Solve the given differential equation by undetermined coefficients
1/4 y'' + y' + y = x2 − 3x

Answer:

y = 3x - 5

Step-by-step explanation:

So first take any two points from the graph.

(0, -5), (2, 1)

The slope is \(\frac{1 + 5}{2 - 0} =3\)

y = mx + b

b is the y intercept

The y intercept is (0, -5) as this is where the line intersects the y axis.

y = 3x - 5

Answer:

1017

Step-by-step explanation:

9063/9=1007

1007+10=1017

Answer:

1,6

Step-by-step explanation:

1,6 thats how

Kylie earns 5.80 dollars more than Kayla per hour

Answer:

x = 26, y = 9

Step-by-step explanation:

Add the bottom equations and set them equal to 180

8x -28 = 180

8x = 208 divide each by 8

x = 26

Find the bottom right, 3(26) - 11

78 - 11 = 67

The unlabeled top left box is also equal to 67 degrees.

So 2y + 5 = 23

2y = 18

y = 9

Answer:

The answer is x = 26 and y = 31.

Step-by-step explanation:

To solve this problem, we should first solve for the value of x.  Since the angles that measure (5x-17) and (3x-11) are supplementary, this means that they must add up to 180 degrees.  This allows us to make the following equation:

(5x - 17) + (3x-11) = 180

When we combine like terms on the left side of the equation, we get:

8x - 28 = 180

Then, we can add 28 to both sides.

8x = 208

Finally, we can divide both sides by 8 to get x alone on the left side of the equation.

x = 26

Now that we know our value for x, we must find our value for y.  To do this, we should notice that the angle 3x-11 has a vertical angle (an angle that is directly across from it).  By the definition of vertical angles, this angle must have the same measure, meaning it will also have the value 3x - 11.  This vertical angle is complementary to the angle 2y + 5, which means that their sum must equal 90 degrees; therefore, we can make the following equation:

3x - 11 = 2y + 5

Since we found our value of x already in the above equation, we can substitute this value into this equation:

3(26) - 11 = 2y + 5

Next, we can perform the multiplication on the left side of the equation.

78 - 11 = 2y + 5

Then, we can perform the subtraction on the left side of the equation.

67 = 2y + 5

Next, we should subtract 5 from both sides of the equation.

62 = 2y

Finally, we should divide both sides of the equation by 2 to get the variable y by itself on the right side of the equation.

y = 31

Therefore, the answer to this problem is x = 26 and y = 31.

Hope this helps!

Answer:

Step-by-step explanation:

Answer: True.

Step-by-step explanation:

The statement is:

"A linear equation has ONE solution when the variable equals zero."

First, a generic linear equation can be written as:

y = a*x + b

Where a and b are known values.

If the variable equals zero, we have:

y = a*0 + b = b

y = b.

Then it has only one solution if x = 0.

So the statement is true, but it is also true for any value in the variable.

So if we rewrite it as (for example):

"A linear equation has one solution when the variable equals 4"

y = a*4 + b.

Because a and b are known, this equation also does have only one solution.

Answer:true

Step-by-step explanation:

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.

When the distribution is normal, we use the z-score formula.

In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:

Z = (X – µ) / σ

The Z-score shows how many standard deviations the measure is from the mean. After finding the Z-score, need to look at the z-score table and discover the p-value associated with the z-score. This p-value is the probability that the value of the measure is smaller than X, means, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

So, in this case, given that:

µ = 249, σ = 20

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:

100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.

Now, put all the values into the formula:

Z = (X – µ) / σ

–0.253 = (X – 249) / 20

X – 249 = –0.253 * 20

X = 244

Hence, the candle burns for 244 minutes.

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In this equation, the slope (m) is 2.

We have,

In the equation y = 2x + 3, the equation is in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.

The slope (m) determines the steepness or inclination of the line.

In this case, the slope is 2, which means that for every 1 unit increase in the x-coordinate, the y-coordinate will increase by 2 units.

So, the line represented by this equation is upward-sloping or ascending.

The y-intercept (b) is the value of y when x is equal to 0.

In this equation, the y-intercept is 3, which means that the line intersects the y-axis at the point (0, 3).

By knowing the slope and the y-intercept, we can easily plot points on the line and draw the line on a graph.

Now,

In this equation, the slope (m) is 2.

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Therefore, the volume of the cone to the nearest whole number is 94 m^3.

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

The units that may be produced in terms of basic units to measure quantities other than those measured in those units are known as derived units. Examples of derived units are the meter per second (distance), mole per cubic meter (material concentration), and specific volume (cubic meter per kilogram).

We are given, the radius of the cone as 3m and a height is 10m

Using formula,

V = (1/3) * pi * r^2 * h

V = (1/3) * 3.14 * 9 * 10

V = 94 m^3

So, The correct answer is B. 94 m^3

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To test the convergence or divergence of the series:

∑(n^2 + 1) / n^8

We can use the p-series test, which states that if the series can be written in the form ∑1/n^p, then it converges if p > 1 and diverges if p ≤ 1.

