(2 x 1016) + (7 x 1016)

The additional information that could be used to prove congruence using AAS or ASA is: Angle A ≅ Angle T and AC (ASA) Angle A ≅ Angle T and BC ≅ PQ (ASA).

To prove that two triangles are congruent using the Angle-Angle-Side (AAS) or Angle-Side-Angle (ASA) criteria, we need specific information about the angles and sides of the triangles.

In this case, we are given three options, and we need to determine which combination of angles and sides would be sufficient to prove congruence using AAS or ASA.

To prove congruence using AAS, we need to show that two angles and the side between them in one triangle are congruent to the corresponding angles and side in the other triangle.

For the given options:

Angle B ≅ Angle P and BC ≅ PQ: This information alone is not sufficient to prove congruence using AAS or ASA. We need additional information about another angle or side in order to establish congruence.

Angle A ≅ Angle T and AC: This option provides information about an angle and a side. If we also have additional information about another angle or side, we can use the Angle-Side-Angle (ASA) criterion to prove congruence.

To determine the third option, we need to consider the remaining combinations of angles and sides:

Angle A ≅ Angle T and BC ≅ PQ: This option provides information about an angle and a side. If we also have additional information about another angle or side, we can use the Angle-Side-Angle (ASA) criterion to prove congruence.

In summary, the additional information that could be used to prove congruence using AAS or ASA is:

Angle A ≅ Angle T and AC (ASA)

Angle A ≅ Angle T and BC ≅ PQ (ASA)

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The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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Answer: are you putting thirty in the bank or taking more out?

if putting it in the bank you will be overdrawn by 120 if taking more out you will be overdrawn by 180

Step-by-step explanation:

Answer:

Yes it’s correct it’s easy all you had to do is do the work glad that it’s correct

Step-by-step explanation:

The correct option is: b. f is continuous but not differentiable at x=2.

f(x) = (5x-3) for x > 2There is only one condition for the function to be continuous and differentiable at a point ‘c’ that is f(x) is continuous at x = c and limit of f(x) at x = c exists and equal to f’(c). Now, if we apply this condition in our given function we have;For x > 2; f(x) = (5x-3)Therefore, f(2) does not exist, therefore, f is not continuous at x=2. Hence, option A is incorrectNow we need to find the derivative of the function at x=2;f(x) = 5x - 3dy/dx = 5The derivative of the function exists and is equal to 5. Therefore the limit of the function at x=2 does not exist, hence the function is not differentiable at x=2.Therefore, the correct option is: b. f is continuous but not differentiable at x=2.

The main point is the limit of the function. For the function to be differentiable at a point, the limit of the function should exist and be equal to the derivative at that point.Let's check the continuity of the function at x=2.For x > 2; f(x) = (5x-3)For x=2, f(x) does not exist as x is defined only for x>2. Therefore, the function is not continuous at x=2.Now we will check the differentiability of the function at x=2.f(x) = 5x - 3dy/dx = 5For x=2, the limit of the function does not exist and it is not equal to the derivative at that point. Hence, the function is not differentiable at x=2.So, the correct option is b. f is continuous but not differentiable at x=2.

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Answer:

The answer is G

If you do the line trick you only get 1 interception on the line each time.

Answer:

To be honest I haven't learned this yet so please reach out to me later

Let 185lb equate to 100%

20lb of fat will be ?

= 10.81%

Dave has 10.81% of body fat and it falls at the athlete category.

Answer:

A. 4,500 + 50g = 6,000

Step-by-step explanation:

25(18) + 50(g) = 6000

4500 + 50g = 6000

The correct option is A.

The elimination method  is another name for the addition method to solve a system of equations in two variables.

What is  The elimination method?

The elimination approach involves removing one of the variables from the system of linear equations by adding or subtracting, as well as multiplying or dividing the variable coefficients.

What are some instances of elimination methods?

Utilizing the addition property of equality, the elimination approach is used to solve systems of linear equations. Each side of an equation can be increased by the same amount.

                               You can therefore add x + y to the left side of the first equation and add 8 to the right side of the equation if your system is x - 6 = 6 and x + y = 8.

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Answer:

At least 8.333 km/hr

Step-by-step explanation:

Using the inequality setup, we have

5/r + 1.25 + .75 + .9 ≤ 3.5

5/r ≤ .6

5 ≤ .6r

r ≥ 25/3 = 8.333

The divided difference table for the given data (0,1), (1,4), (3,40), and (4,85) has been calculated. The third-order interpolating polynomial that passes through these points is f(x) = 1 + 3x + 15x^2 - 10.5x^3.

