(h+3)2 find the square. Simplify your answer.

This expression [tex]s_{i-j}[/tex] describes the distance between two points i and j in a geometric object

In the context of symmetry and rotations, [tex]s_{i-j}[/tex] typically refers to the distance between two points i and j in a geometric object, such as a crystal lattice or a molecule.

It is a vector that points from point i to point j, and its magnitude is the distance between the two points.

The distance vector [tex]s_{i-j}[/tex] is also used to describe the position of a point in the crystal lattice relative to the rotation axis.

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0.685 is a decimal that equals 68.5%.

Answer:

39 divided by 8 is equal to 4 with a remainder of 7.

The quotient is the number of times the divisor goes into the dividend. In this case, 8 goes into 39 4 times with a remainder of 7.

The remainder is the number that is left over after the divisor has been divided into the dividend. In this case, 7 is left over after 8 has been divided into 39.

Here is the long division of 39 by 8:

```

39 / 8

4

32

7

```

Step-by-step explanation:

The quotient of 39 divided by 8 is 4, and the remainder is 7.

We have,

When performing long division, we divide the dividend (39) by the divisor (8) to find the quotient and remainder.

  4

--------

8 | 39

  - 32

    ---

     7

Here's how the long division process works for 39 divided by 8:

-We start by dividing the first digit of the dividend (3) by the divisor (8). Since 3 is less than 8, we can't divide it evenly, so we move to the next digit (9).

- We now have 39 as the remaining portion of the dividend. We divide 39 by 8. The largest multiple of 8 that fits into 39 is 4. We place the quotient, which is 4, above the line.

- We multiply the quotient (4) by the divisor (8), which gives us 32. We subtract 32 from 39, which leaves us with a remainder of 7.

- Since there are no more digits to bring down from the dividend, and the remainder (7) is less than the divisor (8), we stop the division process.

Therefore,

The quotient of 39 divided by 8 is 4, and the remainder is 7.

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Answer: Using the formula i = prt, we have:

i = (104292.12 - 80040) = 24252.12

p = 80040

t = 3

Substituting these values, we get:

24252.12 = 80040 * r * 3

Solving for r, we get:

r = 0.101 or 10.1%

Therefore, the interest rate is 10.1%.

Step-by-step explanation:

if we change the value of 523 to 424 in the list of numbers, then the mean decreases by approximately 3.22 and the median stays the same.

How to calculate the mean?

To calculate the mean, we add up all the numbers in the list and divide by the total number of values. Before the change, the sum of the numbers is:

164 + 225 + 227 + 250 + 261 + 268 + 277 + 379 + 523 = 2494

And there are 9 numbers in the list. So the mean is:

2494 / 9 ≈ 277.11

If we change the value of 523 to 424, then the sum becomes:

164 + 225 + 227 + 250 + 261 + 268 + 277 + 379 + 424 = 2465

And there are still 9 numbers in the list. So the new mean is:

2465 / 9 ≈ 273.89

So the mean decreases by approximately 3.22.

To calculate the median, we find the middle value of the list. If the list has an odd number of values, then the median is the middle value. If the list has an even number of values, then the median is the average of the two middle values. In this case, the list has an odd number of values, so the median is:

261

If we change the value of 523 to 424, then the list becomes:

164, 225, 227, 250, 261, 268, 277, 379, 424

And the median is still:

261

So the median stays the same.

In summary, if we change the value of 523 to 424 in the list of numbers, then the mean decreases by approximately 3.22 and the median stays the same.

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The probability that both people are hopelessly romantic is 0.0025 and the probability that at least one person is hopelessly romantic is 0.0975

Let's denote the event of being hopelessly romantic as "H".

Given that 5% of the population is hopelessly romantic, we have P(H) = 0.05.

Since the events of selecting two people are independent, we can use the multiplication rule of probability to calculate the probability that both people are hopelessly romantic:

P(H and H) = P(H) x P(H) = 0.05 x 0.05 = 0.0025

To calculate the probability that at least one person is hopelessly romantic, we can use the complement rule of probability.

