12a^4+ (-29a^4) simplify

The explicit formula of the geometric sequence is given as follows:

[tex]a_n = 100(4)^{n-1}[/tex]

The recursive formula of the geometric sequence is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio (q). In other words, a geometric sequence is a sequence where each term is a fixed multiple of the previous term.

The explicit formula of the sequence is given as follows:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

For the recursive formula, we just take the first term and each consecutive term is the previous term multiplied by the common ratio.

There are 100 views in day one, hence the first term is given as follows:

[tex]a_1 = 100[/tex]

The number of viewers is multiplied by 4 each day, hence the common ratio is given as follows:

q = 4.

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The area of triangle MNL is approximately 10.44 cm².

What is the sine rule?

The sine rule, also known as the law of sines, is a formula used in trigonometry to find the lengths of the sides and the measure of the angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. In other words:

[tex]a/sin A = b/sin B = c/sin C[/tex]

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides. The sine rule can be used to find the length of a side of a triangle or the measure of an angle if the other two sides and the included angle are known, or if two sides and the angle opposite one of them are known.

To find the area of triangle MNL, we need to first calculate the length of side NL using the sine rule:

sin(38°) / NL = sin(90°) / 4.8

NL = sin(38°) / sin(90°) * 4.8

NL = sin(38°) * 4.8

NL ≈ 2.9 cm

Now we can find the area of the triangle using the formula:

[tex]Area = (1/2) * base * height[/tex]

[tex]Area = (1/2) * 7.2 * 2.9[/tex]

Area ≈ 10.44 cm²

Therefore, the area of triangle MNL is approximately 10.44 cm².

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The value of the double integral of y over D is 160.

The region D is defined as the image of the rectangle R under the transformation Φ(u,v) = (u², u+v). To find the integral of y over D, we need to express y as a function of u and v, and then compute the double integral in terms of u and v.

From the definition of Φ, we have:

u² = x

u + v = y

Solving for v in terms of u and y, we get:

v = y - u

Substituting this expression for v into the second equation, we get:

y = u + (y - u) = y

Therefore, y does not depend on u, and we can write:

y = f(v) = v + u

The integral of y over D can then be written as:

∫∫D y dA = ∫∫R f(v) |J| dA

where J is the Jacobian of the transformation Φ.

The Jacobian of Φ is given by:

J = ∂(x,y)/∂(u,v) =

| 2u 1 |

| 1 1 |

The determinant of J is:

|J| = 2u - 1

Substituting this expression for |J| and the expression for f(v) into the integral, we get:

∫∫D y dA = ∫∫R (v + u)(2u - 1) dudv

To evaluate this integral, we can integrate first with respect to u and then with respect to v:

∫∫D y dA = ∫[0,5]∫[1,9] (v + u)(2u - 1) dudv

= ∫[0,5] [(v+9)³/3 - (v+1)³/3] dv

= [(5+9)⁴/12 - (1+9)⁴/12]

= 480/3

= 160

Therefore, the value of the double integral of y over D is 160.

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Complete question:

Let D= Ф(R), where Φ(u,v)= (u², u+v) and R= [1,9] × [0,5].

Calculate [tex]\mathrm{\int \: \int \: _D ydA}[/tex]

An equation to represent one way you can find how many miles Emily’s plane flew each hour is y = 182x.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Assuming the variable m represent the miles flown each hour, an equation for the number of miles Emily’s plane flew each hour can be calculated as follows;

y = kx

y = (2184/12)x

y = 182x

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Complete Question:

Emily took an airplane trip. Her plane flew an equal number of miles each hour. Write an equation to represent one way you can find how many miles Emily's plane flew each hour.

Use this to help you:

Air travel time: 12 hours

Destination: 2,184 miles​

Answer:

The answer you're looking for is: (4, -9), (6, -9), (4, -1)

Step-by-step explanation:

When translating an image 90º counterclockwise you go one quadrant to the right and use the scale factor: (x, y) --> (y, -x).

When using this scale factor you switch the x and y coordinates and also make sure that x is the opposite operation, it doesn't always mean it's going to be negative.