In this case, we can see that p = 8, which is greater than 1. Therefore, the series converges.

Alternatively, we can also use the limit comparison test. We can compare the given series with a known convergent p-series of the form ∑1/n^7:

lim(n → ∞) [(n^2 + 1) / n^8] / (1 / n^7)

= lim(n → ∞) [(n^2 + 1) / n] * (n^7 / 1)

= lim(n → ∞) [n^9 + n^6] / n

= lim(n → ∞) n^8 + n^5

= ∞

Since the limit is a nonzero value, the series converges by the limit comparison test.

Therefore, the series ∑(n^2 + 1) / n^8 is convergent.

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Answer:

1 is to 2

Ie

1/2

Step-by-step explanation:

hope it helps

Answer:

2 to 1

which equals 2

Step-by-step explanation:

if you look at point B (2,1) and B’ (4,2)

we can see that each value is multiplied by 2

Using angle sum property

\(\\ \sf\longmapsto x+90+30=180\)

\(\\ \sf\longmapsto x+120=180\)

\(\\ \sf\longmapsto x=180-120\)

\(\\ \sf\longmapsto x=60\)

Answer:

answer D

Step-by-step explanation:

A and C have to be equal

B and D have to be equal

A+B+C+D have to equal 360

so, two equations

5y-3=x+3y

4x+5y-3+x+3y=360

4x=156

x=39

5y-3=9+3y

2y=42

y=21

Hope this helps plz hit the crown :D

Accoding to the calculations , the correct answer is:

A) Depreciation charge 16,000; revaluation surplus £20,000

According to IAS 16 Property, Plant and Equipment, the depreciation charge for an asset should be based on its carrying amount, useful life, and residual value.

In this case, the buildings were purchased for £400,000 (£480,000 - £80,000) and had a useful life of 25 years. Since there is no residual value, the depreciable amount is equal to the initial cost of the buildings (£400,000).

To calculate the annual depreciation charge, we divide the depreciable amount by the useful life:

£400,000 / 25 = £16,000

Therefore, the depreciation charge for the year ended 30 September 2021 is £16,000.

Now, let's calculate the balance on the revaluation surplus as at that date.

The revaluation surplus is the difference between the fair value of the property and its carrying amount. On 1 October 2020, the property was revalued to £500,000, and the carrying amount was £480,000 (£400,000 for buildings + £80,000 for land).

Revaluation surplus = Fair value - Carrying amount

Revaluation surplus = £500,000 - £480,000

Revaluation surplus = £20,000

Therefore, the balance on the revaluation surplus as at 30 September 2021 is £20,000.

Based on the calculations above, the correct answer is:

A) Depreciation charge £16,000; revaluation surplus £20,000

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Answer:

I belive it would be c

Step-by-step explanation:

because if you read the question it says the lowest point altho they are equale it still makes sence to put c

Answer:

Point A and point B have 11 units between

Step-by-step explanation:

If the distance between 0 and 10 is 10 also known as the absolute value, you just add one more unit because it starts at -1

So 10 + 1 = 11 and because we are using 10 is greater than 1 its positive so the answer is 11

Hope this helps :)

Answer:

Step-by-step explanation:

1.)12.

To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator.

Thus, the answer to 4 divided by 1/3 in fraction form is:

\(\frac{12}{1}\)

To make the answer to 4 divided by 1/3 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:

12

The answer is rounded to the nearest two decimal points if necessary.

\(\frac{12}{1}\) is an improper fraction and should be written as 12.

2.) 9

Answer:

No, -19 is not a natural number.

Step-by-step explanation:

A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc. Natural numbers are also called "counting numbers" because they are used for counting.

Answer:

The natural numbers (or counting numbers) are the fundamental mathematical set on which all other arithmetic is based. They do not include negative numbers. (The set of integers provides negative numbers.)

Step-by-step explanation:

hope this helps : )

Answer:

y-4=100 and 100=y-5

Step-by-step explanation:

Because the addition property of equality is: The property stating that adding the same number to both sides of an equation does not change the equation.

Equations are used to represent equal expressions

The equivalent equation of y + 4 = 100 is 4 + y = 100

The equation is given as:

y + 4 = 100

Rewrite the equation as follows:

4 + y = 100

Hence, the equivalent equation of y + 4 = 100 is 4 + y = 100

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Answer:

A tiny cat named Tiny sits all day in the window and watches people pass by.

Step-by-step explanation:

Select the sentence with an appositive phrase and a relative pronoun.

A tiny cat named Tiny sits all day in the window and watches people pass by.

The cat, which is a Calico, sits in the window all day.

Tiny, a Calico cat, is a close watcher of all who pass by.

Tiny, a fierce people-watcher, is her cat that is new.