P(neither H nor H) = P(not H) x P(not H) = (1 - P(H)) x (1 - P(H)) = 0.95 x 0.95 = 0.9025

So, the probability that at least one person is hopelessly romantic is:

P(H or H) = 1 - P(neither H nor H) = 1 - 0.9025 = 0.0975

Therefore, the probability that at least one person is hopelessly romantic is 9.75%.

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The answer of the given question based on the  twelve-tone technique is This is equivalent to 479,001,600 possible tone rows.

The twelve-tone technique is a method of musical composition developed by Arnold Schoenberg and his disciples in the Second Viennese School in the early 20th century. It is also known as dodecaphony, which means "twelve sounds" in Greek. The technique involves arranging the twelve notes of the chromatic scale in a specific order called a tone row or series, and then using that row as the basis for the composition.

Using the twelve-tone technique, we can create a tone row of 12 pitches from the chromatic scale in any order, but with no pitch repeated in the row. Since there are 12 pitches to choose from for the first note, 11 pitches for the second note (since we can't repeat the first pitch), 10 pitches for the third note (since we can't repeat either the first or second pitch), and so on, the total number of possible tone rows is:

12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

which simplifies to:

12!

This is equivalent to 479,001,600 possible tone rows.

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The range of the function in the graph is  6≤e≤12. So correct option is A.

In mathematics, range is a term used to refer to the set of all possible output values of a function. It is the set of values that the function can take as its input varies over its entire domain. In other words, the range of a function is the set of all output values that can be obtained by evaluating the function for all possible input values.

For example, consider the function f(x) = x². The domain of this function is all real numbers, but the range is only non-negative real numbers, since x² is always non-negative for any real number x.

The range of a function can be determined by analyzing its graph, which is a visual representation of the function. The range corresponds to the set of all y-values that appear on the graph. For instance, the range of the function f(x) = sin(x) is the closed interval [-1, 1], since the sine function oscillates between -1 and 1 as its input varies over all real numbers.

Sometimes, it is useful to restrict the domain of a function in order to obtain a specific range. This process is called domain restriction or range selection. For example, the inverse function of f(x) = x² can be obtained by restricting the domain of f to non-negative real numbers, which ensures that the inverse function is also a function. The resulting function is f^-1(x) = √x, whose domain is non-negative real numbers and range is the same as the domain of f.

The range of the function in the graph is  6≤e≤12. So correct option is A.

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Answer: Spheres aren’t three-dimensional—they are two-dimensional. This is evident from the fact that in order to specify a point on a sphere, you only need two pieces of information, such as latitude and longitude.

If you include the interior of the sphere, this is instead called a closed ball, and that is three-dimensional. You can specify a point in the closed ball in all sorts of different ways; one of the most convenient would be latitude, longitude, and distance from the center. However, other than convenience, there is no reason to prefer one coordinate system over any other.

(This fact has nothing to do with spheres or closed balls—that is just a statement that is generally true. People who insist that “the three dimensions” are length, width, and height don’t know what they are talking about.)

Step-by-step explanation:

The x⁶y³ term in the expansion will be:  35 x⁶y³.

The x⁸y² term in the expansion will be: 21x⁸y².

The binomial expansion of (x + y)ⁿ is given by the binomial theorem, which states:

(x + y)ⁿ = C(n, 0) * xⁿ * y⁰ + C(n, 1) * xⁿ⁻¹ * y¹ + C(n, 2) * xⁿ⁻² * y² + ... + C(n, k) * xⁿ⁻ᵏ * yᵏ + ... + C(n, n) * x⁰ * yⁿ

where;

Given that the term 210x⁴y⁶ appears in the expansion, we can infer that it corresponds to C(n, k) * x⁴ * y⁶, where k is the number of times y appears in the term, and (n - k) is the number of times x appears in the term.

Comparing this with the given term, we can deduce the values of n, k, and x in the following way:

C(n, k) = 210

x⁴ = x⁴

y⁶ = y³ * y³

Comparing the exponents on x and y, we can set up the following equations:

n - k = 4 (1)

k = 3 (2)

Solving equation (2) for k, we get:

k = 3

Substituting this value of k into equation (1), we can solve for n:

n - 3 = 4

n = 7

So, the value of n is 7.

