can you solve it using a method? and show work

The last option which says  the roots of the auxiliary equation are √6 and -√6 is the correct one.

Auxiliary equation is the equation of characteristic polynomial which is calculated by substituting the right member of a standard differential equation by zero.

The roots of the equation is helpful in determining the nature of the general solution of the given differential equation.

We have the differential equation given in the question,

d²y / dx²  - 6y = 0

Now we can replace d²y / dx² as y''.

y'' - 6y = 0, where y'' is the second derivative of y.

Now we have to find the roots of the auxiliary equation.

Let c = y', then c² = y''

c² - 6 = 0

c² = 6

c = +√6 and -√6

So the roots of the equation are √6 and -√6.

Hence the roots of the auxiliary equation of the differential equation given are +√6 and -√6.

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The slope of the line that passes through the points (2, 8) and (-3, 14) is -6/5 in the simplest form.

A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

The slope of a line is given by the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

Plugging in the given points, we get:

m = (14 - 8) / (-3 - 2)

m = 6 / -5

m = -6/5

so the slope of the line that passes through the points (2, 8) and (-3, 14) is -6/5 in the simplest form.

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The angle measure of the circle graph is as follows:

A travel magazine surveyed 500 of its adult readers about their favourite ways to travel. The circle graph below shows that 125 people like to travel by train, 275 like to travel airplane and 100 people like to travel by boat.

Therefore, let's use the data to create a pie chart with the measured angles.

Hence,

angle for train travellers = 125 / 500 × 360

angle for train travellers = 45000 / 500

angle for train travellers = 90 degrees

angle for the airplane travellers = 275 / 500 × 360

angle for the airplane travellers =  99000 / 500

angle for the airplane travellers = 198 degrees

Finally,

angle for the boat travellers = 360 - 198 - 90 = 72 degrees.

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[tex]13 + n-26 < 38[/tex]

Simplify:

[tex]n-13 < 38[/tex]

Add 13 to both sides:

[tex]n-13+13 < 38+13[/tex]

[tex]\fbox{n} < \fbox{51}[/tex]

Answer:

n<51 but what I got was n+25

Therefore ,the return on investment prior to deducting taxes is known as the net income rate of return.

The amount a company makes prior to taxes is known as pretax investment gains, on the other hand. Income that is subject to taxation is referred to as taxable income.

Here,

Investment income generally refers to, but is also limited to, earnings, profits, corporate taxes, rental and royalty revenues, non-qualified leases, income from businesses that trade investment products or commodities, and businesses which are passive for such taxpayer.

Pretax rates of return refers to an investment's profit or loss before taxes are taken into account.

The government imposes taxes on investment on any extra money made from buying or selling investments. Capital gains taxes must be paid on securities that are successfully sold.

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Answer: Considering both dividends paid and capital gains, Dylan’s pretax profit from his investment is $30. Dylan’s pretax return on investment (ROI) is 24%.

Step-by-step explanation: To determine Dylan’s profit from his investment, add his dividends of $5 and his capital gains of $25.total profit = $25 + $5= $30Before taxes are applied, Dylan can calculate his return on investment (ROI) by dividing his profit by the cost of his investment:30125 = 0.24, or 24%.

The expected value for the given data set is 1.4.

What is expected value?

The value that will most likely be obtained from the following iteration of a statistical experiment is known as the expected value. In order to calculate the expected value for a random trial of an experiment, the probability of each possible result is taken into account.

From the given table we have to find the expected value.

Since,

Expected value = E(X) = μ = ∑ x*P(x)

E(X) = (0*0.4) + (1*0.05) + (2*0.3) + (3*0.25)

E(X) = 0 + 0.05 + 0.6 + 0.75

E(X) = 1.4

Hence, the expected value for the given data set is 1.4.

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On performing addition exercises we get 10 , 11 , 10 , 14 , 17 , 9 , 11 , 10 , 17,  10 , 13 , 12 , 14 , 3 , 9 , 8 , 6 , 11 , 14 , 14 , 16 , 21 .

What is Addition ?

Addition can be defined as the performing addition operation by using operand + between two operators.

3 + 7 = 10

2 + 9 = 11

4 + 6 =10

5 + 9 =14

12 + 5 =17

6 + 3 =9

8 + 3 =11

10 + 0 = 10

9 + 8 = 17

1 + 9 = 10

7 + 6 = 13

9 + 3 =12

6 + 8 = 14

0 + 3 = 3

3 + 6 = 9

7 + 1 = 8

4 + 2 =6

4 + 7 = 11

11 + 3 = 14

7 + 7 = 14

9 + 7 = 16

12 + 9 =21

Hence, On performing addition exercises we get 10 , 11 , 10 , 14 , 17 , 9 , 11 , 10 , 17,  10 , 13 , 12 , 14 , 3 , 9 , 8 , 6 , 11 , 14 , 14 , 16 , 21 .

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Answer:

It is not possible to determine which airplane is closer to the airport without additional information. The distance and direction of each airplane's flight are given, but the starting point for each airplane is not specified. If we knew the starting point of each airplane, we could use the information provided to calculate the final position of each airplane and determine which one is closer to the airport.

