what is the length of a ketchup​

A: The differential equation can be expressed in the form f(x ,y) = g(x)h(y) = 0, indicating that it is homogeneous. Divide both sides of the equation by y to observe this, which results in  dy/dx + sin^2(x) = cos^2(x)

B: Since there is just one function y and its derivative dy/dx involved in the equation, it is an ODE.

D: Because there is only one function y and its derivative  dy/dx involved in the equation, first-order differential equations are what it is.

G: The formula for the equation is a(x)y' + b(x)y = c(x), where a(x)=1, b(x) = sin^2(x), c(x) = cos^2(x) . Given that x and the coefficients of y and dy/dx are constants, the equation is linear.

H: The equation may be written as dy / y =  (cos^2(x))dx/(1+sin^2(x)),and it is a candidate for integrating factors because we can multiply both sides by (1+sin^2(x))dx .

I: The variables x and y can be separated by integrating both sides of the equation, which can be represented as  (dy/y) = (cos^2(x))dx/(1+sin^2(x)) + (sin^2(x))dx .

J: The equation is self-sufficient; it is not dependent on any explicit function of t.

       Therefore, the differential equation  dy/dx+sin^2(x)y=cos^2(x)y .A candidate for integrating factors exists in the first-order linear, homogeneous, separable, and autonomous ODE known as y.

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Answer:

Last on is the answer!! (The relation is a function, and the range is (-2,-1, 1, 3, 4). Hope this helps:)

26.

Step-by-step explanation:

To figure out the missing side of a right triangle, we will use the Pythagorean theorem. This is...

\(a^2+b^2=c^2\)

With this Pythagorean theorem, a and b will always be the legs and the c will always be the hypotenuse, no matter what. Now knowing this, we can plug the legs into the equation.

\(10^2+24^2=c^2\)

\(100+576=c^2\)

Add the legs together.

\(676=c^2\)

Now, since c is squared we will have to find the square root of 676.

\(\sqrt{676}\)

= 26

Answer:

Step-by-step explanation:

If it is a fair spinner (equally likely to fall on any sector) then p(green)  = 1/4.

As a matter of fact, each color = p(color) = 1/4

The area of a 2D form is the amount of space within its perimeter. The surface area of the cone is 108.79967 units².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Given the diameter of the cone is 6 units, therefore, the radius of the cone is 3 units, and the height of the cone is 8 units. Thus, the surface area of the right cone is,

A=πr [r+√(h²+r²)]

A = 108.79967 units²

Hence, the surface area of the cone is 108.79967 units².

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Answer:

x = 96

Step-by-step explanation:

\(log_b \ x = \frac{2}{3}log_b \ 27 + 3log_b \ 2 - log_b \ 3 + \frac{2}{3}log_b \ 64 - log_b \ 4\)

         \(=\frac{2}{3}log_b \ 27 + 3log_b \ 2 + \frac{2}{3}log_b \ 64 -(log_b \ 3 + log_b \ 4) \\\\=(log_b \ (27)^{\frac{2}{3}} + log_b \ 2^3 + log_b \ (64)^{\frac{2}{3}}) -(log_b \ 3 + log_b \ 4) \\\\=log_b \ ( (27)^{\frac{2}{3}} \cdot 2^3 \cdot (64)^{\frac{2}{3}}) -log_b \ (3 \cdot 4) \\\\=log_b \ \frac{( (27)^{\frac{2}{3}} \cdot 2^3 \cdot (64)^{\frac{2}{3}})}{ (3 \cdot 4)} \\\\=log_b (\frac{9 \times 8 \times 16}{3 \times 4})\\\\=log_b (3 \times 8 \times 4)\\\\=log_b \ 96\)

Therefore, x = 96

Carlos's score in his first game was 14.

Addition in maths, a process of combining two or more numbers.

Given that, Carlos scored a total of 60 points in his last three basketball games. be improved in each game by scoring 6 more points than in the previous game.

Let the first score be x,

x+x+6x+6+6=60

3x+18 = 60

3x = 42

x = 14

Hence, Carlos's score in his first game was 14.