Now, we can use the binomial coefficient formula to calculate C(n, k):

C(n, k) = C(7, 3) = 7! / (3! * (7 - 3)!) = 35

Finally, substituting the values of n, k, and C(n, k) into the general term of the expansion, we can find the specific terms:

The x⁶y³ term in the expansion will be:

C(7, 3) * x⁶ * y³ = 35 * x⁶ * y³

The x⁸y² term in the expansion will be:

C(7, 2) * x⁸ * y² = 21 * x⁸ * y²

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Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It is used in a wide range of fields such as science, engineering, social sciences, business, economics, and more.

In statistics, data is collected through various methods such as surveys, experiments, and observations. This data is then analyzed using statistical methods to extract meaningful insights, identify patterns and relationships, and make informed decisions.

Some common statistical techniques include descriptive statistics, inferential statistics, hypothesis testing, regression analysis, and probability theory. These techniques are used to help researchers and analysts to understand and draw conclusions about data, and to test whether their conclusions are statistically significant.

Statistics has many practical applications, such as market research, medical research, quality control, risk assessment, and many others. It plays a critical role in modern society, helping individuals and organizations make informed decisions based on data-driven insights.

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The correct polynomial function of lowest degree with only real coefficients and having the zeros √7, -√7, and 5 is:

OB. f(x) = x³ - 5x² - 7x + 35

What is polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.

The polynomial function of lowest degree with only real coefficients and having the given zeros can be obtained by multiplying the factors (x - √7), (x + √7), and (x - 5) since the zeros are √7, -√7, and 5.

Expanding the product, we get:

(x - √7)(x + √7)(x - 5) = (x² - 7)(x - 5) = x³ - 5x² - 7x + 35

Therefore, the correct polynomial function of lowest degree with only real coefficients and having the zeros √7, -√7, and 5 is:

OB. f(x) = x³ - 5x² - 7x + 35

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This sentence relating to the quotient can be expressed mathematically as:

(30 / x) - 2

This sentence can be expressed mathematically as:

(30 / x) - 2

where x represents the unknown number.

The word "quotient" indicates that we are dividing 30 by the unknown number x. The phrase "is decreased by 2" means that we need to subtract 2 from the quotient.

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Therefore, we can predict that approximately 5,845,200 people left on cruises from this state in the year 2010.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

This linear equation depicts the number of passengers embarking on cruises from a certain state between 2005 and 2009.

It goes like this:

y = 117,000x + 4,919,200

For example, if x = 0, which represents the year 2005, then y = 4,919,200. If x = 1, which represents the year 2006, then y = 4,919,200 + 117,000 = 5,036,200. Similarly, if x = 2, which represents the year 2007, then y = 4,919,200 + 2(117,000) = 5,153,200.

y = 117,000(5) + 4,919,200

y = 5,845,200

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Question:

The number of people, y, leaving on cruises from a certain state from 2005 to 2009 can be approximated by y=117,000x+4,919,200, where x is the number of years after 2005.

===================================================

Explanation:

Focus on triangle BDH

The three inside angles of any triangle always add to 180 degrees.

B+D+H = 180

47+31+H = 180

78+H = 180

H = 180-78

H = 102

Angle BHD is 102 degrees.

It adds to angle x, aka angle BHC, to get 180 degrees. These two adjacent angles combine to a straight line.

(angle BHD) + (angle BHC) = 180

102 + x = 180

x = 180-102

--------------

Shortcut:

Focus on triangle BDH.

Use the remote interior angle theorem to add the given interior angles.

B+D = 47+31 = 78

This is equal to the exterior angle that is not adjacent to either interior angle mentioned. This refers to angle BHC, aka angle x.

In linear equation, Her profit is rupees 4000.

No. of purses she must sell to have neither profit nor loss is 600 nos.

She made loss of rupees 2135.

What is a linear equation in mathematics?

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables. 

The housewife earns,

Profit on 1 purse = 25 rupees

Loss on 1 vanity bag = 20 rupees

So,

Profit on 1000 purses = 25*1000 rupees

                                   = 25000 rupees

Loss on 1050 purses = 20*1050 rupees

                                  = 21000 rupees

Here, Profit > Loss

So,

Total profit = 25000-21000 rupees

                 = 4000 rupees

i) Her profit is 4000 rupees.

