm'lort is 180 seconds (blarsfs) + 20 seconds (crobs) = 200 seconds.

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If Leslie leaves $9,000 in a savings account for 3 years with an annual compound interest rate of 4 percent, the amount of money that will accumulate is approximately $10,174.88.

To calculate the future value of Leslie's investment, we can use the compound interest formula:

Future Value = Principal Amount * (1 + Interest Rate)^Time

Given that the principal amount is $9,000, the interest rate is 4 percent (or 0.04), and the time is 3 years, we can substitute these values into the formula:

Future Value = $9,000 * (1 + 0.04)^3

Future Value ≈ $9,000 * 1.124864

Future Value ≈ $10,174.88

Therefore, if Leslie leaves $9,000 in the savings account for 3 years at an annual compound interest rate of 4 percent, the amount that will accumulate is approximately $10,174.88.

This calculation demonstrates the relationship between interest rates, time, and future sums. As the interest rate increases, the future value of the investment also increases. Similarly, as the time period increases, the future value of the investment grows. This shows that higher interest rates and longer time periods have a compounding effect on the accumulation of funds. It emphasizes the importance of considering both the interest rate and the length of time when making financial decisions, as they significantly impact the growth of an investment.

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Answer:

c

Step-by-step explanation:

Answer:

C: 1/2.

Step-by-step explanation:

the answer is 1/2 because I just took it and got it right.

Answer:

y2uedyhfufj9uygrifurfiutetfueiyfeou5etyotheigteigrhrht5uigurtuutuyryritgtreifgwiiugfeiiugtfeutuotfeyietyoiegtuoteth9h4toutrthutrgbrg865t8h4t8h47586trg

Answer:

48

Step-by-step explanation:

24x2=48

16x3=48

Answer:

48

Step-by-step explanation:

multiples of 16: 16, 32, 48, 64....

multiples of 24:24, 48, 72, 96....

in both situations, it is just multiplying the number by 2 to get the next number

as you can see the only number that appears in both sets and is the smallest is 48.

Hope that helps :)

The total number of fishes present in the lake on my 1 is 840.

The given data for the question-

September is equivalent to a percentage of tagged fish in May.

3/42 = 60/x

x = 60 *42 / 3

x = 840

Thus, the total number of fishes present in the lake on my 1 is 840.

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Therefore , the solution of the given problem of expression comes out to be the simplified expression is (x + 2) / (x - 5)(x - 1).

There is a requirement for mathematical operations as addition, multiplication, and division. When combined, they produce the following: A mathematical operator, some data, and an equation A statement of fact contains values, parameters, and mathematical operations including additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.

Here,

First, let's factor all the quadratics in the expression:

x^2 + 4x + 4 = (x + 2)^2

x^2 - 4 = (x + 2)(x - 2)

x^2 - x - 6 = (x - 3)(x + 2)

x^2 - 5x + 6 = (x - 2)(x - 3)

Now, we can rewrite the expression as:

[(x + 2)^2 / (x + 2)(x - 2)] * [(x - 2)(x - 3) / (x - 3)(x + 2)] * [(x + 2)(x - 3) / (x - 2)(x - 3)] * [(x - 2)(x - 3) / (x - 5)(x - 1)]

Notice that the (x + 2)(x - 3) terms cancel out in the numerator and denominator of the second and third fractions, respectively. Also, (x - 2)(x - 3) cancels out in the numerator and denominator of the third and fourth fractions, respectively.

Simplifying these terms, we are left with:

= [(x + 2) / (x - 2)] * [(x - 2) / (x - 5)(x - 1)]

= (x + 2) / (x - 5)(x - 1)

Therefore, the simplified expression is (x + 2) / (x - 5)(x - 1).

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Answer:

-8 < k

Step-by-step explanation:

4 < 4(k+3)

4 < 4k + 12

-8 < k

\(~~~~~~ \textit{Simple Interest Earned}\\\\I = Prt\qquad\begin{cases}I=\textit{interest earned}\\P=\textit{original amount deposited}\dotfill & \$9500\\r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\t=years\dotfill &5\end{cases}\\\\\\I = (9500)(0.02)(5)\implies \boxed{I = 950}\)

Using a linear function, it is found that her taxi ride was of 5 miles.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which the coefficients are described as follows:

For the cost function, we have that:

Thus the cost for a ride of x miles is of:

C(x) = 3.75x + 1.10.

Her total fee was of $19.85, hence the mileage is found as follows:

19.85 = 3.75x + 1.10

x = (19.85 - 1.10)/3.75

x = 5 miles.

Which was the length of her taxi ride.

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Answer:

c

Step-by-step explanation:

because it makes the most sense

Answer:

I am going to say c

Step-by-step explanation:

Answer:

cool!!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Angle TSW = angle UTV because they are corresponding congruent angles.

Angle STW = angle TUV because they are corresponding congruent angles.

Triangle STW is congruent to triangle TUV because of the Angle-Angle-Side Similarity theorem.

The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.

If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.

A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.

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Answer:false

Step-by-step explanation:

Answer:

JK = 24

Step-by-step explanation:

Δ BKJ and Δ BCA are similar triangles and ratios of corresponding sides are equal, that is

\(\frac{JK}{AC}\) = \(\frac{BK}{BC}\) , substitute values

\(\frac{JK}{40}\) = \(\frac{3}{5}\) ( cross- multiply )

5JK = 120 ( divide both sides by 5 )

JK = 24

the triangles are all similar, because they have proportional sides and equal angles.

if you assume the smallest, equal part of side to be x

the biggest triangle has "5 parts" so BC=5x and BK has 3 parts so BK=3x .

since they're similar, ratio of their corresponding sides is constant or equal.

\( {BK\over BC}={JK \over AC}\)

BK/BC=3/5

and AC=40

so JK = 40*3/5=24

Answer:

B; the angles of the triangle and the hypothnuse can be multiplied.

Answer:

pa pic nyou nalang kung may pic plss

The expected value of the sum of the two extreme numbers is 1/2.

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.

The optimal strategy for you would be to choose the number 0.5, as it maximizes the probability that your pair will have the highest sum, and minimizes the probability that your pair will have the lowest sum.

This is because if all players choose a number uniformly at random, the expected value of the lowest and highest numbers will be 0 and 1 respectively, and the expected value of the middle two numbers will be 0.5. Therefore, by choosing 0.5, you have the best chance of having the highest sum, which means you will have to pay the least amount of money.

Therefore, the expected value of the sum of the two extreme numbers is 1/2.

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There are three a's, we can write a³ instead of a×a×a. This gives us d×b×c×a³

To simplify the expression d×b×c×a×a×a, we can rewrite it using exponents. Since there are three a's, we can write a³ instead of a×a×a. This gives us:

d×b×c×a³

This is the simplified expression using single variables raised to exponents. We can read this as "d times b times c times a to the power of 3".

It's important to note that when we have multiple variables multiplied together, we can simplify the expression by combining them using exponents. This makes it easier to work with and to manipulate algebraic equations.

In this case, we were able to simplify the expression by replacing three instances of a with a³. We could continue to simplify further if we had additional like terms, but in this case, this is the simplest form of the expression.

Overall, simplifying expressions using exponents is a common technique in algebra and can help make solving equations more manageable.

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