The perimeter of the triangle BAG is 43. AG= 16, AB=x+4, and BG= 2x+2. What is the value of x?

The solution of y" + 4y sec(2z) by variation of parameters involves finding the homogeneous solution and integrating to find particular solutions.

a. The associated homogeneous differential equation is y'' + 4y = 0. The characteristic equation is r^2 + 4 = 0, which has roots r = ±2i. Thus, the general solution to the associated homogeneous equation is y_h = c1 cos(2z) + c2 sin(2z).

b. To find a particular solution to the nonhomogeneous equation, we assume a solution of the form y_p = u1(z) cos(2z) + u2(z) sin(2z), where u1(z) and u2(z) are unknown functions to be determined. Taking the first and second derivatives of y_p, we have:

y_p' = u1' cos(2z) + u2' sin(2z) - 2u1 sin(2z) + 2u2 cos(2z)

y_p'' = u1'' cos(2z) + u2'' sin(2z) - 4u1 sin(2z) - 4u2 cos(2z) - 4u1' sin(2z) + 4u2' cos(2z)

Substituting these expressions into the nonhomogeneous differential equation, we have:

u1'' cos(2z) + u2'' sin(2z) - 4u1 sin(2z) - 4u2 cos(2z) - 4u1' sin(2z) + 4u2' cos(2z) + 4u1 sec(2z) cos(2z) + 4u2 sec(2z) sin(2z) = 0

Equating the coefficients of cos(2z) and sin(2z), we get the following system of equations:

u1'' - 4u2' + 4u1 sec(2z) = 0

u2'' + 4u1' + 4u2 sec(2z) = 0

To solve for u1(z) and u2(z), we integrate each equation twice. The first equation gives:

u1' - 2u2 tan(2z) + 2u1 sec(2z) tan(2z) = C1

where C1 is an arbitrary constant of integration. Integrating once more, we have:

u1 = C1 integral of sec(2z) dz + C2

where C2 is another arbitrary constant of integration. Using the identity sec(2z) = 1/cos(2z), we can evaluate the integral to get:

u1 = C1/2 ln|cos(2z)| + C2

Similarly, the second equation gives:

u2' + 2u1 tan(2z) + 2u2 sec(2z) tan(2z) = C3

where C3 is another arbitrary constant of integration.

Integrating once more, we have:

u2 = C3 integral of sec(2z) dz + C4

where C4 is another arbitrary constant of integration. Using the same identity as before, we get:

u2 = C3/2 ln|cos(2z)| + C4

Therefore, the particular solution to the nonhomogeneous differential equation is:

y_p = (C1/2 ln|cos(2z)| + C2) cos(2z) + (C3/2 ln|cos(2z)| + C4) sin(2z)

c. The most general solution to the original nonhomogeneous differential equation is the sum of the general solution to the associated homogeneous equation

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Answer:

Bar graphs are used with nominal or ordinal scores; histograms are used with interval or ratio scores.

Step-by-step explanation:

Answer && Step-by-step explanation:

Simple plug and chug

we know a+b == 6 so replace the set as 6 so:

2(6)+6/6+(6)^2-2

12+1+36-2

49-2

==47

Answer:

16.5

Step-by-step explanation:

11/3 =3 and 1/3 so 55/3 and 1/3 = 16.5 or 16 and 1/2

Answer:

The total cost per month is $190.76 to the nearest cent.

Step-by-step explanation:

From the given table, the monthly service plan costing $52.00 is:

The base calling plan includes two lines.

Therefore, for 4 lines, we will need to pay for 2 additional lines per month:

⇒ $21.99 × 2 = $43.98 per month

If 3,487 minutes are used per month, then the overage of minutes is:

⇒ 3487 - 2000 = 1487 minutes per month

As the overage rate is $0.06 per minute, then the cost of the additional minutes is:

⇒ 1487 × $0.06 = $89.22 per month

Therefore, the total cost per month before tax is:

⇒ $52.00 + $43.98 + $89.22 = $185.20

To apply the federal tax of 3%, multiply the total cost by 1.03:

⇒ $185.20 × 1.03 = $190.756 = $190.76 (nearest cent)

Therefore, the total cost per month is $190.76 to the nearest cent.