If no. of vanity bags sold = 750 nos.

She made loss of = 750*20 rupees

                            = 15000 rupees

ii) No. of purses she must sell to have neither profit nor loss

= 15000/25 nos.

= 600 nos.

Profit on selling 325 purses = 325*25 rupees

                                              = 8125 rupees

Loss on selling 513 vanity bags = 513*20 rupees

                                              =10260 rupees

Here, Profit < Loss

So,

iii) She made loss of = 10260-8125 rupees

                            = 2135 rupees

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The complete question is -

A housewife along with a group of ladies sold bags of different sizes. She earns a profit of 25 on a purse and a loss of 20 on a vanity bag sold. i. She received an order of 1050 vanity bags and 1000 purses. What is her profit or loss? ii. How many purses must she sell to have neither profit nor loss, if the number of vanity bags sold is 750? iii. How much profit/loss did she make in selling 325 purses and 513 vanity bags?

Sin 7π/4 is the value of sine trigonometric function for an angle equal to 7π/4 radians. The value of sin 7π/4 is -(1/√2) or -0.7071 (approx).

315° is comparable to 7 / 4 radians. In general, we multiply the angle measurement in radians by 180/ to translate an angle measurement given in radians to degrees. Therefore, we multiply 7 / 4 by 180 / to convert to radians. We discover that 7/4 radians equals 315 degrees.

We can first convert the angle to degrees as follows:

7π/4 radians = (7/4) × 180 degrees/π ≈ 315 degrees

The trigonometric ratios for 315 degrees (or 7/4 radians) can therefore be calculated using the reference angle of 45 degrees (which is /4 radians), as shown below.

sin(7π/4) = -sin(π/4) = -1/√2

cos(7π/4) = -cos(π/4) = -1/√2

tan(7π/4) = tan(π/4) = 1

csc(7π/4) = csc(-π/4) = -√2/2

sec(7π/4) = sec(-π/4) = -√2/2

cot(7π/4) = cot(-π/4) = 1

Therefore, the trigonometric ratios for the angle 7π/4 radians are:

sin(7π/4) = -1/√2

cos(7π/4) = -1/√2

tan(7π/4) = 1

csc(7π/4) = -√2/2

sec(7π/4) = -√2/2

cot(7π/4) = 1

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The statement that (sin 2x) / (1 + cos 2x) = tan x can be proven.

To prove that (sin 2x) / (1 + cos 2x) = tan x, we will use trigonometric identities.

(sin 2x) / (1 + cos 2x)

(2sin x × cos x) / (1 + (cos²x - sin²x))

(2sin x × cos x) / (cos²x + 2sin x × cos x + sin²x)

We can rewrite the denominator using the Pythagorean identity sin²x + cos²x = 1:

(2sin x × cos x) / (1 + 2sin x × cos x)

(2sin x × cos x) × (1 - 2sin x × cos x) / (1 - (2sin x × cos x)²)

((2sin x × cos x) - (4sin²x × cos²x)) / (1 - 4sin²x × cos²x)

(2sin x - 4sin²x) / (1/cos²x - 4sin²x)

Since tan x = sin x / cos x, we can rewrite the expression:

(2tan x - 4tan²x) / (sec²x - 4tan²x)

(2tan x - 4tan²x) / (1 + tan²x - 4tan²x)

(2tan x - 4tan²x) / (1 - 3tan²x)

2tan x × (1 - 2tan²x) / (1 - 3tan²x)

tan x

So, we have proved that (sin 2x) / (1 + cos 2x) = tan x.

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Answer:

(x - 5)² + (y + 6)² = 16

Step-by-step explanation:

assuming you require the equation of the circle

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (5, - 6 ) and r = 4 , then

(x - 5)² + (y - (- 6) )² = 4² , that is

(x - 5)² + (y + 6)² = 16

Answer: ∡1 = 153°

∡2 = 27°

Step-by-step explanation:

Answer:

angle 2=27°

angle 1= 153°

Step-by-step explanation:

6x-9+x=180

7x-9=180

7x=189

x=27

angle 2=27°

angle 1= 27×6-9=153°

angle 1= 153°

Answer:

2=8m

divide both sides by 8

the 8 cancels out

and your answer is

m= 2/8

Step-by-step explanation:

hope it helped have a nice day!

