Please help me with this Geometry problem, I'm stuck on it :(

Answer:

AC=DC. (Given in figure)

AB=BD. (Given in figure

BC=BC. (Common)

that means triangle BAC is congruent to triangle BDC by SSS criterion

Answer:

The sequence of transformation that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a 90 degrees counterclockwise rotation about point A followed by reflection across the y-axis and a translation of 20 units down.

Explanation:

The sequence of transformations are described in the following figure:

Therefore, the first transformation is a rotation of 90 degrees counterclockwise about point A. After that transformation, we get the figure A'B'C'D'

Then, we reflect the figure across the y axis, so we get A''B''C''D''

Finally, we translate the figure 20 units down to get GHIJ

So, the answers are:

The sequence of transformation that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a 90 degrees counterclockwise rotation about point A followed by reflection across the y-axis and a translation of 20 units down.

Answer:

After 24 days.

Step-by-step explanation:

42 Dollars / 1.75 Dollars per day = 24 Days. This means that at 24 days, the one-way bus ride costs as much as a 30-day pass. After 24 days, the 30-day pass is cheaper.

Answer:

The answer for the question provided is 10^4×4^5

That's the derivative dy/dx of the given expression y = exp(√(4 + 3x7)).

To find dy/dx, we need to take the derivative of y with respect to x. Let's calculate it step by step.

Given: y = exp(√(4 + 3x7))

We can rewrite the expression inside the square root as follows:

4 + 3x7 = 4 + 21x

Now, let's differentiate y with respect to x using the chain rule:

dy/dx = d/dx [exp(√(4 + 3x7))]

= exp(√(4 + 3x7)) * d/dx[√(4 + 3x7)]

To find d/dx[√(4 + 3x7)], we need to apply the chain rule again:

d/dx[√(4 + 3x7)] = (1/2) * (4 + 3x7)^(-1/2) * d/dx[4 + 3x7]

= (1/2) * (4 + 3x7)^(-1/2) * 3

Now, substitute this back into the expression for dy/dx:

dy/dx = exp(√(4 + 3x7)) * (1/2) * (4 + 3x7)^(-1/2) * 3

Simplifying further:

dy/dx = (3/2) * exp(√(4 + 3x7)) * (4 + 3x7)^(-1/2)

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Answer:

C

Step-by-step explanation:

ΔJKL consist of 3 angles: ∠mLJK, ∠mKLJ and ∠mJKL

We are given the measures of ∠mLJK and ∠mKLJ

In order to find ∠mJKH we must find the missing angle in the triangle

Remember that angles in a triangle add up to equal 180

If we are given two angles we can find the missing angle by subtracting the measures of the known angles from 180

so ∠mJKL = 180 - 37 - 69

180 - 37 - 69 = 74

Hence, ∠mJKL = 74°

Now to find ∠mJKH

Angles ∠K, ∠mJKH and ∠mJKL appear to be formed on a straight line

Angles formed on a straight line add up to equal to 180

So ∠K + ∠mJKH  + ∠mJKL = 180 ( note that this is the equation that will be used to solve for ∠mJKH )

∠K is a right angle, indicated by the little square.

Right angles have a measure of 90° so ∠K = 90

We have also calculated the measure of ∠mJKH = ( 74° )

That being said we plug in the given values into the equation created earlier and solve for ∠mJKH

We would have 90 + ∠mJKH + 74 = 180

Now we solve for ∠mJKH

step 1: combine like terms

90 + 74 = 164

now we have 164 + ∠mJKH = 180

step 2 subtract 164 from each side

180 - 164 = 16

164 - 164 cancels out

we're left with ∠mJKH = 16

Hence the answer is C

Answer:

the answer is D and just keep practicing

Answer:

10

Step-by-step explanation:

Answer:

-10

Step-by-step explanation:

8+2=10, but it's negative. Negative+Negative=Negative.

In linear equation, $869,776  will her total payment for the home be .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

You have to use the number in the intersection of the row for 5.25% interest and the column for 20 years.

The number is $6.74.

That means that, for every $1,000 borrowed for 20 years at 5.25% interest you will pay $6.74 every month.

2. Amount borrowed

You will make a 22% down payment:

Thus the amount borrowed is $426,000 - $93,720 = $332,280

3. Monthly payment

Multiply the monthly payment per 1,000 by the amount borrowed divided by 1,000:

4. Total monthly payments:

Multiply the number of payments by the monthly payment.

Number of payments = 20 years × 12 payments /year = 240 payments.

5. Total payment for the home.

The total payment for the home will be the down payment plus the amount paid to the bank:

$322,280 + $537,496 = $869,776

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Marcus ends up paying $37.70 for the two shirts. To calculate the final price Marcus pays for the shirts, we need to follow these steps:

Calculate the discounted price of each shirt: Since the shirts are on a 30% off rack, the discounted price of the first shirt is 0.70 * $28.99 = $20.29, and the discounted price of the second shirt is 0.70 * $30.29 = $21.20.

Calculate the total cost of the shirts before tax: The total cost of the two shirts is $20.29 + $21.20 = $41.49.Apply the additional 10% off discount: To calculate the final price after the additional discount, we need to subtract 10% from the total cost. 10% of $41.49 is 0.10 * $41.49 = $4.15. Subtracting this amount from the total cost gives us $41.49 - $4.15 = $37.34.

Add the sales tax: To calculate the final price including the 6% sales tax, we need to add 6% of $37.34 to the total cost. 6% of $37.34 is 0.06 * $37.34 = $2.24. Adding this amount to the total cost gives us $37.34 + $2.24 = $39.58.

Rounding to the nearest cent, Marcus ends up paying $39.59 for the two shirts. Therefore, the correct answer is option a. $39.59.

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To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

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The least common multiple (LCM) of the polynomials x² - 32x - 10 and 2x + 10 is 2(x + 2)(x - 10)(x + 5).

To calculate the LCM, we need to find the polynomial that contains all the factors of both polynomials, while excluding any redundant factors.

Let's first factorize each polynomial to identify their prime factors:

x² - 32x - 10 = (x + 2)(x - 10)

2x + 10 = 2(x + 5)

Now, we can construct the LCM by including each prime factor once and raising them to the highest power found in either polynomial:

LCM = (x + 2)(x - 10)(2)(x + 5)

Simplifying the expression, we obtain:

LCM = 2(x + 2)(x - 10)(x + 5)

Therefore, the LCM of x² - 32x - 10 and 2x + 10 is 2(x + 2)(x - 10)(x + 5).

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Step-by-step explanation:

1kg of grapes = $1.50

=> 3.5kg of grapes = $1.50 * 3.5 = $5.25

1kg of carrots = $1.00

=> 2.25kg of carrots = $1.00 * 2.25 = $2.25

Total cost = $5.25 + $2.25 = $7.50.

The determinant of the inverse of matrix A, det(A⁻¹ ), is equal to the reciprocal of the determinant of matrix A, i.e., 1/det(A).

If A is an invertible matrix, then the determinant of A is non-zero, i.e., det(A) ≠ 0.

We know that the determinant of a matrix is related to its inverse by the following equation:

det(A) det(A⁻¹) = det(A A⁻¹) = det(I) = 1,

where I is the identity matrix.

Multiplying both sides of the equation by det(A⁻¹), we get:

det(A⁻¹) = 1/det(A)

Therefore, the determinant of the inverse of matrix A, det(A⁻¹), is equal to the reciprocal of the determinant of matrix A, i.e., 1/det(A).

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Answer: 12

Step-by-step explanation:

Answer: I think it's P.E.M.D.A.S

Step-by-step explanation:

When we divide the 464 by 60 we get the following remainder in our answer that is 44.

The Remainder is the name for the value that is left behind after division. If an amount (reward) cannot be divided completely with another number, we are left with only a meaning (divisor). The remaining is the name for this amount. For instance, 10 is not precisely divisible by 3. We can calculate 3 x 3 = 9 because that is the closest value.

7.733333333333333

=7 44/60 ⇔ 7 R 44

464 divided by 60

=7 with a remainder of 44

Here, we provide you the outcome of the dividing with remainder, often known as the Euclidean division, along with a brief explanation of the following terms:

464 divide by 60 yields a quotient and residual of 7 R 44.

464 is the dividend & 60 is the divisor; the division (numeric division) of 464/60 is 7; the remainder ("left over") is 44.

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If the average rate of inflation over the last hundred years was 3.22%, the amount of money one hundred years ago would be equivalent to a million dollars today is approximately 968,805 dollars.

If the average rate of inflation over the last hundred years was 3.22%, we have to determine the amount of money one hundred years ago would be equivalent to a million dollars today.

We know that formula of inflation is:

inflation = (FP−IP)/IP × 100

where, IP stands for the initial basket price or price index.

FP stands for the basket's final price or the price index.

From the question, inflation = 3.22%, FP = 1,000,000

Now putting the values in the formula

3.22 = (1,000,000 - IP)/IP  × 100

Divide by 100 on both side, we get

0.0322 = (1,000,000 - IP)/IP

Multiply by IP on both side, we get

0.0322IP = 1,000,000 - IP

Add IP on both side, we get

1.0322IP = 1,000,000

Divide by 1.0322 on both side, we get

IP = 968,804.5

IP = 968,805(approx)

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This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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Answer:

Step-by-step explanation:

Given;

Loan = $5,000

Interest rate = 13% charged at the end of each year

Question 1. Expression to represent the amount owed, in dollars, after;

a. After 1 year.

Owed amount = Loan + accrued interest= $5000 + ( 13% * $5000 * 1 year )

= 5650

b. After 2 years.

Owed amount = Loan + accrued interest

= $5000 + ( 13% * $5000 * 2 years )

= $6300

c. After t years

Owed amount = Loan + accrued interest= $5000 + ( 13% * $5000 * t years )= $5000 + $650t

Question 2. Explain how to convince someone that your expression for t years is correct.

Amount owned= borrowed amount + accrued interest

Accrued interest = Interest rate per year * Loan amount * time in years ( for simple interest case )

Loan amount = $5000

Time = t years

Interest rate = 13% per year

Accrued interest = 13% * $5000 *t years= $650t

Amount owned will therefore be; = Loan amount + Accrued interest

= $5000 + $650t

Answer:

x=25

x=47

y=25 x=10

y=20

Step-by-step explanation:

2x+10=60

-10 -10

2x=50

2x/2=50/2

x=25

2x+6=100

-6 -6

2x=94

2x/2=94/2

x=47

5y-25=100

+25 +25

5y=125

5y/5=125/5

y=25

11x-30+100=180

11x+70=180

-70 -70

11x=110

11x/11=110/11

x=10

7y-10=3y+70

+10 +10

7y=3y+80

-3y-3y

4y=80

4y/4=80/4

y=20

hopefully this helps :)

Statistics is the science of conducting studies to gather, organize, summarize, and figure out the conclusion from the data.

The science of studies in statistics involves below points :

1. Collection of data is a systematic process of gathering information from relevant sources to conclude the research problem. Example: Survey and questionnaire case studies.

2. Organization of data involves arranging the primary or raw data in an understandable and cauterized order. It includes the process of classification, picture and graphic representation and frequency distribution table. Example: organising marks scored by students in different subjects.

3. Summarizing is the method of outlining and providing information regarding our research data, it draws the value of our data.

4. Analysis is another way of statistics involving the science of collecting data and uncovering patterns and trends in it. Example: making of pie charts.

5. Conclusion is the final stage in the science of statistics studies it results in finding the answers to our research questions. Example: a survey on youth and politics, conclusion: 60 % of youth have no interest in politics.

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The complete question is -

What is Statistics? what is its science of studies?

Answer:

sdsadasdads121

Step-by-step explanation:

Answer:

22:222:222

33:333:333

44:444:444

Step-by-step explanation:

22:222:222

33:333:333

44:444:444

This means ratios which when reduced give us 11:111:111

HOPE THIS HELPED

Answer:

B.

Step-by-step explanation:

A C - chart is used for Number of defects per unit.

What is C - chart?

In statistical quality control, the c-chart is a sort of control chart used to track "count"-type data, often the total number of nonconformities per unit. On rare occasions, it is also used to keep track of all the events that take place in a given period of time.

C-charts are used to assess if a process is predictable and stable as well as to track the results of process improvements before and after they have been made. The C - chart is particularly useful when there are few actual flaws in the subgroup but many potential for defects exist.

Count type data, such as the number of non-conformities per unit, are monitored using a statistical quality control chart known as a C-Chart.

Hence, a C - chart is used for Number of defects per unit.

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Kuo's research emphasizes the role of learning in shaping an animal's behavior and highlights the importance of early experiences in shaping social behavior. This research has important implications for the fields of biology, animal behavior, and animal welfare.

Biologist Zing Yang Kuo's research demonstrated that a cat raised from birth with a rat in the same cage would not attack that specific rat or other rats. This research suggests that the cat's behavior towards rats is learned and not solely based on instinct. The results of this study have implications for understanding the role of early experiences in shaping an animal's behavior towards other species.

The study highlights the importance of socialization in shaping an animal's behavior. Animals raised in isolation from their own species may exhibit abnormal behaviors and may not develop appropriate social skills. In the case of the cat raised with the rat, the presence of the rat from an early age prevented the cat from perceiving the rat as prey.

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Answer:

997

Step-by-step explanation:

Well let's find the square root of 2011 because Paul and his wife are about the same age.

\(\sqrt{2011}\)

= 44.8

Paul is 45 and his wife is 44.

44 + 45 = 1980.

2011 - 1980

= 31

So the children are 15 and 16.

45 + 44 + 15 + 16

= 997

Paul and wife - 45 and 44

Children - 15 and 16

Thus,

13 years ago they would be 997.

Hope this helps :)

a) To find the displacement of the mass, we can use the equation of motion for a mass-spring system. The equation is given by: m * d^2x/dt^2 + b * dx/dt + k * x = 0 Where m is the mass, b is the damping coefficient, k is the spring constant, and x is the displacement from the equilibrium position.

In this case, the mass is 16 pounds, the spring length at equilibrium is 2 feet, and the spring length when displaced is 5 feet. So, the displacement is given by: x = 5 - 2 = 3 feet b) To determine if the motion is under-damped, over-damped, or critically damped, we need to compare the damping coefficient b to the critical damping coefficient, which is given by: b_critical = 2 * sqrt(m * k)

If b < b_critical, the motion is under-damped.
If b > b_critical, the motion is over-damped.
If b = b_critical, the motion is critically damped.

Since the question does not provide the damping coefficient, we cannot determine the type of damping. c) Without additional information about the damping coefficient or the specific equation of motion, we cannot graph x(t) on the given interval [-1,5].

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The total electric flux density at P1(2, 2, 5) is 66,102.3 Nm²/C.

To calculate the total electric flux density at P1(2, 2, 5), we'll use Gauss's law:  ΦE = q/ε₀. Where ΦE represents the total electric flux, q is the net charge inside the closed surface, and ε₀ is the permittivity of free space. We'll need to first determine the total charge enclosed by the Gaussian surface at P1(2,2,5).

Here are the steps to do so:

Step 1: Define the Gaussian surface

We'll define a Gaussian surface such that it passes through P1(2, 2, 5), as shown below: \(\vec{A}\) is the area vector, which is perpendicular to the Gaussian surface. Its direction is pointing outward.

Step 2: Calculate the net charge enclosed by the Gaussian surfaceThe Gaussian surface passes through the three planes x=2, y=4 and z=4, which carry charges of 14nC/m², 17nC/m² and 22nC/m², respectively. The Gaussian surface also passes through four line charges: 10nC/m, 15nC/m, 15nC/m, and 20nC/m.

We'll use these charges to find the total charge enclosed by the Gaussian surface.q = Σqinwhere qin is the charge enclosed by each part of the Gaussian surface. We can calculate qin using the surface charge density for the planes and the line charge density for the lines.

For example, the charge enclosed by the plane x = 2 isqin = σA

where σ = 14nC/m² is the surface charge density and A is the area of the part of the Gaussian surface that intersects with the plane. Since the Gaussian surface passes through x = 2 at y = 2 to y = 4 and z = 4 to z = 5, we can find A by calculating the area of the rectangle defined by these points: A = (4-2) x (5-4) = 2m²

Therefore,qx=2 = σxA = 14nC/m² x 2m² = 28nC

Similarly, the charge enclosed by the planes y = 4 and z = 4 are qy=4 = σyA = 17nC/m² x 2m² = 34nC and qz=4 = σzA = 22nC/m² x 2m² = 44nC, respectively.

For the lines, we'll use the line charge density and the length of the part of the line that intersects with the Gaussian surface. For example, the charge enclosed by the line at x = 10, y = 5 isqin = λlwhere λ = 10nC/m is the line charge density and l is the length of the part of the line that intersects with the Gaussian surface. The part of the line that intersects with the Gaussian surface is a straight line segment that goes from (2, 5, 5) to (10, 5, 5), which has a length of l = √((10-2)² + (5-5)² + (5-5)²) = 8m

Therefore,qx=10,y=5 = λl = 10nC/m x 8m = 80nC

Similarly, the charges enclosed by the other lines are:qy=6,x=10 = λl = 15nC/m x 8m = 120nCqy=5,x=9 = λl = 15nC/m x 8m = 120nCqz=6,x=9 = λl = 20nC/m x 8m = 160nCTherefore, the total charge enclosed by the Gaussian surface is:q = qx=2 + qy=4 + qz=4 + qy=5,x=10 + qy=6,x=10 + qy=5,x=9 + qz=6,x=9= 28nC + 34nC + 44nC + 80nC + 120nC + 120nC + 160nC = 586nC

Step 3: Calculate the total electric flux density at P1(2, 2, 5)We can now use Gauss's law to find the total electric flux density at P1(2, 2, 5).ΦE = q/ε₀ε₀ = 8.85 x 10^-12 F/mΦE = (586 x 10^-9 C)/(8.85 x 10^-12 F/m)ΦE = 66,102.3 Nm²/C

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