Simplify the expression k^4⋅ k^7

Answer:

(2x2- 10x2+ 6x -3x2 + 15x -9) simplified to (-12x2+21x-9)

Step-by-step explanation:

I could explain but you would just be confused because I did it in my head and I don't do it the way they teach us to if you want to make sure my answer is right you should be able to simplify my simplified version back into the original problem

Answer:

i) A. 180º rotation about the origin, ii) \(Q' = (4, 5)\).

Step-by-step explanation:

i) In this case, we understand that vertex \(P = (-5,-3)\) changed to \(P' = (5,3)\) after doing an operation. At first we must calculate the distance of each point regarding origin by Pythagorean Theorem:

Point P:

\(OP = \sqrt{(x_{P}-x_{O})^{2}+(y_{P}-y_{O})^{2}}\)

If we know that \(x_{P} = -5\), \(y_{P} = -3\), \(x_{O} = 0\) and \(y_{O} = 0\), the distance \(OP\) is:

\(OP = \sqrt{(-5-0)^{2}+(-3-0)^{2}}\)

\(OP \approx 5.831\)

Point P':

\(OP' = \sqrt{(x_{P'}-x_{O})^{2}+(y_{P'}-y_{O})^{2}}\)

If we know that \(x_{P'} = 5\), \(y_{P'} = 3\), \(x_{O} = 0\) and \(y_{O} = 0\), the distance \(OP'\) is:

\(OP' = \sqrt{(5-0)^{2}+(3-0)^{2}}\)

\(OP' \approx 5.831\)

As \(OP = OP'\), origin is the center of rotation.

Besides, \(P'\) is a multiple of \(P\), that is:

1) \((-5, -3)\) Given

2) \(((-1)\cdot 5, (-1)\cdot 3)\) \((-a)\cdot b = -a\cdot b\)

3) \((-1)\cdot (5, 3)\) Scalar multiplication of a vector/Result.

The value of the scalar proves that P experimented a 180º rotation about the origin. Hence, the correct answer is A.

ii) If \(Q = (-4, -5)\) and the same operation described in item i) is used, then, the location of \(Q'\) is:

\(Q' = (-1)\cdot Q\)

\(Q' = (-1) \cdot (-4,-5)\)

\(Q' = ((-1)\cdot (-4), (-1)\cdot (-5))\)

\(Q' = (4, 5)\)

Which corresponds to option C.

Answer:

1. A, 2. C

Step-by-step explanation:

Answer:  6000ft2

Step-by-step explanation: Multiply 15*20*20 to find the area of a figure.

The term that suggests that the threat of loss has a greater impact on a decision than the possibility of an equivalent gain is prospect theory.

Prospect theory is a theory that describes how individuals make decisions under uncertainty. The theory suggests that people think about gains and losses differently and that the value they assign to a particular change in their situation depends on their current situation. The theory is based on the observation that people often violate the principle of expected utility. They make decisions that do not maximize their expected utility. The theory suggests that people evaluate outcomes based on changes from a reference point, rather than in absolute terms. This means that people are more sensitive to changes in their situation than to the situation itself.

For example, a loss of $100 is more painful than the pleasure of gaining $100, and the pleasure of gaining $100 is less than the pain of losing $100.

In summary, Prospect theory suggests that the threat of a loss has a greater impact on a decision than the possibility of an equivalent gain.

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Answer:

$270.625

Step-by-step explanation:

\(\frac{x}{250} \frac{108.25}{100} = 270.625\)

To make homemade pizza: Gather ingredients/tools, prepare dough, preheat oven, shape dough, assemble with sauce, cheese, and toppings, bake at 475°F for 12-15 mins, remove, slice, and serve hot. Customize as desired.

Process: How to make a homemade pizza

Gather Ingredients and Tools

Pizza dough (store-bought or homemade)

Tomato sauce

Cheese (mozzarella or your preferred type)

Toppings of choice (e.g., pepperoni, mushrooms, bell peppers, etc.)

Olive oil

Salt

Flour (for dusting)

Rolling pin

Baking sheet or pizza stone

Oven

Prepare the Dough

If using store-bought dough, follow the instructions on the package. If making homemade dough:

a) Combine flour, yeast, salt, and water in a mixing bowl.

b) Knead the dough until it becomes smooth and elastic.

c) Place the dough in a greased bowl, cover it, and let it rise until it doubles in size (usually around 1-2 hours).

Preheat the Oven

Set the oven temperature to 475°F (245°C) and allow it to preheat.

Shape the Dough

Sprinkle flour on a clean surface and place the dough on it.

Roll out the dough with a rolling pin, creating a round or rectangular shape according to your preference.