1. The number divisible by 5 are;

⇒ 135, 205, 330, 275, 365

2. The digits to make 3,71 _ is divisible by 3 are;

⇒ 1, 4 and 7

3. All the factors of the number 30 are;

⇒ 1, 2, 3, 5, 6, 10, 15, 30

4. The composite number is 81.

5.  Factorization of 3,240 = 2³ x 3⁴ x 5

6. The GCF of 140 and 180 = 20

7. The GCF of 24 and 66 = 6

What is Number system?

A system of writing to express the number is called number system.

Given that;

There are some numbers.

Now,

In first question;

A number is divided by 5 is the number in ones place is 0 or 5.

So, The number divisible by 5 are;

⇒ 135, 205, 330, 275, 365

2. Since, A number is divisible by 3 if the sum of all digits of the numbers in divisible by 3.

Here, The number is;

⇒ 3, 71_

⇒ Sum of all the numbers = 3 + 7 + 1 + x

                                        = 11 + x

Put x = 1;

11 + x = 11 + 1 = 12 is divisible by 3.

Put x = 4;

11 + 4 = 15 is divisible by 3.

Put x = 7;

11 + 7 = 18 is divisible by 3.

Thus,  The digits to make 3,71 _ is divisible by 3 are;

⇒ 1, 4 and 7

3. The factors of number 30 = 1, 2, 3, 5, 6, 10, 15, 30

Thus, All the factors of the number 30 are;

⇒ 1, 2, 3, 5, 6, 10, 15, 30

4. The composite number is the number whose factors are more than 1.

So, The composite number is 81.

5. Factorization of 3,240 = 2 x 2 x 2 x 5 x 3 x 3 x 3 x 3

                                      = 2³ x 3⁴ x 5

Thus, Factorization of 3,240 = 2³ x 3⁴ x 5

6. The GCF of 140 and 180 is find as;

140 = 2 x 2 x 5 x 7

180 = 2 x 2 x 3 x 3 x 5

Thus, The GCF of 140 and 180 = 2 x 2 x 5 = 20

7. The GCF of 24 and 66 is find as;

24 = 2 x 2 x 2 x 3

66 = 2 x 3 x 11

Thus, The GCF of 24 and 66 = 2 x 3 = 6

Thus,

1. The number divisible by 5 are;

⇒ 135, 205, 330, 275, 365

2. The digits to make 3,71 _ is divisible by 3 are;

⇒ 1, 4 and 7

3. All the factors of the number 30 are;

⇒ 1, 2, 3, 5, 6, 10, 15, 30

4. The composite number is 81.

5.  Factorization of 3,240 = 2³ x 3⁴ x 5

6. The GCF of 140 and 180 = 20

7. The GCF of 24 and 66 = 6

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Answer:

13.7. with tax it is 14.8

Answer:

2.18 radians

Step-by-step explanation:

125/360=x/2π

2.18 radians

The equations that are true of the values x, y, and z are :

The line that x degrees and 65 degrees is on, is a straight line which means that they will both add up to 180 degrees :

x degrees + 65 degrees = 180 degrees

x and z are congruent angles which means they are both the same angle measure.

y would be equal to 65 degrees because, just like x and z, y and 65 degrees are congruent.

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Options include:

Answer:

To solve the problem:

Location: Swimmers' School

Swimming Lessons: 4 classes for $56

The unit rate for classes at Swimmers' School is:

Unit rate = Total price / Number of classes

Unit rate = $56 / 4 classes

Unit rate = $14 per class

The lower unit rate is: $14 per class

The classes at Divers' Depot:

Price: 10 classes for $120

The unit rate for classes at Divers' Depot is:

Unit rate = Total price / Number of classes

Unit rate = $120 / 10 classes

Unit rate = $12 per class

Based on the unit rates, the classes at Divers' Depot ($12 per class) are the better deal compared to Swimmers' School ($14 per class). Therefore, the answer is:

Location: Divers' Depot

Step-by-step explanation:

To find the better deal, we need to find the cost per class for each option. For Swimmers' School, the cost per class is $56 / 4 = $14. For Divers' Depot, the cost per class is $120 / 10 = $12. Therefore, the better deal is Divers' Depot, because the cost per class is lower.

Answer:

12) \( y = -x - 5 \)

Step-by-step explanation:

\( y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) \)

12) (0, -5), (-1, -4)

\( y - (-5) = \dfrac{-4 - (-5)}{-1 - 0}(x - 0) \)

\( y + 5 = \dfrac{-4 + 5}{-1}(x) \)

\( y + 5 = \dfrac{1}{-1}(x) \)

\( y = -x - 5 \)

Answer:

work is pictured and shown

Answer:

5\(\sqrt{2}\)

Step-by-step explanation:

prime factorising 50 inside root,

\(\sqrt{50}\)=\(\sqrt{5*5*2}\)

      5*5 is a perfect square

    So root of 5*5(or 25) is 5.

Hence 5 comes outside and 2 remains in bracket.

=5\(\sqrt{2}\)