help me please I need help

If ABC is a triangle, which when plotted on the cartesian coordinate system, has it's vertices at A(4, 1), B(-3, -2), and C(-1, 3), then the perimeter of triangle ABC will be [√58/(√2 - 1)]

As per the question statement, ABC is a triangle, which when plotted on the cartesian coordinate system, has it's vertices at A(4, 1), B(-3, -2), and C(-1, 3).

We are required to calculate the perimeter of triangle ABC.

To solve this question, first we need to calculate the distances between AB, BC ad AC, which are the three sides of our concerned triangle ABC, and then add them up to obtain our desired answer. And to calculate the lengths of AB, BC ad AC, we will need to use the distance formula which goes as,

"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by

√[(x₂ - x₁)² + (y₂ - y₁)²]

Considering points A(4, 1) and B(-3, -2), we can say that [(x₁, y₁) = (4, 1)] and [(x₂, y₂) = (-3, -2)]. Therefore, distance AB = √[{(-3) - 4}² + {(-2) - 1}²]

Or, AB = √[{-(3 + 4)}² + {-(2 + 1)}²]

Or, AB = √[(-7)² + (-3)²]

Or, AB = √[(49 + 9)]

Or, AB = √58

Similarly considering points A(4, 1) and C(-1, 3), we can say that

[(x₁, y₁) = (4, 1)] and [(x₂, y₂) = (-1, 3)].

Therefore, distance AB = √[{(-1) - 4}² + (3 - 1)²]

Or, AC = √[{-(1 + 4)}² + (3 - 1)}²]

Or, AC = √[(-5)² + (2)²]

Or, AC = √[(25 + 4)]

Or, AC = √29

Finally considering points B(-3, -2) and C(-1, 3), we can say that

[(x₁, y₁) = (-3, -2)] and [(x₂, y₂) = (-1, 3)].

Therefore, distance BC = √[{(-1) - (-3)}² + {3 - (-2)}²]

Or, BC = √[{-(1) + 3}² + (3 + 2)²]

Or, BC = √[(3 - 1)² + (5)²]

Or, BC = √[(4 + 25)]

Or, BC = √29

Therefore, the perimeter of Triangle ABC  = (AB + BC + AC)

Or, perimeter of Triangle ABC  = (√58 + √29 + √29)

Or, perimeter of Triangle ABC  = [√(29 * 2) + √29 + √29]

Or, perimeter of Triangle ABC  = [(√29*√2) + √29 + √29]

Or, perimeter of Triangle ABC  = √29(√2 + 1 + 1)

Or, perimeter of Triangle ABC  = √29(√2 + 2)

Or, perimeter of Triangle ABC  = (√29*√2)(1 + √2)

Or, perimeter of Triangle ABC  = (√58)(1 + √2)

Or, perimeter of Triangle ABC  = \(\frac{\sqrt{58} (1+\sqrt{2})(1-\sqrt{2}) }{(1-\sqrt{2})} =\frac{\sqrt{58} [(1)^{2}-(\sqrt{2})^2 }{(1-\sqrt{2})}}\)

Or, perimeter of Triangle ABC  = \(\frac{\sqrt{58} [(1-2) }{(1-\sqrt{2})}}=\frac{-\sqrt{58}}{(1-\sqrt{2})}}=\frac{\sqrt{58}}{(\sqrt{2}-1)}}\)

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Let's solve the problems and provide the answers with the correct number of significant figures:

(4.307 × 10^4) × (6.2 × 10^-3)

Multiplying the numbers:

(4.307 × 6.2) × (10^4 × 10^-3) = 26.6974 × 10^1

Since the result is in scientific notation, we multiply the decimal part by the power of 10:

26.6974 × 10^1 = 266.974

To express the answer with the correct number of significant figures, we consider the least number of significant figures in the original values, which is three significant figures in this case.

Therefore, the answer is 267 with three significant figures.

26.127 + 3.9 + 0.0324

Adding the numbers:

26.127 + 3.9 + 0.0324 = 30.0594

To express the answer with the correct number of significant figures, we consider the least number of decimal places in the original values, which is one decimal place in this case.

Therefore, the answer is 30.1 with one decimal place.

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Answer:

hi!

Step-by-step explanation:

The principal reduction in the first payment is $1,995.85. The current balance column shows the remaining loan balance after each payment, and the cumulative interest column displays the total interest paid up to that point.

1. To calculate the principal reduction that will occur in the first payment, we need to determine the monthly payment amount and the interest portion of that payment.