Using the Venn Diagram principles, the number of customers at the supermarket who purchased both shirts and pants is 26.

A Venn Diagram shows a pictorial or graphical representation of the relationship (similarities and differences) between data sets.

In a Venn Diagram, overlapping circles or other shapes can be used to depict the logical relationships between two or more data sets or items.

The total number of customers at a supermarket = 118

The number of customers who purchased shirts, n(A) = 45

The number of customers who purchased pants, n(B) = 59

The number of customers who purchased neither shirts nor pants = 40

Let the number of customers who purchased both shirts and pants = n(A ∩ B)

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

n(A) = 45 n(B) = 59 n(A ∪ B) = 118 - 40 = 78

Substituting values:

78 = 45 + 59 - n(A ∩ B)

Solving for n(A ∩ B), we get:

n(A ∩ B) = 45 + 59 - 78 n(A ∩ B) = 26

Thus, using the formula of Venn Diagram, we can conclude that at this supermarket with 118 customers, 26 customers purchased both shirts and pants.

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Answer:

angles b and c should be 153° each.

Step-by-step explanation:

We know the smaller angle is 27°. The other small angle, vertical to the 27° angle is also 27° because they are vertical angles. Along the lines, two angles should form 180°. So 180-27=153°. All together the angles should be 360°. Check your answer by doing 153+153+27+27=360. therefore the missing angles are both 153°

Answer:

False

Step-by-step explanation:

The angles are different degrees

Answer: false

Step-by-step explanation: dont really have an explenantion

Answer:

1. 7.3

2. 33.3

3. 21.3

4. 31.9

5. 25.6

6. 11.0

7. 42°

8. 64°

9. 13°

10. 51°

Step-by-step explanation:

make sure if you're using a math calculator that it is in degree mode.

SIN, COS, OR TAN. SOH CAH TOA. Sin is Opposite/hypotenus.

Cos is Adjacent(next to it)/hypotenus.

Tan is Opposite/Adjacent.

~~

PROBLEM 1:

So we have 63°, 16 as hypotenus, and x as one of the legs.

1. Figure out whether it is Sin, Cos, or Tan. (It's adj and hyp. of the angle degree (63° listed so it's cos.)

2. Once you set it up, it is Cos 63°= x/16 then flip it around. which makes it 16 COS 63= X.

3. Input it into your calculator as 16cos(63, then it will give you.. 7.263847996

4. Don't forget to round to the nearest tenth, which gives you

x = 7.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 2:

Given: 39°, 27 is opposite of the °, and adj is x. So this is Tan.

1. Set it up, Tan 39° = 27/x can't solve this way so fix it.

2. rewritten as X = 27/tan39

3. round ur answer.

x = 33.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 3:

Given: 49°, adj is 14, hyp is x. So this is Cos.

1. Set up according to CAH, Cos 49=(14/x).

We can't solve it this way since the X is on the bottom. So we have to fix it!

2. Turns into X Cos 49 = 14, which then turns into X= 14/cos49.

3. Put it in your calculator as 14 DIVIDED BY cos 49. ( Put image example)

4. Round.

x= 21.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 4:

Given: 15°, 33 hyp, adj x. Which is Cos.

1. Cos 15= x/33 and rewrite.

2. Input as 33 cos(15 into calculator = 31.875...

3. Round to tenth.

x = 31.9

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 5:

Given: 52°, 20 adj of °, and x opp of °. Will use TAN.

1. Tan 52° = x/20

2. 20 Tan(52 into calculator

3. Round

x = 25.6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 6:

Given: 27°, opp of ° is 5, hyp is x. Will use Sin.