Therefore, the wire Ryan wants to walk is approximately 107.9 ft long.

Trigonometric functions are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The most commonly used trigonometric functions are sine, cosine, and tangent, often abbreviated as sin, cos, and tan respectively.

The sine function (sinθ) gives the ratio of the length of the side opposite an angle θ in a right triangle to the length of the hypotenuse (the longest side). The cosine function (cosθ) gives the ratio of the length of the adjacent side to θ to the length of the hypotenuse, while the tangent function (tanθ) gives the ratio of the length of the opposite side to θ to the length of the adjacent side.

Other trigonometric functions include cosecant (cscθ), secant (secθ), and cotangent (cotθ), which are the reciprocals of the sine, cosine, and tangent functions, respectively.

A represents the top of the tower, B represents the point where the wire is attached 30 ft away from the tower, and the wire itself is represented by the line segment AB. The angle between the wire and the ground is θ, and we want to find the length of the wire, which is represented by y.

We can use the trigonometric function tangent to relate the angle θ to the sides of the triangle:

tan(θ) = y/x

Solving for y, we get:

y = x * tan(θ)

We know that x = 30 ft, and θ = 74º, so we can plug those values in and calculate y:

y = 30 ft * tan(74º) = 107.9 ft (rounded to the nearest tenth)

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Answer: 119

Step-by-step explanation:

We know that we must find the least common multiple of 15 and 27 in order to solve the problem because when we are finding remainders that are the same, there must be some relationship between the integer and the two dividing numbers.

Thus, we have the least common multiple 135 and its multiples which will all have a 0 remainder when divided by 15 and by 27.

We can take each of the numbers (7) and the 15 consecutive numbers after each of them, because of modulo becoming the same after 15. If we take the total of all these numbers, which will have the same remainder after division by 15 and 27, we are left with:

15 * 8 - 1 = 119

Answer: To calculate the probability that the shipment is rejected, we need to find the probability that at least one of the three components selected is defective.

First, we can find the probability that none of the three components selected is defective, which would mean the shipment is accepted. To do this, we use the hypergeometric distribution formula:

P(X = k) = (C(N-k,n-K) * C(K,k)) / C(N,n)

where:

N = total number of components in the shipment (160)

K = number of defective components in the shipment (4)

n = number of components selected for testing (3)

k = number of non-defective components among the selected components (i.e., all 3 components are non-defective)

Plugging in the values, we get:

P(all 3 components are non-defective) = (C(160-4-3,3-0) * C(4,0)) / C(160,3)

= (C(153,3) * C(4,0)) / C(160,3)

= (22,446 * 1) / 6,384,320

= 0.00352

Therefore, the probability that the shipment is accepted is 0.00352.

To find the probability that the shipment is rejected, we can subtract this probability from 1, since the probabilities of all possible outcomes must add up to 1:

P(at least one component is defective) = 1 - P(all 3 components are non-defective)

= 1 - 0.00352

= 0.99648

Therefore, the probability that the shipment is rejected is 0.99648, or approximately 99.65%.

Step-by-step explanation:

Answer: the speed of the boat is approximately 9.43 miles per hour.

Step-by-step explanation: To find boat speed, add vectors. Boat goes east at 8 mph, with 5 mph north wind. Boat velocity is a vector eastward and current velocity is a vector northward. To combine velocities, use vector addition. Use Pythagorean theorem to find resultant velocity: resultant speed = √89 ≈ 9.43 mph.