If you prefer a thinner crust, roll it out more; for a thicker crust, keep it slightly thicker.

Assemble the Pizza

Transfer the shaped dough to a greased baking sheet or pizza stone.

Brush olive oil over the surface of the dough to prevent it from getting soggy.

Spread a layer of tomato sauce evenly over the dough, leaving a small border for the crust.

Sprinkle a generous amount of cheese over the sauce.

Add your desired toppings on top of the cheese.

Bake the Pizza

Place the baking sheet or pizza stone with the assembled pizza in the preheated oven.

Bake for approximately 12-15 minutes or until the crust is golden brown and the cheese is bubbly and melted.

Remove and Serve

Carefully remove the pizza from the oven using oven mitts.

Let it cool for a few minutes before slicing it into desired portions.

Serve hot and enjoy!

Remember to customize the process based on personal preferences and dietary restrictions. Experiment with different toppings and techniques to create your perfect homemade pizza.

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To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Transportation has become an essential part of our daily lives. It has transformed over time and has improved access to transportation services, increased connectivity, and intermodal options.

To meet the various transportation needs, different modes of transportation have evolved, including water, air, rail, 3PL, cross-docking, truck, intermodal, and pipeline. Each mode of transportation has unique characteristics and advantages. In this regard, matching the following transportation characteristics with the appropriate mode of transportation is necessary.

The most capable mode of transportation is the water mode of transportation. It has the highest capacity and can transport a vast amount of goods over long distances. It can transport large, heavy, and bulky goods that are difficult to transport by other modes of transportation. The mode of transportation that provides the most accessibility is the truck mode of transportation. It can reach almost any location as it can travel on roads and highways. It offers door-to-door service, which means that it can pick up the goods from the sender and deliver them to the receiver. The most reliable mode of transportation is the rail mode of transportation. It is not affected by traffic or weather conditions, which means that it can transport goods on time. It also has a low risk of accidents or delays, which makes it a reliable mode of transportation.

The fastest mode of transportation over a long distance is the air mode of transportation. It is the quickest mode of transportation as it can travel at high speeds and can cover long distances in a short time. This makes it ideal for transporting goods that need to be delivered urgently. The mode of transportation that has the lowest per-unit cost is the water mode of transportation. It is the most cost-effective mode of transportation as it can transport a large number of goods at once, which reduces the cost per unit.

Match the following descriptions with the appropriate transportation intermediary. The transportation intermediary that consolidates LTL shipments into FTL shipments is cross-docking. It takes small shipments from multiple companies and consolidates them into larger shipments. The transportation intermediary that is a nonprofit cooperative that arranges for members' shipments is 3PL.The transportation intermediary that brings shippers and carriers together is the intermodal mode of transportation. It provides an intermodal network to connect different modes of transportation to transport goods efficiently.

The transportation intermediary that purchases blocks of rail capacity and sells it to shippers is rail transportation. It makes it easier for shippers to transport goods using the rail mode of transportation.

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Answer:

The time it takes Ms. Croft to reach the cruise ship by speedboat = 6.11 hours

The time it takes Ms. Croft to reach the cruise ship by helicopter = 6.25 hours

since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

Step-by-step explanation:

The given parameters are;

The elapsed time by which Ms. Croft missed the boat = 5 hours

The speed of the cruise ship = 528 mi/day

The speed of the speedboat = 100 miles in 2.5 hours

The speed of the helicopter = 90 mph

The time it would take Ms. Croft to arrive at the harbor = 3.5 hours

Therefore, we have;

The cruise ship's speed = 528 miles per 24 hours = 528/24 mph = 22 mph

The location of the cruise after the first 5 hours = 5 × 22 = 110 miles

The speed of the speedboat = 100 miles per 2.5 hours = 100/2.5 = 40 mph

By traveling with a speed boat

The time at which Ms. Croft will intercept the cruise ship is given by the following relation;

40 mph × t = 22 mph × t + 110 miles

Which gives;

40 mph × t - 22 mph × t = 110 miles

18 mph = 110 miles

t = 110 miles/(18 mph) = 55/9 hours ≈ 6.11 hours

By taking the helicopter, we have;

Upon arrival at the harbor, after 3.5 hours, we find

90 mph × t = 22 mph × t + 22 mph × 3.5 hours + 110 miles

90 mph × t - 22 mph × t = 22 mph × 3.5 hours + 110 miles

68 mph × t = 77 miles + 110 miles = 187 miles

t = 187 miles/(68 mph) = 11/4 hours = 2.75 hours

The total time it takes Ms. Croft to reach the cruise ship by taking the helicopter = 3.5 + 2.75 = 6.25 hours

Therefore, since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

The total volume is,

= 350 + 100

= 450 in³

And, The total surface area is,

= 150 + 70 + 140 + 50

= 410 in²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

For Top prism:

To find the volume of the top prism, multiply the area of the base by the height. This is 1/2 times width times height times length.