In this case points (-9, -4), (-9, -6), and, (-1, -4) were translated to (4, -9), (6, -9), (4, -1) accordingly.

I hope this was helpful!

On evaluating the expression (1 - 1i) + (3 + 2i), the value for a and b are 4 and 1 respectively.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

To evaluate the expression (1 - 1i) + (3 + 2i), we simply add the real parts and the imaginary parts separately -

(1 - 1i) + (3 + 2i)

= (1 + 3) + (-1i + 2i)

= 4 + i

The value for a is obtained as 4

The value for b is obtained as 1.

Therefore, the result is 4 + i, which is in the form a + bi.

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The perimeter of the shape formed is,

⇒ P = 24√13 units

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Three congruent rectangles are joined as shown.

And, The length of each rectangle is 3 times its width.

Here, The area of each rectangle is 39 square units.

Let the length of the rectangle = 3x

And, The width of the rectangle = x

Hence, We get;

Area of rectangle = Length x Width

⇒ 39 = 3x × x

⇒ 39 = 3x²

⇒ x² = 13

⇒ x = √13

Hence, The length of the rectangle = 3√13

And, The width of the rectangle = √13

Thus, The perimeter of the figure is,

⇒ P = 3 × [ 2 (3√13 + √13) ]

⇒ P = 6 × 4√13

⇒ P = 24√13 units

Therefore, The perimeter of the shape formed is,

⇒ P = 24√13 units

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Set 2:

T. Slope = (9-5)/(10-7) = 4/3 __16.  Slope = (2-(-2))/(9-(-5)) = 4/14

B. Slope = (-4-2)/(-5-(-8)) = -6/3 __ 8.  Slope = (-8-(-6))/(2-(-10)) = -2/12

H.  Slope = (-1-(-2))/(-4-2) = -3/-6 __ 3.  Slope = (-7-1)/(-8-(-2)) = -8/6

S.  Slope = (7-9)/(-11-(-4)) = -2/-7 __ 5. Slope = (3-(-2))/(-3-(-4)) = 5/1

O. Slope = (-6-(-1))/(4-5) = -5/-1 __ 14.  Slope = (6-(-4))/(-7-(-2)) = 10/-5

Set 3:

K. Slope = (-3-(-3))/(2-1) = 0/1 __ 9.  Slope = (-4-(-1))/(6-8) = -3/-2

R. Slope = (5-0)/(-3-3) = 5/-6 __ 1.  Slope = (-5-(-6))/(-8-(-11)) = 1/3

E. Slope = (-2-4)/(8-12) = -6/-4 __ 15. Slope = (3-4)/(-5-(-5)) = -1/0

U.  Slope = (-9-(-3))/(7-7) = -6/0 __ 12. Slope = (9-(-3))/(-5-(-2)) = 12/3

O.  Slope = (5-1)/(2-3) = 4/-1 ____ 6.  Slope = (8-8)/(7-(-3)) = 0/10

H.  Slope = (-8-(-6))/(-7-(-1)) = -2/-6 _ 10. (-5, 3) and (7, -7) Slope = (-7-3)/(7-(-5)) = -10/12

A set is a collection of distinct objects, usually numbers, that are grouped together in a manner that follows specific rules. Sets can be used to determine if an element belongs to the set or not, and can also be used to perform operations such as unions and intersections. Sets are an important tool in mathematics, and they can help simplify complex problems.

The Mathematician had to calculate the slope between two points for each of the sets given. To calculate the slope, the Mathematician had to subtract the y-values of the two points and divide by the difference between the x-values of the two points. The Mathematician then had to match the answers to the corresponding letter or number and write the letter in the matching numbered box at the bottom of the page. By doing this, the Mathematician was able to solve the riddle and arrive at work on time.

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The minimum number of streetlights that can be installed along the street is 1641 + 1182 = 2823.