1. Write out as I have the last few times, Sin 27 = 5/x rewrite cause x can't be at the bottom.

2. Input into calculator as: 5/sin 27 which equals 11.01...

3. Round.

x = 11.0

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 7:

Given: x°, 6 as hyp, 4 opp. now we have to solve this different since we don't know the degree. Now when we input into the calculator you will press 2nd, then sin/cos/tan so it will be negative this is depending on which one ur solving for.

We will be using SIN, x is still a °.

1. Sin X = 4/6 Rewrite.

2. X= Sin^-1 (4/6)

Make sure ur sin is negative in calculator when doing this.

3. It SHOULD give you 41.81, round.

x = 42°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 8:

Given: x°, 29 opp, 14 adj. TAN.

1. Tan x°= 29/14 or..

2. X = Tan^-1(29/14) solve..

3. gives u 64.23.... round.

x = 64°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 9:

Given: x°, hyp 54, opp 12. SIN

1. Sin x°=(12/54)

2. X= Sin^-1(12/54) solve. (dont put x= into calculator.)

3. Don't Forget to round, answer unrounded: 12.839..

x = 13°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 10:

Given: x°, adj 25, hyp 40. COS

1. Cos x°=25/40 rewrite.

2. X= Cos^-1(25/40) Solve.

3. Round.

X= 51°

Answer: The lines below are perpendicular.

Step-by-step explanation: They are perpendicular because they start at one side and end at the side across.        Hope this helped!!! :)

Answer:

Step-by-step explanation:

Here it is

Answer: In order: 320, 100, 80, 25 , and 80

Step-by-step explanation: did the assignment.

It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.

To multiply the square roots V7 and V2, we can combine the numbers inside the square roots and simplify the result.

V7 * V2 = V(7 * 2) = V14

Multiplying the numbers under the square roots, we get 7 * 2 = 14. Therefore, the product of V7 and V2 is V14.

This means that the square root of 14 is the result of multiplying V7 and V2. However, it is important to note that V14 cannot be further simplified because 14 does not have any perfect square factors.

In summary, the product of V7 and V2 is V14. It is worth mentioning that when multiplying square roots, we can multiply the numbers inside the square roots and keep the square root symbol intact, unless the numbers inside have perfect square factors that can be simplified further.

It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.

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Answer: Find answers in the attached documents

Step-by-step explanation:

In this case, we have to use the knowledge of probability and calculate the chance of the event to occur, so we have to:

A) No have problem, because every person can be chosen once or not be chosen at all.

B) The event that everybody has been chosen maximally once is equal to the event that we have chosen the sample without replacement.

So that way, we have to analyze to know how the event will occur, so:

A)In this case we choose the sample with replacement, so the probability that there will be birthday match.

B) Using the formula, we have:

\(P=1-P\\=1-\frac{(10^6/10^3)}{(10^6)^{(10^3)}}\)

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a. The chart is prepared below.

b. At the end of 4 years, Ross still owes his parents $1,576.92.

To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.

The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.

The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.

Here are the steps for calculating the balance for each year:

Year 1:

Beginning balance = $2,500.00

Interest for the year = $2,500.00 x 0.032 = $80.00

Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00

Year 2:

Beginning balance = $2,280.00

Interest for the year = $2,280.00 x 0.032 = $72.96

Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96

Year 3:

Beginning balance = $2,052.96

Interest for the year = $2,052.96 x 0.032 = $65.76

Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72

Year 4:

Beginning balance = $1,818.72

Interest for the year = $1,818.72 x 0.032 = $58.20

Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92

Here's a table that shows the details:

Year ,principal ,Interest rate, interest, Payment ,annual owing

1 $2,500.00 $80.00 $300.00              $2,280.00

2 $2,280.00 $72.96 $300.00              $2,052.96

3 $2,052.96 $65.76 $300.00               $1,818.72

4 $1,818.72         $58.20  $300.00       $1,576.92

b. At the end of 4 years, Ross still owes his parents $1,576.92.

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Yes, the cubic power of an odd integer is odd. So, the following conjecture are

a) False ; 7³ = 342 --> True

b) False ; 9³ = 728 -->True

c) False; 5³ = 126 --> True

We have, some conjecture related to the cubic power of an odd integer is odd.