V = 1/2 × l × w × h

   = 1/2 × 5 × 10 × 4

   = 100 in.

To find the surface area of a prism, find the area of the triangular base and the area of each rectangular side.

Area of the base is,

A = 1/2  bh = 1/2 × 7 × 4 = 14 .

Since there are 2 bases, the area is 28.

Now, Area of the rectangular side is,

A = bh

   = 10 x 5  = 50 in².

Since there are two,

Hence, the area is,

A = 2 × 50 = 100

And, The surface area of the prism is ,

50 + 100 = 150 in²

Bottom prism:

To find the volume of the bottom prism, multiply the width times the height times the length.

V = lwh

   = 10 x 5 x 7

   = 350 in³

And, To find the surface area of the bottom prism, find the area of the base and each side of the house.

A = 10 x 5 = 50 in

A = 10 × 7 = 70 which occurs twice so it has a total area of 140.

A = 5 x 7 = 35 which occurs twice so it has an area of 70

Hence, The total volume is,

350 + 100

450 in³

And, The total surface area is,

= 150 + 70 + 140 + 50

= 410 in²

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The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.

To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).

Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.

Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

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There are 210 different committees that can be formed by selecting 6 people from a list of 10 people.

What is the combination?

Combinations are a way to count the number of ways to choose a subset of objects from a larger set, where the order of the objects does not matter.

To calculate the number of different committees that can be formed, we can use the concept of combinations.

In this case, we want to select 6 people from a list of 10 people, and the order in which the committee members are selected does not matter.

The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

where C(n, r) represents the number of combinations of selecting r items from a set of n items, and ! denotes factorial.

Using this formula, we can calculate the number of different committees that can be formed:

C(10, 6) = 10! / (6! * (10 - 6)!)

Simplifying:

C(10, 6) = 10! / (6! * 4!)

10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

6! = 6 * 5 * 4 * 3 * 2 * 1

4! = 4 * 3 * 2 * 1

Substituting these values:

C(10, 6) = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((6 * 5 * 4 * 3 * 2 * 1) * (4 * 3 * 2 * 1))

C(10, 6) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)

C(10, 6) = 210

Therefore, there are 210 different committees that can be formed by selecting 6 people from a list of 10 people.

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Answer:

36 correct answers

Step-by-step explanation:

Given that,

The ratio of the number of problems Josie got incorrect to the number of problems she got correct is 2:9.

Josie missed 8 questions

Let incorrect answers be 2x and that of correct answers be 9x.

ATQ,

2x = 8

x = 4

Correct answers = 9x

= 9(4)

= 36

Hence, she will get 36 correct answers.

Answer:

34r+48

Step-by-step explanation:

36r+48-2r=34r+48

Answer:

8√2

Step-by-step explanation:

This is a 45-45-90 right triangle with a Pythagorean triple of (x, x, x√2). Because this is a 45-45-90, both legs have the same measure, namely 8. Therefore, according to the Pythagorean triple, x = 8 (NOT the x in your diagram...the x in the Pythagorean triple). That means that the hypotenuse has a measure of 8\sqrt{2}8

2

, which is d.

To simplify

First of all, Octavia error can be spotted from the correct steps below

Step1: Expand the expression

Step2: Collect like terms

Step 3: Simplify by using exponents laws

Step 4: Combine the terms.

The value is

Her error was that she didn't apply the exponents' law properly.

One of the laws she violated was

Her mistake was that she did

So she missed it from our step 1 above

Answer:

\(y = \frac{Pa}{b} - za\)

Step-by-step explanation:

See picture below :)

Answer:

y=x3−13x−12

Step-by-step explanation:

The velocity of the boat when it reaches the buoy is approximately 17.32 m/s. This is found using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, and s is the displacement.

To solve this problem, we can use the equations of motion. The initial velocity of the boat, u, is 30 m/s, the acceleration, a, is -3.0 m/s² (negative because the boat is slowing down), and the displacement, s, is 100 m. We need to find the final velocity, v, when the boat reaches the buoy.

We can use the equation: v² = u² + 2as

Substituting the given values, we have:

v² = (30 m/s)² + 2(-3.0 m/s²)(100 m)

v² = 900 m²/s² - 600 m²/s²

v² = 300 m²/s²

Taking the square root of both sides, we find:

v = √300 m/s

v ≈ 17.32 m/s

Therefore, the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

The problem provides the initial velocity, acceleration, and displacement of the boat. By applying the equation v² = u² + 2as, we can find the final velocity of the boat. This equation is derived from the kinematic equations of motion. The equation relates the initial velocity (u), final velocity (v), acceleration (a), and displacement (s) of an object moving with uniform acceleration.