In Euclidean geometry, the distance between two points is defined as the length of the shortest path between them. This is often referred to as the "straight-line distance" or "Euclidean distance." It is calculated using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The total distance between A and C is the sum of the distances AB and BC:

AC = AB + BC = 1625 + 1170 = 2795 m

Since we need to install streetlights at points A, B, and C, there will be two segments of the street with streetlights:

From A to B, which has a distance of 1625 m

From B to C, which has a distance of 1170 m

We want to install streetlights along each segment with equal distance between the lights. Let's call the distance between each pair of adjacent streetlights "d".

For the first segment, there will be "n" streetlights, so the total distance covered by the streetlights will be (n-1)d. Similarly, for the second segment, there will be "m" streetlights, and the total distance covered by the streetlights will be (m-1)d.

The total distance covered by the streetlights should be equal to the distance AC, so we have:

(n-1)d + (m-1)d = AC

Substituting the values we know, we get:

1624d + 1169d = 2795

2793d = 2795

d = 2795/2793

d ≈ 0.999

We can round down to 0.99 to ensure that we don't have more streetlights than necessary.

Therefore, the distance between each pair of adjacent streetlights should be 0.99 m. To find the minimum number of streetlights required, we can divide the distance of each segment by 0.99 and round up to the nearest integer:

For the first segment: ceil(1625/0.99) = 1641

For the second segment: ceil(1170/0.99) = 1182

So the minimum number of streetlights that can be installed along the street is 1641 + 1182 = 2823.

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the width of the garden is approximately 6.77 feet, and the length is approximately 11.77 feet (since it is 5 feet more than the width).

what is rectangle?

A rectangle is a four-sided polygon with opposite sides that are parallel and equal in length.

Let's denote the width of the garden by x. Then, according to the problem statement, the length of the garden is x + 5.

The total width of the garden and the walkway is x + 2(3) = x + 6, and the total length is x + 5 + 2(3) = x + 11.

The area of the garden itself is x(x + 5), and the area of the garden and the walkway is (x + 6)(x + 11).

The area of the walkway is the difference between the two: (x + 6)(x + 11) - x(x + 5) = 210.

Expanding and simplifying this expression, we get:

x^2 + 17x - 135 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = 17, and c = -135, so we have:

x = (-17 ± sqrt(17^2 - 4(1)(-135))) / 2(1)

x = (-17 ± sqrt(769)) / 2

We can discard the negative solution, so we have:

x = (-17 + sqrt(769)) / 2

x ≈ 6.77

Therefore, the width of the garden is approximately 6.77 feet, and the length is approximately 11.77 feet (since it is 5 feet more than the width).

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Answer:

False

Step-by-step explanation:

The absolute value of a number is defined as its distance from zero on the number line. Distance is always a non-negative quantity, so the absolute value of a number can never be negative.

Therefore, the absolute value of any number, whether positive or negative, is always a non-negative value.

The equivalent expressions are A3, B2, C3, D4 and E5.

Expression in math is a combination of numbers, symbols, and operations that represent a value or a relationship between values. Expressions are used to represent relationships between numbers, variables, and other mathematical objects. Expressions are the basic building blocks of algebra and calculus, and allow us to solve problems and describe relationships between different quantities. Expressions help us to understand math better, as they allow us to express complex ideas in concise, clear, and concise form.

Once the wires are connected by matching the equivalent expressions, the code word is 8+7+(-3).

This is happening because in order to unlock the communication system, you need to match the equivalent expressions in order to find the code word. By evaluating each expression, you can determine which of the expressions are equivalent and then connect the wires accordingly. By connecting the wires, you can then find the code word which will unlock the communication.

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A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. Thus, option D is correct.

The degree of operating leverage (DOL) formula is:

DOL = Contribution Margin / Net Operating Income

We can calculate the contribution margin using the CM ratio:

Contribution Margin = Sales x CM ratio

Contribution Margin = $200,000 x 0.60

Contribution Margin = $120,000

Now we can calculate the DOL:

DOL = Contribution Margin / Net Operating Income

DOL = $120,000 / $30,000

DOL = 4.00

Therefore, the company's degree of operating leverage is 4.00.

The answer is (D) 4.00.