Step-by-step explanation:

The trigonometric function y = sin(3x + π) = 0 for -π/3 ≤ x ≤ π/3.

A trigonometric function is a function that uses one of the trigonometric ratios.

Given that we have the trigonometric function y = sin(3x + π) for -π/3 ≤ x ≤ π/3.

To find the range of output values for the range of input values given, we insert the given values of the input into the equation.

So, for the minimum value of y, we substitute x = -π/3 into the equation.

So, y = sin(3x + π)

y = sin(3(-π/3) + π)

y = sin(-π + π)

y = sin(0)

y = 0

For the maximum value of y, we substitute x = π/3 into the equation.

So, y = sin(3x + π)

y = sin(3(π/3) + π)

y = sin(π + π)

y = sin(2π)

y = sin2π

y = 0

So, y = 0 for -π/3 ≤ x ≤ π/3.

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The data and the image both characterize the object as a rectangle because its length is 12 and its width is 9.

A quadrilateral having four right angles, or rectangle, in Euclidean plane geometry. A quadrilateral that is equiangular, or one in which all of the angles are equal, is another way to describe it. Also possible is a straight angle in the parallelogram. With four sides that are of the same size, a square is a rectangle. Four 90-degree vertices and equal parallel sides make up a quadrilateral with a rectangle-like shape. Its equirectangular rectangle moniker derives from this. The term "parallelogram" also refers to a rectangle, which has equal and parallel opposite sides.

given

in 8 th question

The illustration depicts a rectangle with four sides and two opposite sides that are the same length as a square with equal lengths on all four sides.

The data and the image both characterize the object as a rectangle because its length is 12 and its width is 9.

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Step-by-step explanation:

It would be 4w=36

÷4 on both sides

W=9

The cottage cheese contains 3.9 g of fat and the apple has 0.13 g, making a total of 4.03 g of fat in the dessert.

Relationships that always have the same ratio are said to be proportional. For instance, the number of trees in an orchard and the number of apples in a harvest of apples are determined by the average number of apples per tree. A linear relationship between two numbers or variables is referred to as proportional in mathematics. When the first quantity doubles, the other number does as well. When one of the variables is reduced to 1/100th of its previous value, the other also decreases. If two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two quantities remains constant throughout all values. The diameter and circumference of a circle serve as an example.

given

fat grams from the apple, where a

a +30a = 4.03g

31a/31 = 4.03 / 31

a = 0.13

The cottage cheese has 30(0.13) = 3.9 g fat, compared to the apple's 0.13 g.

The cottage cheese contains 3.9 g of fat and the apple has 0.13 g, making a total of 4.03 g of fat in the dessert.

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The solution to the system of equation y = 2x + 3 and y = -3x + 3 is (0, 3)

An equation is an expression that shows the relationship between variables and numbers.

The linear equation is in the form:

y = mx + b

where m is the rate of change and b is the y intercept.

Given the equation:

y = 2x + 3     (1)

y = -3x + 3      (2)

To solve by elimination method, subtract equation 2 from 1:

0 = 5x + 0

x = 0

substitute x = 0 in equation 1:

y = 2(0) + 3 = 3

The solution to the equation is (0, 3)

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Answer:

[tex]6^2=36[/tex]

Step-by-step explanation:

[tex]10^2-4^3=100-64=36=6^2[/tex]

Side a of the oblique triangle is 25.57 units and side b is 9.42 units.

The number of sides of a triangle and how their individual sine angles are equal are determined by the law of sines. Other names for the sine law are sine rule, sine formula, and sine law. The law of sine is used to determine the side or unknown angle of an oblique triangle.

Given:

∠A = 107

∠B = 21

∠C = 52

c = 21

So, using the law of sines

b/sin B = c/ sin C

b/sin 21 = 21/sin 52

b = (21 × sin 21) / sin 52

= (21 × 0.35) / (0.78)

b ≈ 9.42

Similarly, side a of the triangle is given by

a/ sin A = c/ sin C

a/sin 107 = 21/sin 52

a = (21 × sin 107) / sin 52

= (21 × 0.955) / (0.78)

a  ≈ 25.57

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Each pair of athletic shoe cost $20 and each pair of athletic shoe cost $35, in the given arithmetic problem.

By doing addition, subtraction, multiplication, and division on numbers, arithmetic is defined as the study of numbers.

Let 20x be the cost of manufacturing 20 athletic shoes and 10y be the cost of manufacturing 10 casual shoes, then

20x + 10y = 750

10y =  750 - 20x

y =  75 -2x

Let 25x be the cost of manufacturing 25 athletic shoes and 20y be the cost of manufacturing 20 casual shoes, then

25x + 20y = 1200  

20y = 1200 - 25x

y = 60 - 25x/20

y = 60 - 1.25x

Equalise the y terms

75 -2x = 60 - 1.25x

75 - 60 = -1.25x + 2x

15 = 0.75x

x = 15/ 0.75

x = 20

Substitute the value of x in y =  75 -2x

y =  75 -2(20)

y = 75 - 40

y = 35

Thus, each pair of athletic shoe cost $20 and each pair of athletic shoe cost $35.