The values are;

1. x = 6 ,y = 6√2

2. x = 9√2, y = 18

3. x = y = 9

4. x = 12, y = 12√2

5. x = y = 4√2

6. x = y =( 3√2)/2

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

There are some special angles , in which 45 is part of them.

sin 45 = 1/√2

cos 45 = 1/√2

tan 45 = 1

1. x = 6 ( isosceles triangle)

y = 6 × √2 = 6√2

2. x = 9√2 ( isosceles triangle)

y = 9√2 × √2 = 9×2 = 18

3. x = 9√2/√2 = 9

x = y = 9 ( isosceles triangle)

4. x = 12 ( isosceles triangle)

y = 12×√2 = 12√2

5. x = 8/√2 = 8√2/2 = 4√2

x = y = 4√2( isosceles triangle)

6. x = 3/√2 = (3√2)/2

x = y =( 3√2)/2 ( isosceles triangle)

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Answer: Option A:

To calculate the total amount Owen will spend on Option A, we need to calculate the monthly payment and then multiply it by the number of months:

First, we need to calculate the total amount of the loan. Owen is making a down payment of $3200, so he will be borrowing $28,820 (the price of the car minus the down payment).

Next, we can use the formula for calculating the monthly payment for a loan:

P = (r * A) / (1 - (1 + r)^(-n))

where P is the monthly payment, r is the monthly interest rate, A is the total amount of the loan, and n is the number of months.

For Option A, the monthly interest rate is 1.3% / 12 = 0.01083, the total amount of the loan is $28,820, and the number of months is 36. Plugging these values into the formula, we get:

P = (0.01083 * 28,820) / (1 - (1 + 0.01083)^(-36)) = $860.45

Therefore, the total amount Owen will spend on Option A is:

36 * $860.45 = $30,975.98

Option B:

For Option B, we need to take into account the $1500 cash back that Owen will receive as part of the down payment. This means that the total amount of the loan will be $32,020 - $3200 - $1500 = $27,320.

To calculate the monthly payment, we can use the same formula as before:

P = (r * A) / (1 - (1 + r)^(-n))

For Option B, the monthly interest rate is 5.2% / 12 = 0.04333, the total amount of the loan is $27,320, and the number of months is 36. Plugging these values into the formula, we get:

P = (0.04333 * 27,320) / (1 - (1 + 0.04333)^(-36)) = $825.53

Therefore, the total amount Owen will spend on Option B is:

36 * $825.53 + $1500 = $30,316.08

Therefore, Option A will cost Owen a total of $30,975.98, and Option B will cost him a total of $30,316.08. Therefore, Option B is the cheaper option for Owen.

Step-by-step explanation:

The surface area of the triangular prism with rectangular base is 736 cm².

Surface area refers to the total area that the surface of an object covers. It is a measure of how much exposed area there is on the outside of an object. The surface area of an object is usually expressed in square units, such as square meters, square centimeters, or square feet.

Here,

The formula for the surface area of a triangular prism with rectangular base is:

SA = 2lw + lh + wh

where l is the length of the rectangular base, w is the width of the rectangular base, h is the height of the triangular prism.

Given:

Side of triangle = 16 cm and 12 cm

Side of rectangle = 20 cm and 10 cm

Since we are not given the height of the triangular prism, we cannot calculate the exact surface area. However, we can give a general formula for the surface area in terms of the height h:

SA = 2(20)(10) + (16)(h) + (12)(h)

SA = 400 + 28h

So the surface area of the triangular prism with rectangular base is 400 + 28h, where h is the height of the triangular prism in cm.

h=12 cm

400+28h=400+28*12

=736 cm²

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Answer: 2x^3y^4

Step-by-step explanation:

The expression ^4√16x^12y^16 can be simplified as follows:

^4√16 = 2, since 2^4 = 16

x^12 can be written as (x^3)^4, and ^4√(x^3)^4 = x^3

y^16 can be written as (y^4)^4, and ^4√(y^4)^4 = y^4

Therefore, ^4√16x^12y^16 simplifies to:

2x^3y^4

[tex]\cfrac{5^7}{5^{-13}}\times\left( \cfrac{4^3}{7^{-2}} \right)^{-2}\implies 5^7\cdot 5^{13}\times \left( \cfrac{7^{-2}}{4^3} \right)^{+2}\implies 5^7\cdot 5^{13}\times\left( \cfrac{7^{-4}}{4^6} \right) \\\\\\ 5^{7+13}\times\left( \cfrac{1}{4^6\cdot 7^4} \right)\implies \cfrac{5^{20}}{4^6\cdot 7^4}\implies \cfrac{95367431640625}{9834496}[/tex]