Step-by-step explanation:

Identify the relevant values from the problem statement:

Net operating income = $30,000

Fixed expenses = $90,000

Sales = $200,000

CM ratio = 60%

Calculate the contribution margin using the CM ratio:

Contribution Margin = Sales x CM ratio

Contribution Margin = $200,000 x 0.60

Contribution Margin = $120,000

Use the contribution margin and net operating income to calculate the degree of operating leverage:

DOL = Contribution Margin / Net Operating Income

DOL = $120,000 / $30,000

DOL = 4.00

Interpret the result:

A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. This indicates that the company has a high degree of operating leverage, which means that it is more sensitive to changes in sales volume. In other words, small changes in sales can have a big impact on the company's profitability.

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A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. Thus, option D is correct.

The degree of operating leverage (DOL) formula is:

DOL = Contribution Margin / Net Operating Income

We can calculate the contribution margin using the CM ratio:

Contribution Margin = Sales x CM ratio

Contribution Margin = $200,000 x 0.60

Contribution Margin = $120,000

Now we can calculate the DOL:

DOL = Contribution Margin / Net Operating Income

DOL = $120,000 / $30,000

DOL = 4.00

Therefore, the company's degree of operating leverage is 4.00.

The answer is (D) 4.00.

Identify the relevant values from the problem statement:

Net operating income = $30,000

Fixed expenses = $90,000

Sales = $200,000

CM ratio = 60%

Calculate the contribution margin using the CM ratio:

Contribution Margin = Sales x CM ratio

Contribution Margin = $200,000 x 0.60

Contribution Margin = $120,000

Use the contribution margin and net operating income to calculate the degree of operating leverage:

DOL = Contribution Margin / Net Operating Income

DOL = $120,000 / $30,000

DOL = 4.00

Interpret the result:

A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. This indicates that the company has a high degree of operating leverage, which means that it is more sensitive to changes in sales volume. In other words, small changes in sales can have a big impact on the company's profitability.

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Answer:

To calculate Mr. Dladla's gross profit per day, we first need to calculate his total revenue and total cost per month:

Total revenue per month = Selling price x Expected market share per month

Total revenue per month = R500 x (50% of 4500 customers) = R112,500

Total cost per month = Cost per course x Number of courses per month

Total cost per month = R300 x 20 days = R6,000

Gross profit per month = Total revenue per month - Total cost per month

Gross profit per month = R112,500 - R6,000 = R106,500

To calculate his gross profit per day, we can divide the gross profit per month by the number of days the training company opens per month:

Gross profit per day = Gross profit per month / Number of days per month

Gross profit per day = R106,500 / 20 days = R5,325 per day

Therefore, Mr. Dladla's gross profit per day is R5,325.

Step-by-step explanation:

The line goes through the point and has a slope of 4, a y-intercept of -6, and a slope of 4. (0, 6).

The proportion of the increase in the y-value to the change inside the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) and Q := (4,1) on the line.

A line's slope is how steeply it slopes form LEFT to RIGHT. Divide the rise, or vertically increase, by the run, or horizontally start changing, to get the line's gradient.

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The complete question is:

X in graphs the equation y = 4x - 6.

Select all statements about Xin's graph that are true.

a. The graph is a curved line.

b. The line passes through the origin.

c. The line passes through the point (0, 6).

d. The slope of the line is 4.

e. The y-intercept of the line is -6.

Answer:

62 miles per hour

Step-by-step explanation:

62 x 6 gets you 372 easy

Answer: Two 1/6

Step-by-step explanation:

It takes two 1/6 to make the same amount as 1/3 because 1/6 is half of 1/3, so all it takes is two 1/6 to make 1/3.

Answer:

1/3 is equal to 2/6, so it takes 2 sixths to make the same amount as 1/3.

We can write the quadratic equation as -

y = - (x - 25)² + 625

The general form of a quadratic equation is -

y = ax² + bx + c

where -

a, b and c are constants.

Given is that Sameen wants to build a fence around a rectangular area of her yard. The graph shows the area {y} in square feet that she can surround with the fencing that she has, where the breadth is width {x} in feet of the rectangle.