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Answer:

13

Step-by-step explanation:

x/y = 4

x=4y

x - y = 39

4y - y = 39

3y = 39

y= 13

a. The areas of the square is 81m² and for rectangle is 72m²

b. The perimeter of the square is 40m

a. To determine the area of the shapes in which we have that have a perimeter of 36m, we can consider rectangle and square.

For a square;

Perimeter of square = 4L

36 = 4L

L = 9m

The area of the square will be L² = 9² = 81m²

For a rectangle;

The perimeter of rectangle is;

P = 2(L + W)

We can assume that two numbers which will represent the length and width are;

L = 12m, W = 6m or L = 6m, W = 12m

A = 12 * 6 = 72m²

b.

The area of the wire is 100m², the perimeter for this can be calculated when we consider square and rectangle;

Perimeter of square = 4L

Area of square = L² = 100m²

L = 10m

The perimeter of the wire is 4(10) = 40m

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Given the equation:

Let the blank be represented by the letter y.

We can then rewrite the equation as:

First, we open the brackets on the left-hand side.

Comparing both sides of the equation, we have that:

Therefore, the number which will be used to fill the blank is 8.

That is:

Answer:

The half-life of a radioactive substance is the time it takes for half of the initial amount of the substance to decay. We can use the fact that 8% of the original amount remains after 100 days to determine the half-life of the isotope.

Let's assume that the initial amount of the substance is 1 unit (it could be any amount, but we're assuming 1 unit for simplicity). After one half-life, half of the original amount remains, or 0.5 units. After two half-lives, half of the remaining amount remains, or 0.25 units. After three half-lives, half of the remaining amount remains, or 0.125 units. We can see that the amount of substance remaining after each half-life is half of the previous amount.

We can use this information to set up the following equation:

0.08 = (1/2)^n

where n is the number of half-lives that have elapsed. We want to solve for n.

Taking the logarithm of both sides, we get:

log(0.08) = n*log(1/2)

Solving for n, we get:

n = log(0.08) / log(1/2) = 3.42

So the number of half-lives that have elapsed is approximately 3.42. Since we know that 100 days is the time for three half-lives (from the previous calculation), we can find the half-life by dividing 100 days by 3.42:

Half-life = 100 days / 3.42 = 29.2 days (rounded to one decimal place)

Therefore, the half-life of the radioactive isotope that leaked into the stream is approximately 29.2 days.

The amount paid to vehicle A is less than to vehicle B so, Vehicle A is suitable to purchase based on a monthly payment.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

For vehicle A,

The Principal amount of the car, P = $25000,

The rate of interest, r = 5% = 5/100 = 0.05,

The tenure, n = 60 months = 60/12 = 5 years,

Calculate the amount by the formula given below,

A = P (1 + r)ⁿ

Here A is the amount,

Substitute the values,

A = 25000 (1 + 0.05)⁵,

A = $31907.03

Similarly,  for vehicle b

A = 29000 (1 +0.04)⁶

A = $36694.25

As the amount of vehicle A is less than the of vehicle B Therefore, vehicle A is suitable to buy.

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Using the arrangements formula, it is found that the number of different arrangements that can be made using all of the letters of TOPIC is given by:

c. 120

The number of possible arrangements of n elements is given by the factorial of n, that is:

\(A_n = n!\)

In this problem, the word TOPIC has 5 non-repeating letters, hence the number of arrangements is given by:

\(A_5 = 5! = 120\).

Which means that option C is correct.

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Answer:

Extrema: relative minimum (1.25,-3.25), relative maximums (3.25,10) and (0,0)

Zeros: (0,0), (2,0), and (4,0)

End behavior: As x approaches infinity, the function approaches negative infinity. As x approaches negative infinity, the function approaches negative infinity.

Intervals of increase and decrease: increasing on (-∞, 0) and (1.25, 3.25), decreasing on (0, 1.25) and (3.25, ∞)

Positive and negative intervals: positive on (2, 4), negative on (-∞, 0), (0, 2), and (4, ∞)

Answer:

The elevation is positive on the interval (2,4) .

The elevation reaches a relative maximum of about 1,000 feet above the starting point.

The domain of the function is 0<x<4 .