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Full question:-

Ranger Shoe Company manufactures two types of shoes, athletic shoes and casual shoes. The cost of manufacturing 20 pairs of athletic shoes and 10 pairs of casual shoes is $750. If 25 pairs of athletic shoes and 20 pairs of casual shoes were manufactured, the cost would be $1200. How much does it cost to manufacture each type of shoe?

Shirts = 10$ Pants = 10$

Step-by-step explanation:

50 / 5 = 10$

3/1 = 10$

In this system of simultaneous equations, the cost of each shirt (x) equals $5 and the cost of each pair of pants (y) is $25.

This is a system of simultaneous equation problems in Mathematics. Let's denote the cost of one shirt as x and one pair of pants as y. Based on the problem information, you have these two equations:

1) 2x + 3y = 50

2) 3x + y = 40

To solve for x, you can multiply the second equation by three and subtract the first equation from it:

3*(3x + y) - (2x + 3y) = 50

After simplifying, you find that x (cost of each shirt) equals 5.

In order to find y (cost of each pair of pants), you can now substitute x = 5 into the second original equation: 3*5 + y = 40, which gives you y = $25, the cost of each pair of pants.

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The equation that models the future cost of gasoline, if the price increases by 0.3% per month, is option D: y = 1.19(1.003)

In this equation, y represents the cost of gasoline at a certain time (measured in months) in the future. The initial cost of gasoline is represented by 1.19 (since this is the base value we are starting with), and the increase in price over time is represented by (1.003)^z where z represents the number of months in the future.

The equation 1.19(1.003)^z to model the future cost of gasoline is correct, the base cost multiplied by a number representing an increase in the price each month (1.003) raised to the power of the number of month. Each time z increases by 1, the price increases by 0.3%

Therefore, increasing z by 1 increases the price of gasoline by 0.3%. If you want to calculate the price for a certain number of months in the future, you can plug in that number for z in the equation and calculate the result.

Answer:y=1.19(1.003)x

Step-by-step explanation:

Answer:

See below!

Step-by-step explanation:

8, 3, 8, 6, 3, 3, 3, 6, 7

Here, Range is:

= Highest value - Lowest value

= 8 - 3

= 5

Here, the mode is:

= 3 (occurring 4 times)

[tex]\rule[225]{225}{2}[/tex]

Answer:

x= 3

Step-by-step explanation:

6x =18

divide 6 by both sides.

x=3

Answer:

The answer to both parts is (C)

In the first 9/3.9 = 2.31        half lives elapsed

(1/2)^2.31 = .5^2.31 = .202     pressure at 9 mi above sea level

P = .202 * 31 = 6.26 mi

In the second:

19/5 = 3.8 half-lives

.5^3.8 = .072 left after 3.8 half lives

635.8 * .072 = 45.6

Answer: 14.7868

Step-by-step explanation: There are 29.5734 milliliters in a US fluid ounce. Since we need .5 oz, we multiply this number by .5.

Answer:

0.6 > 0.49 > 0 > -0.2 > -0.32

Step-by-step explanation:

Please let me know if this helped!!!

The requried scaled length of the actual length is given as 4 inches.

The scale factor is defined as the ratio of the modified change in length to the original length.

here,
In the question,
Scale 3 in = 24ft
Scale factor = modified length / original length
Scale factor = 3 / 24 = 1/8

Now,
For an actual length of 36 ft,
Scaled length is given as = 36 × 1/8 = 4 inches

Thus, the requried scaled length of the actual length is given as 4 inches.

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Value of x = 12.5 that is determined by solving equation.

Two angles are called complementary to each other when the sum of these two angles is equal to 90 degrees.

given, two angles are complementary two each other.

value of one angle = 18 degrees

the other angle is given by = (8x - 28) degrees

As the above two are complementary so the sum of the two is equal to 90 degrees.

The equation will be.

18 + (8x - 28) = 90

8x - 10 = 90

8x = 100

x= 12.5

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At this rate, how will swim 16 laps in 8 minutes.

A rate is a ratio in which the two terms being compared have different units.

Instead of using the "to" form for ratios (for example, 3 red ball to 2 blue balls), rates often use the word per. Rate is a ratio that compares two different quantities which have different units.

When two quantities of different units are compared and expressed as a ratio, we refer to it as 'Rate'.

5:2 1/2

x:8

x = (5 x 8) /5/2

x = (40) / 5/2

x = 16laps

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X and y are both 20 degrees because all triangles = 180 degrees and 140 + 20+20= 180

Answer:

Step-by-step explanation:

if you may, try finding 180 degrees, which y is 40 and x is 0

the answer is inconsistent i think

The minimum of the function is at x = -10. The minimum on the interval [-10,6] is -2.67.

What is a function?

A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

Given function is f(x) = ³√(x-9)

The graph of the given function increases with the increase of the value of x and decreases with the decrease of the value of x.

Thus the minimum value of f(x)on the interval [-10,6] is at x = -10

Putting x = -10 in the given function.

f(-10) = ³√(-10-9)

f(-10) = ³√(-19)

f(-10) = -2.668

f(-10) = -2.67 (rounded to 2 decimal places).

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