In this case, the boat is decelerating with a constant acceleration of -3.0 m/s². By substituting the given values into the equation and solving for v, we find that the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

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Answer:

Step-by-step explanation:

the value of X is 1

Answer: the height of the pole is 16.782 meters

Step-by-step explanation: Let us take the height of the pole as "h".

i) Finding the height of the pole:

distance from the pole is 20m.

The angle of elevation is 40°

\(tan(40°) = h/20\)

Multiply both sides by 20:

\(20 * tan(40°) = h\)

\(h ≈ 20 * 0.8391 ≈ 16.782 meters\)

Therefore, the height of the pole is 16.782 meters.

ii) Finding the angle of depression

The angle of depression is the angle formed between the horizontal ground and the line of sight from the point of observation to the foot of the pole.

angle of depression = angle of elevation = 40°

Therefore, the angle of depression of the foot of the pole from the point of observation is 40°.

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Using trigonometric methods, it is determined that the height of the pole is found by using the formula for tangent, and adding the height of the observer. The angle of depression equals the angle of elevation, so both are 40 degrees.

To solve the problem, we use the properties of a right triangle and trigonometric functions. Since we know the angle of elevation and the length of one side, we can find the length of the other side using the tangent function.

For the height of the pole: we know that tan(θ) = opposite/adjacent, so,
tan(40) = height/20
height = tan(40) * 20

Let's denote the observer's height as h=1.54m, so the total height of the pole is height + h.

For the angle of depression: In a right triangle, the angle of depression and the angle of elevation are equal. Therefore, the angle of depression is also 40 degrees.

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Answer:

Step-by-step explanation:

Area of trapezium

Area of rectangle - Area of triangle

Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

To find the limit of cos(x)/(1-sin(x)) as x approaches (π/2)+, we can use l'Hospital's Rule.

First, we can take the derivative of both the numerator and denominator with respect to x: lim cos(x)/(1 − sin(x)) x → (π/2)+ = lim [-sin(x)/(cos(x))] / [-cos(x)] x → (π/2)+ = lim sin(x) / [cos(x) * cos(x)] x → (π/2)+

Now, plugging in (π/2)+ for x, we get: lim sin(π/2) / [cos(π/2) * cos(π/2)] x → (π/2)+ = 1 / (0 * 0) = undefined

Since the denominator approaches 0 as x approaches (π/2)+, and the numerator is bounded between -1 and 1, the limit does not exist.

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Step-by-step explanation:

The number of cups of red paint is always 15 of the total number of cups. 0.2 of the total number of cups.

She writes the equation r = 15t (r = 0.2t) to describe the relationship.

In this case, the total no. of cups is an independent variable. No. of cups do not depend on any term.

The number of cups of red paint is a dependent variable as it depends on the number of cups.

The rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

What is volume?

Volume refers to the amount of three-dimensional space occupied by an object or a substance.

To find the rate of increase in the volume V of a sphere when the surface area S becomes 100π square inches, we need to use the formulas relating the surface area and volume of a sphere to its radius.

The surface area S of a sphere is given by the formula:

\(S = 4\pi r^2,\)

where r is the radius of the sphere.

The volume V of a sphere is given by the formula:

\(V = (4/3)\pi r^3.\)

To find the rate of increase in volume with respect to time, we need to differentiate the volume formula with respect to time.

Given that the radius r is increasing at a uniform rate of 0.3 inches per second, we can write:

dr/dt = 0.3 inches per second.

Now, let's differentiate the volume formula with respect to time:

\(dV/dt = d/dt [(4/3)\pi r^3].\)

Using the power rule of differentiation, we get:

\(dV/dt = (4/3)\pi * 3r^2 * (dr/dt).\)

Simplifying further, we have:

\(dV/dt = 4\pi r^2 * (dr/dt).\)

Since we want to find the rate of increase in cubic inches per second, we need to express the volume in cubic inches.

Substituting the value of the surface area S = 100π square inches into the surface area formula:

\(100\pi = 4\pi r^2.\)

Dividing both sides by 4π, we get:

\(r^2 = 25.\)

Taking the square root of both sides, we find:

r = 5.

Now, we can substitute the value of r into the rate of increase formula:

\(dV/dt = 4\pi(5^2) * (0.3).\)

Simplifying the expression:

dV/dt = 4π(25) * 0.3.

dV/dt = 30π cubic inches per second.

Therefore, the rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

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Answer:

C

Step-by-step explanation:

Look in your old textbooks

Answer:

m = N/A

Step-by-step explanation:

Can you give me a curve or something?