To form the divided difference table for the given data, we need to calculate the divided differences recursively. The table will have four columns - one for each data point - and the divided differences will be written in the rows below each data point. Here's how to calculate the table is shown.

Here, f[x] represents the function value at x, and f[x, x+1] represents the first divided difference between x and x+1, calculated as (f[x+1] - f[x])/(x+1 - x) = (f[x+1] - f[x]). Similarly, f[x, x+1, x+2] represents the second divided difference, calculated as (f[x, x+1] - f[x+1, x+2])/((x+2) - x) = (f[x, x+1] - f[x+1, x+2])/2. The process is continued recursively until we reach the final divided difference, which is the slope of the interpolating polynomial at x.

In this case, we have a third-order polynomial, since we have four data points. The coefficients of this polynomial can be found from the divided difference table as follows

f[0] = 1

f[1, 0] = 3

f[3, 1, 0] = 18

f[4, 3, 1, 0] = 22.5

The interpolating polynomial is therefore:

f(x) = 1 + 3(x - 0) + 18(x - 0)(x - 1) + 22.5(x - 0)(x - 1)(x - 3)

Simplifying this expression, we get:

f(x) = 1 + 3x + 15x^2 - 10.5x^3

Therefore, the interpolating polynomial that passes through the four given points is:

f(x) = 1 + 3x + 15x^2 - 10.5x^3

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Answer:

  circumcenter

Step-by-step explanation:

You want to know the name of the point equidistant from the vertices of a triangle.

The circle that passes through the vertices of a triangle is called a "circumcircle". It circumscribes the triangle. Its center is equidistant from all points on the circle, so is equidistant from the triangle's vertices.

The point equidistant from the vertices of a triangle is the circumcenter.

__

Additional comment

The circumcenter is at the intersection of the perpendicular bisectors of the sides of the triangle.

The probability that at least one of them is a boy is 0.9947

The probability = (1 - P) none of these 7 is a boy

= 1 - P (all girls)

1 - 0.473^7

1 - 0.00529697

= 0.9947

Hence in a certain​ country, the true probability of a baby being a girl is 0.473 . among the next seven randomly selected births in the​ country, the probability that at least one of them is a boy is 0.9947

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Answer:

D all real numbers

Step-by-step explanation:

Hope this helped

The number of people in group A is 13

Algebraic expressions are defined as expressions made up of terms, factors, coefficients, variables and constants.

They are also made up of mathematical operations such as;

From the information given, we have that;

If A and B have the same number of people then, let's add them as one variable (2x)

2x + C = 38

Substitute the value of C

2x + 12 = 38

collect like terms

2x = 38 - 12

2x = 26

Make 'x' the subject of formula by dividing both sides by 2

2x/2 = 26/2

x = 13 people

But we have that Group A = x

Group A = 13 people

Thus, the number of people in group A is 13

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Answer:

see explanation

Step-by-step explanation:

The perimeter is the sum of the sides of the figures

(1)

The figure has 5 congruent sides , then perimeter P

P = 5 (\(\frac{2}{5}\) x + 1) ← multiply each term in the parenthesis by 5

  = 2x + 5

(2)

There are 4 congruent sides of (\(\frac{5}{2}\) x - y) and 8 of y , then

P = 4(\(\frac{5}{2}\) x - y) + 8y ← distribute parenthesis by 4

  = 10x - 4y + 8y ← collect like terms

  = 10x + 4y

(3)

P = 2(\(\frac{2a-b}{2}\) ) + 2(\(\frac{3b}{2}\) ) + 2a ← distribute parenthesis

  = 2a - b + 3b + 2a ← collect like terms

  = 4a + 2b

Answer:

120 buttons in each box

Step-by-step explanation:

What you are looking for is the least common multiple. List out what the multiples of each number are and when ever you find two numbers that match you have your answer.

Answer: 137

Step-by-step explanation:

29, 38, 47, 56, 65, 74, 83, 92, 119, 128, 137

The eleventh digit in list is 119.

A sequence in which the next term in the sequence is obtained by adding a constant to each term is known as an arithmetic progression. The common difference is the added constant. It is a succession to such an extent that the contrast between any two sequential terms in the grouping is dependably a consistent.

Consider the terms of an arithmetic progression sequence as n1, n2, n3, n.

Given a series 29, 38, 47, ….

for an AP aₙ = a₁ + (n - 1)d

where a₁ = first term of AP

n = number of terms, and d = difference between the terms

here d = 9, n = 11 and a₁ = 29

a₁₁ = 29 + (11 - 1)x9

a₁₁ = 29 + 10 x 9

a₁₁ = 119

Hence the term is 119.

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Based on the given 95% confidence interval of (-2, 7) pounds for the average weight change, it includes zero. This means that there is a possibility that the average weight change could be zero, indicating no significant weight loss or gain.

Therefore, the claim made by Professor Ramos that the diet program works at reducing weight for obese teenagers may not be supported by the data. The confidence interval suggests that there is uncertainty regarding the effectiveness of the diet program, and further investigation or analysis may be required to draw a conclusive conclusion.

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Answer:

1=4

Step-by-step explanation:

I don't want to do it all but I gave you one of them!

Answer:

Step-by-step explanation: 1. distribute

distribute the x into (3x-5) -> 3x*x=3x^2 and x*-5=-5x. you will get

3x^2-5x+3(3x-5)

now distribute the 3 into the other (3x-5) -> 3*3x=9x and 3*-5=-15. you will get

3x^2-5x+9x-15

2. Combine like terms

3x^2-5x+9x-15 can be simplified to 3x^2+4x-15 by combining -5x and 9x.

3. Factor (there are many strategies use the one easiest for you)

In this case no number can be taken out to simplify the equation so set up your answerer as (3x   ) (x  ). you can do this because your first term will have to be 3x^2 and the only multiples are 3 and 1.

By using your 3rd term (-15) you can get the possible numbers after the x's by its multiples 5*3 and 15*1

Using the middle term (4x) find what multiplies to -15 (only one number can be negative) and is able to add up to 4 while one number is multiplied by 3 because of the 3x ( -5*3=15 and 3*3-5 -> 9-5=4)

plug your numbers in (3x-5) (x+3)

feel free to ask any questions!

Answer:

preserve

Step-by-step explanation:

because 8 divided by is equal to 1 soo....

when the acceleration of gravity is 9.81 m/s 2 and the density of sea water is 1025 kg/m3. Then the ocean's depth is 20.15 meters.

Given that,

Pressure \(P= 3 P atm\)

atmospheric pressure \(Patm = 1.013\) × \(10{5} Pa\)

Gravitational acceleration = 9.81 m/s2

The density of sea water is 1025 kg/m3.

We need to figure out how deep the ocean is.

 \(h = P -Po \\ pg\)

Using the Depth Formula

\(h = 3 x 1.013 x 10 *5 -1.013 x10*5/ 1025 x9.81\\ \\ \\ h =20.15m\)

In this case, =Atmospheric pressure

P stands for total pressure.

g = gravitational acceleration

\(p\) = seawater density

Fill in the value inside the formula

Hence, The depth of the ocean is 20.15 meters.

How else do you determine debt to assets and equity ratio ?

The equity multiplier is calculated based:

Total Assets / Total Shareholder Equity = Investment Multiplier.

Total Capital is equal to the sum of total debt and total equity.

Total debt divided by the total assets equals the debt ratio.

Debt to Equity Ratio = 1 - (1/Equity Multiplier)

Net Profit Margin x Total Investments = ROE Financial Leverage Ratio x Inventory Turnover.

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Answer:

y = 4x + -5

Step-by-step explanation:

Answer:

\(y=4x-5\)

Step-by-step explanation:

parallel lines have the same gradient so line P's gradient would also be 4

line P's equation is \(y=4x+c\) but we don't know the c variable yet, so we just plug in the coordinate values

\(-5=4(0)+c\)

\(-5=c\)

so line P's equation is \(y=4x-5\)

The value of the function is f(-3) equals -27 and f(2) equals -2.

A function is a rule that assigns each input value (x) to a unique output value (f(x)). In our case, the function f(x) = -2x² + 3x is a quadratic function because it has an x² term. To find f(-3), we substitute -3 for x in the given function:

f(-3) = -2(-3)² + 3(-3)

Now, let's solve this expression step by step:

Simplify within the parentheses first:

f(-3) = -2(9) + 3(-3)

Multiply within each set of parentheses:

f(-3) = -18 + (-9)

Add the two terms together:

f(-3) = -27

Therefore, the value of f(-3) is -27.

Similarly, to find f(2), we substitute 2 for x in the function:

f(2) = -2(2)² + 3(2)

Now, let's solve this expression step by step:

Simplify within the parentheses first:

f(2) = -2(4) + 3(2)

Multiply within each set of parentheses:

f(2) = -8 + 6

Add the two terms together:

f(2) = -2

Therefore, the value of f(2) is -2.

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Complete Question:

Given f(x) = -2x²+3x find each of the following: f(-3); f(2)