The given coordinates on the parabola are -

(8, 336)

(42, 336)

(25, 625)

Here, the point (25, 625) represents the vertex (h, k) of the parabola.

We can write the equation of parabola as -

y = a(x - h)² + k

y = a(x - 25)² + 625

For the point (8, 336), we can write -

336 = a(8 - 25)² + 625

336 - 625 = a(8 - 25)²

a(8 - 25)² = - 289

a(- 17)² = -289

a = -289/289

a = -1

So, we can write the quadratic equation as -

y = - (x - 25)² + 625

Therefore, we can write the quadratic equation as -

y = - (x - 25)² + 625

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NO || PR using the converse of the Triangle Proportionality Theorem are not parallel.

The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Conversely, if a line divides two sides of a triangle proportionally, then it is parallel to the third side.

In this problem, we are given a right triangle NQM, where line PR intersects the sides NM and QM at points P and R, respectively. We are also given that NM = 16, PM = 12, RM = 6, and QR = 8. We want to verify that NO || PR.

To do this, we will use the converse of the Triangle Proportionality Theorem. We know that PR divides NM proportionally, so we need to show that it also divides QM proportionally.

Using the ratios of corresponding side lengths of similar triangles, we can write:

PM / RM = PN / RN

Substituting the given values, we get:

12 / 6 = PN / (16 - 6)

2 = PN / 10

PN = 20

Similarly, we can write:

QR / RM = QN / RN

Substituting the given values, we get:

8 / 6 = QN / (16 - 6)

4 / 3 = QN / 10

QN = 40 / 3

Now we can check if PR divides QM proportionally:

PM / QN = 12 / (40 / 3) = 9 / 5

PN / RM = 20 / 6 = 10 / 3

Since these ratios are not equal, we can conclude that PR does not divide QM proportionally.

Therefore, by the converse of the Triangle Proportionality Theorem, we can conclude that NO is not parallel to PR.

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Answer:

y=-1/4x-2/3

Step-by-step explanation:

Answer:??? Bio?

Step-by-step explanation:give a good expample

q^2 is the resulting expression for the exponent

Given the expression below

[tex]\frac{q}{q^{-1}\cdot q\cdot q^{-1}}[/tex]

Using the product and division law of indices, we will have:

a^m * a^n. = a^m+n

a^m/a^n = a^m-n

Applying this law, the denominator of the expression will be:

[tex]\frac{q}{q^{-1}\cdot q\cdot q^{-1}} = \frac{q}{q^{-2+1}}\\\frac{q}{q^{-1}\cdot q\cdot q^{-1}}=\frac{q}{q^{-1}}\\\frac{q}{q^{-1}\cdot q\cdot q^{-1}}=q^{1+1}=q^2[/tex]

Hence the resulting expression of the exponents is q^2

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The function describes this graph is y = x² + 9x + 18.

In mathematics, a graph is defined as a graphical representation or diagram that organises facts or values. The graph's points frequently reflect the relationship between two or more things.

Given:

We can see from the Graph touches the x axis at -6 and -3.

So, the factors of function are (x +6) and (x+ 3).

Then, the function represented by the graph is

y = (x+ 6) (x + 3)

y = x² + 6x + 3x + 18

y = x² + 9x + 18

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Answer:

The perimeter of the shape is 41

Step-by-step explanation:

You have to add 12 plus 9 plus 7 plus 8 plus 2 plus 3, which equals forty one. I got the two and three from the little corner which isn’t labeled. I got it by subtracting 8 from 12, and 7 from 9.

Answer:

94.3/C

Step-by-step explanation:

Hope this helps!

Answer: You have a probability of 1/2.

Step-by-step explanation: Since there are 12 marbles in total, and there are 6 green marbles, you have a 1 in 2 chance to draw a green marble.

Answer:

z=89

Step-by-step explanation:

42+z=131

take 42 away from both sides

z= 89

Answer:

z = 89

Step-by-step explanation:

42 + z = 131

z = 131 - 42

z = 89