Odd number : In mathematics, an integer is even if it is a multiple of two, and odd if it is not. Let us consider 2n be a even numbers then , 2n+ 1 must be an odd number.

taking cube power of 2n+ 1 we get,

(2n + 1)³ = (2n)³ + 1³ + 3×2n×1( 2n + 1)

[ Since, (a + b)³ = a³ + b³ + 3ab(a+b), here a = 2n and b = 1]

So, (2n + 1)³= 8n³+ 1 + 6n( 2n + 1)

= 8n³+ 1 + 12n² + 6n = 2n(4n² + 3n + 3) + 1

As we see clearly, first factor is multiple of 2n that is it's even number then (even number + 1 ) implies to an odd number. Thus, the cube power of odd number is again an odd number, i.e 3³ = 27 ; 5³ = 125 ......

a) False ; 7³ = 342 , it is true

b) False ; 9³ = 728 , it is true

c) False; 5³ = 126 , it is also true

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The probability is closer to one than zero.

Probability theory is used to analyze and predict the likelihood of events happening in various fields such as statistics, gambling, physics, finance, and more. It allows us to make informed decisions based on the likelihood of different outcomes. In probability theory, the total number of possible outcomes is important to determine the probability of a single event occurring. By comparing the favorable outcomes to the total outcomes, we can calculate the probability of an event happening.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for Class 10 is an important topic for the students which explains all the basic concepts of this topic. The probability of all the events in a sample space adds up to 1.For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T). But when two coins are tossed then there will be four possible outcomes,  i.e {(H, H), (H, T), (T, H), (T, T)}.

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On November 1, Year 1, a company paid an $25,200 premium on a 36-month insurance policy for coverage beginning on that date. The table is done below.

The balance sheet of the insurance policy coverage is

                          accrual basis     cash basis       acrrual basis

December 31   (25200 - 1400)     25200                   25200 x 2 months

year 1                  23800                               year 1       1400

December 31   (23800 - 8400)          0                       25200 x 12 months

year 2                  15400                               year 2      8400

December 31   (15400 - 8400)           0                          25200 x 2 months

year 3                  7000                                 year 3      8400

December 31   (7000 - 7000)            0                         25200 x 2 months

year 4                  0                                        year 4      7000

                                                                      total          0

Therefore, if On November 1, Year 1, a company paid an $25,200 premium on a 36-month insurance policy for coverage beginning on that date, the balance sheet is mentioned above.

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Answer:

x = -4/17

Step-by-step explanation:

Answer:

310.86

Step-by-step explanation:

so V=Bh

and B=pi *r^2

so that means 3.14*9 (since 3^2 is 9)

3.14*9=28.26

then 28.26*11= 310.86

Answer:

it is . what it is lol

Step-by-step explanation:

Answer:

Explanation:

Here, we want to simplify the given expression

To do this, we have to multiply the value outside the parentheses by each of the values inside it

Mathematically, we have this as:

Answer:

Step-by-step explanation:

x² - 3x - 1 = 0

a = 1, b = -3, c = -1

x₁ = (3 + sqrt(-3² - 4(1(-1))))/(2(1))

x₁ = (3 + sqrt(9 + 4))/2

x₁ = (3 + sqrt(13))/2

x₁ = 3.302...

x₂ = (3 - sqrt(-3² - 4(1(-1))))/(2(1))

x₂ = (3 - sqrt(9 + 4))/2

x₂ = (3 - sqrt(13))/2

x₂ = -0.302...

The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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The initial deposit is PV=$840.

The annual interest rate is r=2% not compounded.

The period we are evaluating is 6 month, or n=0.5 years.

As the interest is not compounded, we can calculate the interest I can be calculated as:

Answer: the interest is $8.40.

Answer:

b=130

Step-by-step explanation:

b+(-43)=87

b+(-43+43)=87+43

b=130

Hope this helps. Have a great day, you amazing bean child.

(Yes you are now my bean child. Get over it)

Answer:

b=130

Step-by-step explanation: