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5. We have Angle, Angle and Side to constitute the AAS theorem and prove the triangles are congruent.

6. We have Side, Side and angle not between them so we don't have enough information to prove the congruency of the triangles.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

5. We have Angle, Angle and Side to constitute the AAS theorem and prove the triangles are congruent.

6. We have Side, Side and angle not between them so we don't have enough information to prove the congruency of the triangles.

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To find the magnitude of vector a, we need to determine its components. From the given information, we can set up two equations: a + b = 6i + j and a - b = -4 + 7j.

Solving these equations will allow us to find the components of vector a.Let's solve the equations to find the components of vector a.From the first equation, a + b = 6i + j, we can equate the corresponding components: a_x + b_x = 6 (equation 1) , a_y + b_y = 1 (equation 2),Similarly, from the second equation, a - b = -4 + 7j, we have: a_x - b_x = -4 (equation 3), a_y - b_y = 7 (equation 4). Adding equations 1 and 3, we get: 2a_x = 2 => a_x = 1. Substituting the value of a_x in equation 1, we find: 1 + b_x = 6 => b_x = 5. Adding equations 2 and 4, we obtain:

2a_y = 8 => a_y = 4. Substituting the value of a_y in equation 2, we find:

4 + b_y = 1 => b_y = -3

Now that we know the components of vector a are a_x = 1 and a_y = 4, we can find its magnitude using the formula: |a| = sqrt(a_x^2 + a_y^2)=sqrt(1^2 + 4^2) = sqrt(1 + 16) = sqrt(17) . Therefore, the magnitude of vector a is sqrt(17).

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Answer:

the total price is 165.5

B. Both functions are decreasing, but function g is decreasing at a faster average rate on that interval.

Let's clarify the comparison between the functions f(x) and g(x) and explain the rates of decrease more accurately.

The given table represents the values of function g(x) for different values of x: x = 0, 1, 2, 3, 4.

The corresponding values of g(x) are 75, 43, 27, 19, and 15, respectively.

Function f is described as an exponential function that has an initial value of 64 and decreases by 50% as x increases by 1 unit.

However, we don't have the specific values of f(x) for the interval [0, 4].

So, we cannot compare the exact values of f(x) and g(x) directly.

Now, let's compare the average rates of decrease between the two functions:

For function f, we know that it decreases by 50% as x increases by 1 unit. This means that for every unit increase in x, the value of f(x) decreases by half of its previous value.

On the other hand, for function g, we can observe the values in the table. As x increases from 0 to 1, g(x) decreases from 75 to 43.

This is a decrease of 32, which represents a decrease of (32/75) \(\times\) 100% ≈ 42.67%.

From the given information, we can conclude that function g is decreasing at a faster average rate compared to function f on the interval [0, 1].

However, without further information or additional data points, we cannot make a definitive comparison for the entire interval [0, 4].

Therefore, the correct statement regarding the comparison of the two functions on the interval [0, 4] would be:

B. Both functions are decreasing, but function g is decreasing at a faster average rate on that interval.

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The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Answer:

18

Step-by-step explanation:

The fifth term of the arithmetic sequence is -1190.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n - 1) * d

where aₙ represents the nth term, a₁ is the first term, n is the position of the term, and d is the common difference.

Given that the 100th term is -1240 and the common difference is -25, we can substitute these values into the formula.

Since the fifth term corresponds to n = 5, we can calculate:

a₅ = -1240 + (5 - 1) * (-25)

= -1240 + 4 * (-25)

= -1240 - 100

= -1340

Therefore, the fifth term of the arithmetic sequence is -1190.

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Answer:

-3/8 is the slope of the line

Step-by-step explanation:

Answer:

1.2^2

Step-by-step explanation:

1 11/25=36/25

square rout of 36/25=1.2

Answer:

1 11/25 is the same as 36/25. Since 36 and 25 are 6² and 5² respectively the answer is (6 / 5)².

The statement that is not always true is "(Complement of B) is a subset of (Complement of A)."

To understand why this statement is not always true, let's consider a counterexample. Suppose U is the universe of all real numbers, A is the set of even numbers, and B is the set of positive numbers. In this case, A is a subset of B because all even numbers are also positive numbers. However, the complement of B consists of all non-positive numbers, which includes negative numbers and zero. The complement of A consists of all odd numbers and non-integer real numbers. Therefore, the complement of B, which includes negative numbers, is not necessarily a subset of the complement of A, which does not include negative numbers. Hence, the statement "(Complement of B) is a subset of (Complement of A)" is not always true.

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Answer: The value of 2c²d would be 2 * (0.5)² * 3 = 2 * (0.25) * 3 = 0.5 * 3 = 1.5

This is because you first square the value of c (0.5² = 0.25), then you multiply it by 2 (0.25 * 2 = 0.5) and then by d (0.5*3 = 1.5)

Step-by-step explanation:

\( \large \underline{ \tt \: \: Given \: : \: } \\ \: \: \: \: \boxed{ \red{\tt c : 0.5}} \\ \: \: \: \: \boxed{ \green{ \tt \: d : 3 \: \: \: }}\)

\( \: \)

put the value of c nd d in given eqⁿ ~

\( \: \)

\( \large \tt \: 2 { \red{c}^{2}}\green{d}\)

\( \: \)

\(\large \tt \: 2 \times { \red{0.5}^{2}} \times \green{3}\)

\( \: \)

\(\large \tt \: 2 \times { \red{0.25}} \times \green{3}\)

\( \: \)

\( \large \tt \: 2 \times { \purple{0.75}}\)

\( \: \)

\( \underline{ \boxed{ \large \tt \purple{ \: \: 1.5 \: \: }}}\)

\( \: \)

hope it helps!:)

The solution to the equation 810x + y = 8 is given by the expression y = 8 - 810x, where x can take any integer or fraction value, and y will be determined accordingly

To solve the equation 810x + y = 8, we need to isolate either variable. Let's solve for y in terms of x.

First, subtract 810x from both sides of the equation:

y = 8 - 810x.

Now, we have expressed y in terms of x. This means that for any given value of x, we can find the corresponding value of y that satisfies the equation.

For example, if x = 0, then y = 8 - 810(0) = 8.

If x = 1, then y = 8 - 810(1) = 8 - 810 = -802.

Similarly, we can find other values of y for different values of x.

Note: The equation does not have a unique solution. It represents a straight line in the x-y coordinate plane, and every point on that line is a solution to the equation.

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Answer: 32 apples

Step-by-step explanation:

The ratio of apples to oranges sold is given as 4 to 2. Since Tia wants to sell a total of 48 apples and oranges, the number of apples that she should sell would be:

= 4/(4+2) × 48

= 4/6 × 48

= 32

Therefore, he should sell 32 apples.

The value of the expression at z =8 and w = 8 will be 72.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given expression is 2z + 7w. The value of the expression will be calculated as below:-

E = 2z + 7w

E = 2 x 8 + 7 x 8

E = 16 + 56

E = 72

Therefore, the value of the expression at z =8 and w = 8 will be 72.

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The average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

Calculate the definite integral of the function over the interval [a, b], then divide it by the interval's length (b - a), in order to determine the average value of a function f(x) over the interval.

Given that the interval is [0, 3] and the function f(x) = (x + 2), we have:

= (1/3) × [1/2 x² + 2x] evaluated from x=0 to x=3

= (1/3) × [(1/2 × 3² + 2×3) - (1/20² + 20)]

= (1/3) × [(9/2 + 6) - 0]

= (1/3) × (21/2)

= 7/2

Therefore, the average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

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Answer:

12

Step-by-step explanation:

Volume= pi x radius squared x height

substitiute values

540π= π x r^2 x 15

divide 540π by π and 15

so thats 36= radius squared

so the radius is 6 as 6 squared is 36

so the diameter is radius x2

so the answer is 12

When you are doing calculations, you can usually tell when you need to change base by looking at the problem. If the problem includes fractions, a base other than 10 may be more efficient. If the problem includes exponents, a base other than 10 may be necessary.

When working with numbers, it is important to know what base the numbers are in in order to correctly perform calculations. The base of a number is the number of digits used to express it, meaning that the base of a number can range from base 2 (binary) to base 36 (base 36 uses the numbers 0-9 and the letters A-Z).

Changing the base of a number can be helpful when dealing with fractions, exponents, and other complex calculations. To change the base of a number, divide the number by the base and then divide the remainder by the base, continuing to divide until the remainder equals 0.

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The Maclaurin series of f(x) is given by;f(x) = f(0) + f'(0)x + f''(0)x²/2! + f'''(0)x³/3! + ..... where f(0) = 0, f'(0) = 9, f''(0) = 0, f'''(0) = - 9*8, and so on.Now, the derivative of x^9 sin x is given by;f'(x) = 9x^8 sin x + x^9 cos xDifferentiating the expression above,

we obtain;f''(x) = 72x^7 sin x + 18x^8 cos x - 9x^9 sin xDifferentiating the expression above, we obtain;f'''(x) = 504x^6 sin x + 504x^7 cos x - 216x^7 cos x - 81x^9 cos x - 81x^8 sin xDifferentiating the expression above, we obtain;f''''(x) = 3024x^5 sin x + 4032x^6 cos x - 2016x^7 sin x - 1944x^8 cos x - 567x^9 sin x - 486x^8 cos x

Now we will substitute these values into the series expansion to get;f(x) = 0 + 9x + 0*x²/2! - 9*8*x³/3! + 0*x⁴/4! + 9*8*7*x⁵/5! + .....+ (-1)ⁿ (9*(9-1)*(9-2)*.....*(9-n+1)) x^n/n!Where n! denotes the factorial of n, i.e, n! = n*(n-1)*(n-2)*.....2*1. And thus, the required Maclaurin series of f(x) is given by;f(x) = [infinite sum] (-1)ⁿ (9*(9-1)*(9-2)*.....*(9-n+1)) xⁿ/n!, n = 0, 1, 2, 3, .....

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For a larger input size of 320,000 elements, it will take 240 ms to sort each half and 24 ms to merge the sorted halves, resulting in a total time of 264 ms.

The given information describes the time required for sorting and merging operations on two different input sizes. For 80,000 elements, it takes 18 ms to sort each half, resulting in a total of 36 ms for sorting. Merging the two sorted halves with 80,000 numbers in each takes 40 - 18 = 22 ms.

When the input size is doubled to 320,000 elements, the sorting time for each half increases to 240 ms, as it scales linearly with the input size. The merging time, however, remains constant at 4 ms since the size of the sorted halves being merged is the same.

Thus, the total time for sorting and merging 320,000 elements is the sum of the sorting time (240 ms) and the merging time (4 ms), resulting in a total of 264 ms.

Therefore, based on the given information, the total time required for sorting and merging 320,000 elements is 264 ms.

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The work done during the reversible isothermal compression of the gas is approximately -119.63 Joules. The negative sign indicates that work is done on the system during compression.

To calculate the work done during the reversible isothermal compression of an ideal gas, we can use the formula:

Work = -nRT ln(Vf/Vi)

Where:

- n is the number of moles of the gas

- R is the ideal gas constant (8.314 J/(mol·K))

- T is the temperature in Kelvin

- Vi is the initial volume

- Vf is the final volume

Given:

n = 0.05 mol

R = 8.314 J/(mol·K)

Vi = 12 L

To calculate the work done for the given pressure change, we need to find the final volume (Vf). We can use the ideal gas law to relate pressure, volume, and moles:

PV = nRT

Initial pressure (Pi) = 2.5 atm

Final pressure (Pf) = Pi + pressure change = 2.5 atm + 15 atm = 17.5 atm

Using the ideal gas law, we can solve for Vf:

Vf = (nRT) / Pf

Vf = (0.05 mol * 8.314 J/(mol·K) * T) / (17.5 atm)

Since the process is isothermal, the temperature remains constant. Let's assume it is 298 K:

Vf = (0.05 mol * 8.314 J/(mol·K) * 298 K) / (17.5 atm)

Vf ≈ 8.483 L

Now we can calculate the work done using the equation:

Work = -nRT ln(Vf/Vi)

Work = -(0.05 mol * 8.314 J/(mol·K) * 298 K) * ln(8.483 L / 12 L)

Work = -(0.05 mol * 8.314 J/(mol·K) * 298 K) * ln(8.483 L / 12 L)

Calculating the expression:

Work = -(0.05 mol * 8.314 J/(mol·K) * 298 K) * ln(0.7069)

Using a scientific calculator or math software to evaluate the natural logarithm:

Work ≈ -119.63 J

Therefore, the work done during the reversible isothermal compression of the gas is approximately -119.63 Joules. The negative sign indicates that work is done on the system during compression.

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Answer:

14.7, because 5x + 90 + 16.5 =180

so 180-90-16.5=5x

x= 14.7

The simplified expression is  \(8x^4y^4\).

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression: 4 + 6 + 5.

Here the given expression is

=> \((4x^3y^3)(2x.2y)\)

=> \(4\times x^3\times y^3\times2x\times2y\)

=> \(4\times2\times2\times x^3\times x \times y^3\times y\)

=> 8\(\times x^{3+1}\times y^{3+1}\)

=> \(8x^4y^4\)

Hence the simplified expression is  \(8x^4y^4\).

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Answer:

Trust me I guarantee you it's correct.

Step-by-step explanation:

D. 8x^5y^4

In solving the problem of calculating the number of ways a bank can pay out a given withdrawal amount using dynamic programming, we define the subproblem as DP[i] = the number of ways the bank can pay out $i.

The base case for this problem is DP[0] = 1, representing the number of ways to pay out an amount of $0.

The base case DP[0] = 1 represents the fact that there is exactly one way to pay out $0, which is by not giving any bills. This serves as the starting point for building up the solution for larger withdrawal amounts.

Using dynamic programming, we can calculate the number of ways to pay out higher amounts by considering the two possible bill options: $1 and $5. For each withdrawal amount i, we can either choose to use a $1 bill or a $5 bill as the first bill in the payment.

To calculate DP[i], we consider two cases:

1. If we use a $1 bill as the first bill, we need to determine the number of ways to pay out the remaining amount (i - 1). This can be represented as DP[i - 1].

2. If we use a $5 bill as the first bill, we need to determine the number of ways to pay out the remaining amount (i - 5). This can be represented as DP[i - 5].

Therefore, the recurrence relation becomes:

DP[i] = DP[i - 1] + DP[i - 5]

By iteratively applying this recurrence relation for increasing values of i, we can calculate DP[A], where A is the given withdrawal amount. This dynamic programming approach allows us to efficiently determine the number of ways the bank can pay out the desired withdrawal amount.

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Answer:

the last one

Step-by-step explanation:

a number used to multiply a variable

Answer:

pnQnR= {}

Step-by-step explanation:

there is no number common in set P, set Q and set R.

So the answer is null

{}

Answer:

{} there is no number common to the three sets so it is an empty set

Step-by-step explanation:

Answer: It is not a function.

Step-by-step explanation:

A function is something that "eats" an input and transforms it into an output.

We write them as y = f(x)

Where x is the input, and y is the output.

Now, a function has an important rule, for each input x, the function can only "transform it" (or map it) into only one possible output.

This means that, for example, if we have, for x = x1.

And a single

f(x1) = y1

f(x1) = y2

where y1 and y2 are different values.

Then this is not a function, because it is mapping the value x1 into two different outputs.

In this case, we would have:

f(Z) = A.

So Z is the input, but we know that a ZIP code works for an entire city, and in a given city we have lots of different street addresses, then for a single value of the input, Z, we have a lot of possible values of the output.

This means taht the set (Z, A) can not represent a function.

Answer:

 3.47 x 103

hope this helps

Answer:

what>???????????????????/

Step-by-step explanation:

Answer:

9x+4=24+x; x=2.5

Step-by-step explanation:

A frequency table is a simple tabular representation of the number of times a particular value or range of values appears in a data set.

It lists the values in one column and the corresponding frequencies in another column. For example, if we have data on the heights of a group of people, a frequency table could list the heights (in cm) in one column and the number of people with that height in the other column.

A frequency distribution is a graphical representation of the same information as a frequency table. It shows the number of occurrences of values in a data set by grouping the values into classes or intervals, and then plotting the frequency of each class or interval. For example, a histogram is a type of frequency distribution where the data is divided into equal-width intervals and the height of each bar represents the frequency of the data that falls within that interval.

A frequency table can be used for both qualitative and quantitative data, whereas a frequency distribution can only be used for quantitative data. This is because the classes or intervals used in a frequency distribution require a numerical representation of the data, which is not possible for qualitative data.

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Answer: 14b +13

Step-by-step explanation:

combine like terms and then add and then subtract the other numbers