Step-by-step explanation:

edmentum

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Using the fact that ∠A is congruent to ∠B and ∠C is a complement of ∠A, we determined that the measure of ∠B is 65° based on the given measure of ∠C as 25°.

If ∠A is congruent (≅) to ∠B and ∠C is a complement of ∠A, we can use the properties of complementary angles to find the measure of ∠B.

Given that m∠C = 25° and ∠C is a complement of ∠A, we know that ∠A + ∠C = 90°.

Since ∠A is congruent to ∠B, we can replace ∠A with ∠B in the equation:

∠B + ∠C = 90°.

Substituting the given value, we have:

∠B + 25° = 90°.

To isolate ∠B, we subtract 25° from both sides of the equation:

∠B = 90° - 25°.

Simplifying, we get:

∠B = 65°.

Therefore, the measure of ∠B is 65°.

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Answer:

y=-1

Step-by-step explanation:

Divide both sides by 4

y-2=-3

Then move -2 to -3 and change it's sign to a +

y=-3+2

Then solve for y

The solution of the inequality 3x < 13 is x < 4.33.

None of the given option is correct.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality,

3x < 13.

Simplifying,

x < 4.33

The graph is given in the attached image.

Therefore, the solution is x < 4.33.

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Value of m and b of the straight line in the graph is 0 and 2 respectively.

In mathematics, slope refers to the steepness or inclination of a line, and is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. It is often represented by the letter m. The slope of a line can be positive, negative, zero, or undefined.

Let us assume that the equation of line be y=mx+b.

where m is the slope

and b is the intercept

The line in the graph is parallel to x axis

so, slope is 0

m=0

the line passes through(0,2)

Putting the value in the equation, we get

b=2

Hence, the equation of line be y=2

Therefore, value of m=0 and b=2.

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The complete question is:

The graph is showing the equation of straight line y=mx+b, find the value of m and b.

Image is attached below:

Answer:

We conclude that a diagonal of a quadrilateral is a line segment that joins two opposite vertices of the quadrilateral.

Step-by-step explanation:

From the attached diagram, it is clear that the line segment AC of the parallelogram quadrilateral joins two opposite vertices A and C.

It is also clear that the other line segment BD of the parallelogram quadrilateral joins two opposite vertices B and D.

Therefore, we conclude that a diagonal of a quadrilateral is a line segment that joins two opposite vertices of the quadrilateral.

Answer:

Excise tax

Step-by-step explanation:

Correct me if I'm wrong <3

The school needs to rent 4 buses for the field trip.

A rent refers to tenant's regular payment to a landlord for the use of car, property or land.

To know number of buses needed, we need to calculate the total number of people going on the trip and then divide it by the capacity of each bus.

Total number of people = Number of fifth graders + Number of teachers

Total number of people = 145 + 6

Total number of people = 151

Number of buses needed = Total number of people / Capacity of each bus

Number of buses needed = 151 / 42

Number of buses needed = 3.6.

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The odds in favor of the cube show a number less than 3 is 1 : 2.

Option D is the correct answer.

We have,

To determine the odds in favor of an event, we need to find the ratio of the favorable outcomes to the unfavorable outcomes.

In this case, we need to find the number of favorable outcomes, which is the number of outcomes where the cube shows a number less than 3. There are two numbers less than 3 on a fair die: 1 and 2.

Since there are 2 favorable outcomes, and the die has 6 sides in total, the number of unfavorable outcomes is:

= 6 - 2 = 4.

Now,

The odds in favor of the cube showing a number less than 3.

= 2 : 4

which can be simplified,

= 1 : 2.

Thus,

The odds in favor of the cube show a number less than 3 is 1 : 2.

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Answer:

(4,5)

Step-by-step explanation:

Your answer is : (kindly refer to the attachment above)

Answer:

1/3

Step-by-step explanation:

Fastest = 7/12 Simon

Slowest = 11/12 Gilbert

Difference = 4/12

in simple form its 1/3

I don't know about part 2 sorry

Answer:

For the first equation the answer is 3.14

For the second equation the answer is \(-7f^2\)

Step-by-step explanation: