Which ordered pair is the solution to the system of equations?

−5x−3y=12
y=x−12

The statement is not true in general. The correct formula relating the second differential equations of y with respect to x and t is:

(d²y)/(dx²) = [(d²y)/(dt²)] / [(d²x)/(dt²)]

This formula is known as the Chain Rule for Second Derivatives, and it relates the rate of change of the slope of a curve with respect to x to the rate of change of the slope of the curve with respect to t. However, it is important to note that this formula only holds under certain conditions, such as when x is a function of t that is invertible and has a continuous derivative.

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The polar coordinates of the point (10, -10) can be determined by calculating the magnitude (r) and the angle (θ) in radians. In this case, the polar coordinates are (14.142, -0.7854).

To find the polar coordinates (r, θ) of a point given its rectangular coordinates (x, y), we use the following formulas:

r = √(x² + y²)

θ = arctan(y / x)

For the point (10, -10), the magnitude (r) can be calculated as:

r = √(10² + (-10)²) = √(100 + 100) = √200 = 14.142

To find the angle (θ), we can use the arctan function:

θ = arctan((-10) / 10) = arctan(-1) ≈ -0.7854

Therefore, the polar coordinates of the point (10, -10) are (14.142, -0.7854), with the angle expressed in radians.


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Answer:

m² - 100 = -99

Step-by-step explanation:

Two numbers are 10 units away from the midpoint m in different directions.

So, one number is (m + 10 ) away form 'm' and another is ( m + 10) away from 'm' in opposite direction.

(m + 10) ( m-10) = -99

m² - 10² = -99

m² - 100 = -99

Answer:

Yes

12 * (12 * 18) = b will give the total number of brownies to be made

Step-by-step explanation:

Here, we want to select which of the equations will give the number of brownies to be made

The total number of brownies is b

For each pan, we have 18 rows , with 12 per row

So the total number of brownies per pan is 12 * 18

Since they are making 12, the total number of brownies b will be;

12 * (12 * 18) = b

Answer:

260

570

850

920

410

710

660

120

that all for now they out of order

Step-by-step explanation:

Answer:

Step-by-step explanation:

You better give brainliest for that also please refrain from these type of questions. I bet people would apprieate it

Responder:

$ 555,911.5

Explicación paso a paso:

Dado

Principal = $ 545,680

Interés = 2,25%

Tiempo = 10 meses = 10/12 años

Debemos buscar la cantidad después de 10 meses.

Monto = Principal + Intereses

Interés = PRT / 100

Interés = 545,680 * 2,25 * 10/1200

Intereses = 12,277,800 / 1200

Interés = 10.231,5

Cantidad = 545,680 + 10,231.5

Cantidad = 555,911.5

por lo tanto, la cantidad después de 10 meses es $ 555,911.5

The teacher can use a combination of these methods to help the students understand that a triangle is equivalent to half a square.

In order to help the students understand that the triangle is equivalent to half a square, the teacher can adopt different methods, including the following:

1. Drawing diagrams of the triangle and the square to show the comparison. The teacher can draw diagrams of a triangle and a square on the board and label the different parts.

They can then show the students that a triangle can be created by halving the square diagonally. This way, the students will be able to visualize the comparison and understand it better.

2. Demonstrating the concept practically. The teacher can also demonstrate the concept by using physical objects such as paper or cardboard.

They can show the students how to create a triangle by folding a square diagonally and cutting it along the fold. This way, the students will be able to see the practical application of the concept.

3. Using real-world examples. The teacher can also use real-world examples to help the students understand the concept better.

For example, they can show the students pictures of tents or rooftops that are shaped like triangles and explain how they are related to squares.

4. Conducting group discussions. The teacher can conduct group discussions where the students can share their understanding of the concept and ask questions.

This way, the students will be able to learn from each other and clarify any doubts they may have.

Overall, the teacher can use a combination of these methods to help the students understand that a triangle is equivalent to half a square.

The key is to use different approaches that cater to different learning styles and to encourage the students to participate actively in the learning process.

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Answer:

Pretty sure it's four hundred twenty-one and seven-eighths ft2 given the information you gave.

Step-by-step explanation:

The area of the parallelogram is \(421 \frac{7}{8} \; ft^2\) whose base is \(22 \frac{1}{2}\) ft and height is \(18 \frac{3}{4}\) ft.

Thus, option (b) is correct.

Given:

Base of parallelogram = 22  1/2 feet

                                     = 45/2

                                     = 22.5 feet

Height of parallelogram = 18 3/4 feet

                                        = 18.75 feet

Now, the formula for area of a parallelogram

Area = base × height

Substituting the value base= 22.5 feet and height = 18.375 feet into the formula

Area = 22.5 feet × 18.75 feet

         = 421.875 square feet

         = \(421 \frac{7}{8} \; ft^2\)

Therefore, the area of the parallelogram is 421.875 square feet.

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Answer:

To compare who saves the most of their salary each month among Amy, John, and Emily, we need to calculate the amount of salary each person saves.

Let's assume that the monthly salary of each person is 'S'. Then we can calculate the amount saved by each person as follows:

Amy:

Amount saved = 20% of S = 0.2S

Amount spent = S - 0.2S = 0.8S

John:

Amount spent = 2/5 of S = (2/5)S

Amount saved = S - (2/5)S = (3/5)S

Emily:

Let's assume that Emily saves '5x' and spends '8x' of her monthly salary.

Then, according to the question, we have:

Amount saved = 5x

Amount spent = 8x

We know that the ratio of the amount saved to the amount spent is 5:8, so we can write:

Amount saved / Amount spent = 5/8

Substituting the values of amount saved and amount spent, we get:

5x / 8x = 5/8

5x = (5/8) x 8x

5x = 5x

Therefore, the ratio of amount saved to amount spent is equal to 5:8. This means that Emily saves 5/13 of her monthly salary and spends 8/13 of her monthly salary.

So, the amount saved by each person is:

Amy: 0.2S

John: (3/5)S

Emily: 5/13 of S

Now, we need to compare these amounts to find out who saves the most.

To compare these amounts, we can write them in terms of a common denominator:

Amy: 0.2S

John: (3/5)S = (0.6)S

Emily: (5/13)S = (0.3846)S (approx.)

Therefore, we see that John saves the most of his salary each month, followed by Amy and then Emily.

Working out:

Let's assume that each person earns $1000 per month.

Amy:

Amount saved = 20% of $1000 = $200

Amount spent = $800

John:

Amount spent = 2/5 of $1000 = $400

Amount saved = $1000 - $400 = $600

Emily:

Let's assume that Emily saves $5x and spends $8x of her monthly salary.

Then, we have:

Amount saved = $5x

Amount spent = $8x

We know that the ratio of the amount saved to the amount spent is 5:8, so we can write:

$5x / $8x = 5/8

Solving for x, we get:

x = 8/13

Substituting the value of x, we get:

Amount saved = $5 x (8/13) x $1000 = $384.62 (approx.)

Amount spent = $8 x (8/13) x $1000 = $615.38 (approx.)

Therefore, we see that John saves the most of his salary each month, followed by Amy and then Emily.

Using Green's Theorem, the counterclockwise circulation of F around the closed curve C is 14.

To compute the counterclockwise circulation of the vector field F = xy i + xj around the closed curve C, we can apply Green's Theorem.

First, let's parameterize the three sides of the triangle C.

For the side from (0, 0) to (2, 0), we have x = t and y = 0, where t ranges from 0 to 2.

For the side from (2, 0) to (0, 10), we have x = 2 and y = 10t, where t ranges from 0 to 1.

For the side from (0, 10) to (0, 0), we have x = 0 and y = 10 - 10t, where t ranges from 0 to 1.

Now, let's calculate the circulation along each side and sum them up:

Circulation = ∮C F · dr = ∫_C (xy dx + x dy)

For the first side, we have:

∫_(C1) (xy dx + x dy) =

\(\int\limits^2_0 (t * 0 dt + t dt) = \int\limits^2_0 t dt = [t^2/2]_{(0 \ to\ 2)} = 2\)

For the second side, we have:

∫_(C2) (xy dx + x dy) =

\(\int\limits^1_0 (2 * (10t)\ dt + 2 dt) = \int\limits^1_0 (20t + 2) dt = [10t^2 + 2t]_{(0 \ to\ 1)} = 12\)

For the third side, we have:

∫_(C3) (xy dx + x dy) =

\(\int\limits^1_0 (0 * (10 - 10t)\ dt + 0 \ dt) = 0\)

Finally, summing up the contributions from each side, we get:

Circulation = 2 + 12 + 0 = 14

Therefore, the counterclockwise circulation of F around the closed curve C is 14.

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Answer:

Yes you are correct :)

Step-by-step explanation:

Used a graphing calculator

The measure of angle Z, considering the similarity of triangles ABC and XYZ, is given as follows:

a. 123.2º.

Similar triangles are triangles that share these two features listed as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the value of x is obtained as follows:

23 + x + 3 + 4x = 180

5x = 154

x = 154/5

x = 30.8.

Angle Z is the equivalent angle to angle C, hence it's measure is given as follows:

m < Z = 4x = 4 x 30.8 = 123.2º.

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Answer:

0.4/1

Step-by-step explanation:

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 30

On solving the provided question, we can say that Length of the wooden strip required to frame the photograph= Perimeter of the photograph = 106 cm

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

The length of the photograph = 32cm

The breadth of the photograph = 2 lcm

Length of the wooden strip required to frame the photograph= Perimeter of

the photograph

= 2 x (length + breadth)

= 2 x (32 +21)cm

= 2 53cm

= 106cm

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Answer:

8x

Step-by-step explanation:

8x

Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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The probability that the first person who subscribes to the five-second rule is the 5th person you talk to is q⁴ * p.

To calculate the probability that the first person who subscribes to the five-second rule is the 5th person you talk to, we need to consider the following terms: probability, independent events, and complementary events.

Step 1: Determine the probability of a single event.
Let's assume the probability of a person subscribing to the five-second rule is p, and the probability of a person not subscribing to the five-second rule is q. Since these are complementary events, p + q = 1.

Step 2: Consider the first four people not subscribing to the rule.
Since we want the 5th person to be the first one subscribing to the rule, the first four people must not subscribe to it. The probability of this happening is q * q * q * q, or q⁴.

Step 3: Calculate the probability of the 5th person subscribing to the rule.
Now, we need to multiply the probability of the first four people not subscribing (q^4) by the probability of the 5th person subscribing (p).

The probability that the first person who subscribes to the five-second rule is the 5th person you talk to is q⁴ * p.

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Answer:

Step-by-step explanation:

Answer: ABCD is a quadrilateral

To prove : ∠AOB=

2

1

​

(∠C+∠D)

AO and BO is bisector of A and B

∠1=∠2∠3=∠4...(1)

∠A+∠B+∠C+∠D=360

(Angle sum property)

2

1

​

(∠A+∠B+∠C+∠D)=180...(2)

In △AOB

∠1+∠3+∠5=

2

1

​

(∠A+∠B+∠C+∠D)

∠1+∠3+∠5=∠1+∠3+

2

1

​

(∠C+∠D)

∠AOB=

2

1

​

(∠C+∠D)

​

Explanation: In a quadrilateral ABCD. AO and BO are bisectors of angle A and angle B respectively. Prove that ∠AOB=

2

1

​

{∠C+∠D}.

The probabilities of the independent events are as given as follows:

Since all the events are independent events, the probabilities are calculated as follows:

P (B) = 3/10, P (A and B) = 27/200; find P (A)

P (A) =  P (A and B) / P (B)

P (A) = (27/200) / (3/10)

P (A) = 9/20

2. P (A)= 2/5, P (A and B)= 3/10, find P (B)

P (B) = (3/10) / (2/5)

P (B) = 3/4

3. P (B) = 0.25, P (A and B) = 0.1, find P (A)

P (A) = 0.1/0.25

P (A) = 0.4

4. P (A) = 0.3, P (A and B) = 0.075, find P (B)

P (B) = 0.075/0.3

P (B) = 0.25

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Answer:

Step-by-step explanation:

Rewrite the equation as  

8(y+4)=m

Divide each term in 8(y+4)=m by 8

and simplify

y+4=\(\frac{m}{8}\)

Subtract  

4 from both sides of the equation

y=\(\frac{m}{8}\)−4

Answer: 1,127 km.

Disclaimer: There are a plethora of ways to solve this problem, but I decided to utilize proportions to solve it, as I believe that it is the easiest method to solve these types of questions.

1. Set up your proportion

2. Set up a basic algebraic equation: 1x=700

In other words, what times 1 is 700?

Multiply 1*700, which is 700, and do the same for the bottom.

1.61*700= 1,127

3. The final answer is 1,127 kilometers. Please refer to the pictures attached for a more visual and thorough explanation. Cross mutiplying could also be used. Simply cross multiply in your proportion to get your answer.

Answer:

The image is not clear but get the idea

The trip would have taken 6 hours.

(300 mi) / (50 mi/h) = 6 h

Bayes' Theorem states that the probability of an event A occurring, given that event B has already occurred, is equal to the probability of event B occurring given that event A has already occurred, times the probability of event A occurring, divided by the probability of event B occurring.

In this problem, we are trying to determine the probability that coin B was selected, given that the selected coin came up heads 3 times. We can use Bayes' Theorem to calculate this probability as follows: P(B|HHH) = P(HHH|B)P(B)/P(HHH)

where:

We are given that the probabilities of selecting coin A and coin B are P(A) = 0.1 and P(B) = 0.9. We are also given that the probabilities of getting heads on coin A and coin B are P(H|A) = 0.6 and P(H|B) = 0.2.

The probability that the selected coin came up heads 3 times, given that coin B was selected, is P(HHH|B) = (0.2)^3 = 0.008. The probability that the selected coin came up heads 3 times, regardless of which coin was selected, is P(HHH) = P(HHH|A)P(A) + P(HHH|B)P(B) = (0.6)^3(0.1) + (0.2)^3(0.9) = 0.0216.

Plugging in these values into Bayes' Theorem, we get:

P(B|HHH) = (0.2)^3(0.9)/(0.008 + 0.0216) = 0.0072/0.0288 = 0.25

Therefore, the probability that coin B was selected, given that the selected coin came up heads 3 times, is approximately 0.25.

Bayes' Theorem is a powerful tool for calculating the probability of an event occurring, given that another event has already occurred. It is used in a wide variety of applications, including medical diagnosis, fraud detection, and weather forecasting.

In this problem, we used Bayes' Theorem to calculate the probability that coin B was selected, given that the selected coin came up heads 3 times. We were able to do this by calculating the probability of each event occurring, and then using Bayes' Theorem to combine these probabilities.

The result of our calculation was that the probability that coin B was selected, given that the selected coin came up heads 3 times, is approximately 0.25. This means that if we see a coin that has come up heads 3 times, we are approximately 25% likely to be looking at coin B.

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The given function f(x) = x² + x + 6 has a minimum value. Using the formula x = -b/2a, we find the x-coordinate of the minimum point as -1/2. Substituting this value back into the function, we get a y-coordinate of 5.75. Therefore, the parabola has a minimum value of 5.75. The correct answer is D.

The given function is f(x) = x² + x + 6. We can determine the maximum or minimum value of a parabola by analyzing its quadratic term (x²) coefficient.

In this case, the coefficient of the quadratic term is positive (1), indicating that the parabola opens upwards and has a minimum value.

To find the x-coordinate of the minimum point, we can use the formula x = -b/2a, where a is the coefficient of the quadratic term and b is the coefficient of the linear term.

For our function f(x), a = 1 and b = 1, so the x-coordinate of the minimum point is x = -1/(2*1) = -1/2.

Substituting this value back into the function, we can find the y-coordinate of the minimum point: f(-1/2) = (-1/2)² + (-1/2) + 6 = 1/4 - 1/2 + 6 = 5.75.

Therefore, the parabola modeled by function f has a minimum value of 5.75. Hence, the correct answer is D.

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The correct question would be as

Select the correct answer.

Consider function f.

f(x) = x² = x + 6

Which statement is true about the parabola modeled by function f?

A. The parabola has a maximum value of 0.5.

B. The parabola has a maximum value of 5.75.

C. The parabola has a minimum value of 0.5.

D. The parabola has a minimum value of 5.75.

Answer:

c

Step-by-step explanation:

yea im so gud at math ikr