First, let's calculate the loan amount by subtracting the down payment (20%) from the total home price:

Loan amount = $416,000 - 20% of $416,000

Loan amount = $416,000 - ($416,000 * 0.2)

Loan amount = $416,000 - $83,200

Loan amount = $332,800

Next, let's calculate the monthly interest rate. Since the interest is compounded monthly, we divide the annual interest rate by 12 months:

Monthly interest rate = 6.8% / 12

Monthly interest rate = 0.068 / 12

Monthly interest rate = 0.00567

Now, we can calculate the monthly payment using the loan amount, loan term, and monthly interest rate, using the formula for a fixed-rate mortgage:

Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of payments))

Monthly payment = ($332,800 * 0.00567) / (1 - (1 + 0.00567)^(-30 * 12))

Monthly payment = $1,995.85

To find the principal reduction in the first payment, we subtract the interest portion from the monthly payment. The interest portion can be calculated by multiplying the current loan balance by the monthly interest rate:

Interest portion = Current loan balance * Monthly interest rate

Principal reduction = Monthly payment - Interest portion

Now let's calculate the principal reduction in the first payment:

Principal reduction = $1,995.85 - (Current loan balance * 0.00567)

Note: Since we haven't started making payments yet, the current loan balance is equal to the initial loan amount.

Therefore, the principal reduction in the first payment is the full monthly payment amount:

Principal reduction = $1,995.85

2. Here is a sample spreadsheet that shows each payment, the principal and interest components, the current balance, and the cumulative interest paid:

| Payment | Monthly Payment | Principal Payment | Interest Payment | Current Balance | Cumulative Interest |

|---------|----------------|------------------|-----------------|-----------------|---------------------|

| 1       | $1,995.85      | $332.80          | $1,663.05       | $332,800.00     | $1,663.05           |

| 2       | $1,995.85      | $333.36          | $1,662.49       | $332,466.64     | $3,325.54           |

| 3       | $1,995.85      | $333.92          | $1,661.93       | $332,132.72     | $4,987.47           |

| ...     | ...            | ...              | ...             | ...             | ...                 |

| n       | $1,995.85      | $x               | $y              | $z              | $Cumulative_interest |

This spreadsheet demonstrates the payment schedule over the 30-year period, including the breakdown of principal and interest components for each payment.

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Answer:

r = \(\sqrt{7}\), centre = (6, - 4 )

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

with (h, k) the coordinates of the centre and r the radius

(x - 6)² + (y + 4)² = 7 ← is in standard form

with centre = (6, - 4) and r² = 7 , hence r = \(\sqrt{7\)

Completing the equalities using the given options, we have:

\(a) sin^(-1)(1) = 90°\\b) cos^(-1)(1/2) = 60°\\c) tan^(-1)(√3) = 60°\)

a) \(sin^(-1)(1) = 90°\)

The inverse sine function, \(sin^(-1)(x)\)gives the angle whose sine is equal to x. In this case, we are looking for the angle whose sine is equal to 1. The angle that satisfies this condition is 90 degrees, so\(sin^(-1)(1) = 90°\).

b) \(cos^(-1)(1/2) = 60°\)

The inverse cosine function, cos^(-1)(x), gives the angle whose cosine is equal to x. Here, we are looking for the angle whose cosine is equal to 1/2. The angle that satisfies this condition is 60 degrees, so \(cos^(-1)(1/2)\)= 60°.

c) \(tan^(-1)(√3) = 60°\)

The inverse tangent function, tan^(-1)(x), gives the angle whose tangent is equal to x. In this case, we are looking for the angle whose tangent is equal to √3. The angle that satisfies this condition is 60 degrees, so tan^(-1)(√3) = 60°.

Completing the equalities using the given options, we have:

\(a) sin^(-1)(1) = 90° b) cos^(-1)(1/2) = 60°c) tan^(-1)(√3) = 60°\)

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a) The completed equalities are:

sin-¹(x) = 30°, sin-¹(x) = 45°, sin-¹(x) = 60°

b) The completed equalities are:

cos-¹(x) = 30°, cos-¹(x) = 45°, cos-¹(x) = 60°

c) The completed equalities are:

tan-¹(x) = 30°, tan-¹(x) = 45°, tan-¹(x) = 60°. C.

a) sin-¹(x) = 30°, 45°, 60°

The inverse sine function, sin-¹(x), gives the angle whose sine is equal to x.

Let's find the angles for each option given:

sin-¹(x) = 30°:

If sin-¹(x) = 30°, it means that sin(30°) = x.

The sine of 30° is 0.5, so x = 0.5.

sin-¹(x) = 45°:

If sin-¹(x) = 45°, it means that sin(45°) = x.
The sine of 45° is √2/2, so x = √2/2.

sin-¹(x) = 60°:

If sin-¹(x) = 60°, it means that sin(60°) = x.

The sine of 60° is √3/2, so x = √3/2.

The completed equalities are:

b) cos-¹(x) = 30°, 45°, 60°

The inverse cosine function, cos-¹(x), gives the angle whose cosine is equal to x.

Let's find the angles for each option given:

cos-¹(x) = 30°:

If cos-¹(x) = 30°, it means that cos(30°) = x.

The cosine of 30° is √3/2, so x = √3/2.

cos-¹(x) = 45°:

If cos-¹(x) = 45°, it means that cos(45°) = x.
The cosine of 45° is √2/2, so x = √2/2.

cos-¹(x) = 60°:

If cos-¹(x) = 60°, it means that cos(60°) = x.

The cosine of 60° is 0.5, so x = 0.5.

Therefore, the completed equalities are:

c) tan-¹(x) = 30°, 45°, 60°

The inverse tangent function, tan-¹(x), gives the angle whose tangent is equal to x.

Let's find the angles for each option given:

tan-¹(x) = 30°:

If tan-¹(x) = 30°, it means that tan(30°) = x.

The tangent of 30° is 1/√3, so x = 1/√3.

tan-¹(x) = 45°:

If tan-¹(x) = 45°, it means that tan(45°) = x.

The tangent of 45° is 1, so x = 1.

tan-¹(x) = 60°:

If tan-¹(x) = 60°, it means that tan(60°) = x.

The tangent of 60° is √3, so x = √3.

The completed equalities are:

tan-¹(x) = 30°, tan-¹(x) = 45°, tan-¹(x) = 60°. c)

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Answer:

Option A

Step-by-step explanation:

Any number that can be written in the form of a fraction \((\frac{p}{q})\) will be a rational number.

From the given options,

Option (A)

Given expression \(\sqrt{\frac{x^2+2x-5}{2x^2-3x+4}}\) can't be written in the form of a fraction \((\frac{p}{q})\) (Without square root).

Therefore, given function is not a rational function.

Rest all options represent a rational function.

Option A will be the answer.  

Answer:

Children = 51

Adults = 42

Students= 84

Step-by-step explanation:

Children = $2

Students = $3

Adults = $4

Total sales = $522

Total people who attended = 177

Adults =a

Students = s= 2a

Children = c

c+s+a = 177 (1)

2c+3s+4a=522 (2)

Substitute s=2a into the equations

c + 2a + a = 177

c + 3a = 177 (3)

2c + 3(2a) + 4a = 522

2c + 6a + 4a = 522

2c + 10a = 522 (4)

c + 3a = 177 (3)

2c + 10a = 522 (4)

Multiply (3) by 2

2c + 6a = 354 (3b)

2c + 10a = 522

Subtract (3b) from (4)

10a - 6a = 522 - 354

4a = 168

Divide both sides by 4

a= 168/4

= 42

a= 42

s= 2a

= 2(42)

= 84

s= 84

Substitute the value of s and a into (1)

c+s+a = 177 (1)

c + 84 + 42 = 177

c + 126 = 177

c = 177 - 126

= 51

c=51

Children = 51

Adults = 42

Students= 84

144x² - 24x + 1 = 12²x² - 24x + 1 = (12x)² - 2(12x) + 1² = (12x - 1)²

Answer:

5x + 15

Step-by-step explanation:

Given

9x + 6 - 4x + 9 ← collect like terms

= (9x - 4x) + (6 + 9)

= 5x + 15

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(a) The predictor variable is Fall in feet and the response variable is Duration in seconds.

(b) The slope is in seconds per foot.

(c) The slope may be negative, as greater drop heights generally result in longer travel times.

(a) The predictor variable in this regression is Drop, which represents the drop height of the roller coaster, in feet, in feet. The response variable is Duration, which represents the duration of the trip, in seconds, in seconds.

(b) The units of slope in this regression are seconds per foot. This means that for each unit of increase in descent height in feet, the travel time will increase or decrease the value of the slope, measured in seconds per foot.

(c) The slope can be negative, as greater drop heights generally result in longer ride times, and the Tower of Terror roller coaster, which was exceptionally short despite its large drop height, has were removed from the analysis.

Therefore, the remaining 90 roller coasters in the dataset likely exhibit a negative relationship between drop height and time, meaning that as drop height increases, ride time decreases .

The Low R-value squared 29.4% means that the relationship between roller coaster drop and ride time in the data set is highly variable, but the negative slope indicates a general downward trend.

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Mining has a negative effect on home prices in the county, reducing the price of a 2,000-square-foot house with three bedrooms by approximately $8,400.

Comparative statics is a method used to analyze how changes in one variable affect another. In this case, we are examining the effect of mining on home prices in the county. We are given that the company mines 300,000 tons of coal per year, which is worth $79 per ton. Therefore, the annual value of coal production is 300,000 tons * $79 = $23,700,000.

Now, let's consider the effect on home prices. We are given that the average price for a 2,000-square-foot house with three bedrooms located more than 20 km away from the mining site is $210,000. However, for a similar house within 4 km of the mine, the price is 4 percent lower.

To calculate the price reduction, we can multiply $210,000 by 4 percent (0.04). The reduction in price is $210,000 * 0.04 = $8,400. Therefore, the effect of mining on home prices in the county is a decrease of approximately $8,400 for a 2,000-square-foot house with three bedrooms.

It's important to note that this analysis assumes a linear relationship between the proximity to the mine and home prices. Other factors, such as environmental concerns or changes in the local economy, may also influence home prices in the area.

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a. The ODE is solved by finding an integrating factor.

b. The ODE is shown to be exact, and then solved as an exact equation using a potential function.

c. The domain of the solution is (0, ∞), representing positive and non-zero values of x.

a. To solve the given ODE using an integrating factor, we first rewrite it in the form M(x, y)dx + N(x, y)dy = 0, where M(x, y) = y/x + 6x and N(x, y) = ln(x) - 2. By finding an integrating factor, we can transform the equation into an exact equation.

b. To show that the ODE is exact, we calculate the partial derivatives: ∂M/∂y = 1/x and ∂N/∂x = 1/x. Since these partial derivatives are equal, the ODE is indeed exact. We proceed to solve the ODE as an exact equation by finding the potential function.

c. To find the domain of the solution, we consider the restrictions imposed by the natural logarithm and the division by x. Since the natural logarithm is only defined for positive values, we have x > 0.

Additionally, the division by x in the equation ln|x|/x = 2 - 2y - D requires that x ≠ 0. Therefore, the domain of the solution is the interval (0, ∞) in interval notation, indicating that x must be positive and non-zero.

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Answer:

D

Step-by-step explanation:

(x+7)²+(y-12)²=9

____________

Answer:

\(\text{D. }(x+7)^2+(y-12)^2=9\)

Step-by-step explanation:

The equation of a circle with radius \(r\) and center \((h, k)\) is given by:

\((x-h)^2+(y-k)^2=r^2\)

The probability of the intersection of two mutually exclusive events, such as A and B, is always zero. Therefore, P(A∩B) = 0.

Mutually exclusive events are events that cannot occur simultaneously. If events A and B are mutually exclusive, it means that if one event happens, the other event cannot happen at the same time.

In such cases, the intersection of these events is an empty set, and the probability of the intersection is zero.

Since A and B are mutually exclusive with given probabilities P(A) = 0.3 and P(B) = 0.5, we can conclude that the probability of their intersection, P(A∩B), is equal to 0.

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Answer:

-20

Step-by-step explanation:

because -32 plus 12 is -20

hope that helps!!

a) The cable provider would use a discrete uniform distribution to model the selection of customers in the telephone exchange b) The probability that a randomly selected number from the 452 exchange belongs to a new business that does not subscribe to digital TV is 1

To model the selection of customers in a particular telephone exchange, the cable provider would use a uniform distribution. This is because they are selecting numbers with equal probability from a set of 10,000 possible numbers. In a uniform distribution, each value has an equal chance of being selected, making it suitable for this scenario

Second, we are given that the new business incubator was assigned the 500 numbers between 452-2000 and 452-2499, and these businesses don't subscribe to digital TV. To find the probability of randomly selecting a number from this range that doesn't subscribe to digital TV, we need to determine the proportion of numbers in that range that meet the condition.

In this case, there are 500 numbers in the range 452-2000 to 452-2499, and all of them don't subscribe to digital TV. Since we are selecting from a specific range, the probability of selecting a number that doesn't subscribe to digital TV is 100% or 1.

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Lowes Depot uses a (Q, R) policy to manage its stock levels for a popular mini drill with a replacement lead time of 14 weeks. Historical demand during the replacement lead time is normally distributed with a mean of 90.4616 and a standard deviation of 14.3795. Each drill costs $6, and backorders result in a loss of goodwill of $10. The supplier charges $15 per order, and holding costs are based on a 30% annual interest rate.

To determine the optimal order quantity Q and reorder point R, we need to use the (Q, R) policy. The policy specifies that when the inventory level reaches the reorder point R, an order of size Q is placed. We need to determine Q and R such that the total annual cost is minimized.

The total annual cost consists of three components: ordering costs, holding costs, and shortage costs. Ordering costs are the costs associated with placing an order, which is given by (number of orders per year) x (ordering cost per order). The number of orders per year is the annual demand divided by the order quantity, which is Q. The ordering cost per order is $15. Therefore, the ordering cost is 15 X (Demand rate/Q).

Holding costs are the costs associated with holding inventory, which is given by (inventory level) x (holding cost per unit per year). The holding cost per unit per year is 30% of the unit cost, which is 0.3 x $6 = $1.8.

Shortage costs are the costs associated with backordering, which is given by (expected shortage per year) x (shortage cost per unit). The expected shortage per year is the probability of a stockout during the lead time multiplied by the expected demand

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Answer:

Samantha's age = 27 years

Step-by-step explanation:

As Samantha is one year less than twice her brother Jack’s age.

As the sum of their ages is 41.

Thus, the equation become

x+2x-1 = 41

3x-1 = 41

3x = 42

Dividing both sides by 3

x = 14

It indicates that Jack's age = 14 years

Therefore,

Samantha's age = 2x-1 = 2(14)-1 = 27 years

Answer: B

Step-by-step explanation:

Answer:

I think it will be D, because you will be decreasing 0.25x and increasing 0.75x, you will add 0.25x to -0.25x to get rid of 0.25x. Then you will need to do the same thing to the other side. You will add 0.25x to 0.75x so you will be increasing 0.75 since you will be adding to it.

Step-by-step explanation:

X – 0.25x = 0.75x

X-0.25x+0.25x=0.75x+0.25x

X= 1.00x

All you need to do is add 0.25x to both -0.25x and positive 0.75x. That way it will be equal.

So, I believe it will be D

Tu tenías $825.

Dado que tu tenías $50, tu mamá te dio $100, tu papá te dio $500, tus tíos te dieron $100 y tu tenías otros $75, para determinar cuanto dinero tenías en total se debe realizar la siguiente operación matemática, consistente en una suma:

Por lo tanto, en total tu tenías $825.

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The steps in Mia's method were smaller than in Jenna's, which was an advantage.

The same result will be obtained by adding the products of multiplying the sum of two or more addends by a number as opposed to multiplying each addend separately by the number.

The direct algorithm process suggested in this paper is known as the direct calculation method (DCM), and it can deal with using confinement loss as an incremental step to simulate the effect of moving tunnel face excavation, calculating the stresses and displacements in each step, and drawing the results.

Jenna's technique:

\(\begin{aligned}&5(30+4) \\&=(5)(30)+(5)(4) \\&=150+20 \\&=170\end{aligned}\)

Mia's technique:

\(\begin{aligned}&5(30+4) \\&=(5)(34) \\&=170\end{aligned}\)

Both used the right approach, albeit in different ways.

One uses the distributive property, whereas the other uses direct calculation.

Consequently, Jenna and Mia came to the same conclusion.

However, Mia's approach has one advantage over Jenna's: it requires fewer steps.

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Answer:

Everything is in the image

Step-by-step explanation:

Answer:

12.2

Step-by-step explanation:

Answer:

A) k = 0.037

B) 186°F

Step-by-step explanation:

List initial (T₀) and air (Tₐ) temperature

\(T_0=280^\circ\\T_a=67^\circ\\\)

Part A

\(T=T_a+(T_0-T_a)e^{-kt}\\193^\circ=67^\circ+(208^\circ-67^\circ)e^{-k(3)}\\193=67+141e^{-3k}\\126=141e^{-3k}\\\frac{126}{141}=e^{-3k}\\\ln(\frac{126}{141})=-3k\\-\frac{1}{3}\ln(\frac{126}{141})=k\\k\approx0.037\)

Part B

\(T=T_a+(T_0-T_a)e^{-kt}\\T=67+(208-67)e^{-0.037(4.5)}\\T\approx186^\circ\text{F}\)

test static=0.0913,P-value=0.37

answer

Amar owes $2,000 on his credit card with a minimum percentage of 4% or $60, whichever is higher.

The Minimum Payment due is $ 80 as it is higher from the minimum payment of $60.

Given :

Credit Card amount = $2000

Minimum Percentage = 4%

By using the below formula we can find the minimum balance

Minimum Balance = Credit Card Amount * Minimum Percentage

Minimum Balance = $2000 * 4%

            = $80

So According to the question Amar owes $2000 on his credit card with a minimum percentage of 4% or a minimum payment of $60, whichever is higher.

So the minimum percentage of 4% or minimum balance is higher than $60.

So that’s why the minimum payment due is $80.

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