Find the sum of -4x^{2}-8x−4x 2 −8x and -x^{2}-6x+8−x 2 −6x+8.

The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

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Answer:

The volume of a cylinder:

\(V \approx 2035.75\) \(ft^3\)

Step-by-step explanation:

-To find the volume of a cylinder, you first need the formula:

\(V = \pi (\frac{d}{2})^2 h\)

\(d =\) diameter

\(h =\) height

-Use the following diameter and height for the formula:

\(V = \pi (\frac{18}{2})^2 8\)

-Then, you solve:

\(V = \pi (\frac{18}{2})^2 8\)

\(V = \pi \times (\frac{18}{2})^2 \times 8\)

\(V = \pi \times (9)^2 \times 8\)

\(V = \pi \times 81 \times 8\)

\(V = \pi \times 648\)

\(V = 648\pi \approx 2035.752\)

-Since the hundredth place is 2, It cannot be rounded to the nearest hundredths place, so it would be:

\(V \approx 2035.75\) \(ft^3\)

The interest earned by Mrs Grey over the 7 years is R5670. The cost of the television set 5 years ago was R20,600.

4.1.1 To calculate the interest earned by Mrs Grey over 7 years, we use the formula for simple interest: Interest = Principal x Rate x Time. Mrs Grey's principal is R18,000 and the rate is 4.5% per annum. The time is 7 years. Using the formula, we can calculate the interest as follows:

Interest = R18,000 x 0.045 x 7 = R5670. Therefore, Mrs Grey has earned R5670 in interest over the 7 years.

4.1.2 To calculate the cost of the television set 5 years ago, we need to account for the inflation rate. The cost of the television set now is R27,660. The average rate of inflation over the last 5 years is 6.7% per annum. We can use the formula for compound interest to calculate the original cost of the television set:

Cost 5 years ago = Cost now / (1 + Inflation rate)^Time

Cost 5 years ago = R27,660 / (1 + 0.067)^5 = R20,600. Therefore, the cost of the television set 5 years ago was R20,600.

4.1.3 To determine the rate of simple interest Mrs Grey should have invested her money at 7 years ago, we can use the formula for interest: Interest = Principal x Rate x Time. We know the principal is R18,000, the time is 7 years, and the interest earned is R5670. Rearranging the formula, we can solve for the rate:

Rate = Interest / (Principal x Time)

Rate = R5670 / (R18,000 x 7) ≈ 0.0448 or 4.48% per annum. Therefore, Mrs Grey should have invested her money at a rate of approximately 4.48% per annum to have earned enough interest to purchase the television set using only her original investment and the interest earned over the 7 years.

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Since the subsequence {an} = 1, 2, 3, 4, 5, 6, 7, … is convergent to the limit ∞, thus the original sequence {an} = 1, 2, 3, 4, 5, 6, 7, … must also be unbounded.

If every term of the sequence is either greater than or equal to (≥) some number M or less than or equal to (≤) some number N (finite numbers), then the sequence is said to be bounded.

Otherwise, the sequence is said to be unbounded. And, if a sequence has a convergent subsequence, then the sequence is called bounded.

Let’s look at the example to answer the question.

Example of an unbounded sequence that has a convergent subsequence:

Let {an} = 1, 2, 3, 4, 5, 6, 7, …It is an unbounded sequence since there is no number that can be defined as M or N, that will make every term of the sequence less than or equal to (≤) or greater than or equal to (≥) this number (M or N).

However, {an} = 1, 2, 3, 4, 5, 6, 7, … has a convergent subsequence which is {an} = 1, 2, 3, 4, 5, 6, 7, … itself.

And, since the subsequence {an} = 1, 2, 3, 4, 5, 6, 7, … is convergent to the limit ∞, thus the original sequence {an} = 1, 2, 3, 4, 5, 6, 7, … must also be unbounded.

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The height of the tower is 969 feet.

Let CD be the tower and A be the point from a window in the building, a person determines that the angle of elevation to the top of the tower is 42 degrees.

In triangle AED

tan42° = ED/AE

tan42° = h₁/615

h₁ = tan42° × 615

= 553.74

Rounding to the nearest integer

h₁ = 554

In triangle AEC

tan34° = EC/AE

tan34° = h₂/615

h₂ = tan34° × 615

= 414.82

Rounding to the nearest integer

h₂ = 415

Height of tower = EC + ED

= h₁ + h₂

= 554 + 415

= 969

Therefore, the height of the tower is 969 feet.

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The probability that a student prefers to go to an amusement park can be determined by dividing the number of students who chose the amusement park by the total number of students surveyed.

Out of the students surveyed in the school cafeteria, every sixth student was asked about their preference for the school's spring outing. There were 15 students who chose an amusement park out of the total surveyed group. To calculate the probability, we need to divide the number of students who chose the amusement park by the total number of students surveyed.
If we assume that the total number of students surveyed is represented by 'N', and we know that every sixth student was surveyed, we can calculate the total number of students surveyed by multiplying 6 by the number of students who chose the amusement park. In this case, the total number of students surveyed is 6 * 15 = 90.
Therefore, the probability that a student prefers to go to an amusement park is the number of students who chose the amusement park (15) divided by the total number of students surveyed (90). Hence, the probability is 15/90, which simplifies to 1/6 or approximately 0.167 (or 16.7%).

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Answer:

A and B

Step-by-step explanation:

The equation that shows the relationship between the angles in the triangle is m∠1 + m∠2 + m∠3 = 180.

The equation that shows the relationship between the angles in the triangle is determined as follows;

The sum of angles in a triangle is equal to 180 degrees.

So based on this information, the equation that shows the relationship between the angles in the triangle is formulated as;

angle 1 + angle 2 + angle 3 = 180

We can re-write the equation as follows;

m∠1 + m∠2 + m∠3 = 180

Thus, the equation that shows the relationship between the angles in the triangle is the sum of angle 1 plus angle 2 plus angle 3.

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Answer:

Step-by-step explanation:

Let the number be x

Half a number is written as 1/2x

So we have

Four times the sum of half a number and 6 is 48 is written as

\(4( \frac{1}{2} x + 6) = 48 \\ 2x + 24 = 48 \\ 2x = 48 - 24 \\ 2x = 24\)

Divide both sides by 2

That's

\( \frac{2x}{2} = \frac{24}{2} \)

We have the final answer as

Hope this helps you

 the number of ways to assign 20 different people to three different rooms with at least one person in each room.We can solve this problem using the concept of combinations and the Principle of Inclusion-Exclusion.

1. First, let's calculate the total number of ways to assign 20 people to 3 rooms without any constraints. This can be done using the multiplication principle: each person has 3 choices for a room, so there are 3^20 ways to assign the people.

2. Next, we need to subtract the cases where at least one room is empty. For this, we can use the Principle of Inclusion-Exclusion.

3. There are 3 ways to choose the empty room. Once we've chosen the empty room, there are 2 choices for each of the remaining 20 people, so there are 3 * 2^20 ways to assign people with exactly one empty room.

4. However, we have double-counted cases with two empty rooms, so we need to add them back. There are 3 ways to choose the room with people, and all 20 people will be in that room, so there are 3 ways to assign people with exactly two empty rooms.

5. Finally, we can calculate the answer by combining these cases:

Total ways = 3^20 - 3 * 2^20 + 3

This gives us the number of ways to assign 20 different people to three different rooms with at least one person in each room.

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Answer:

∡2 = 115°

Step-by-step explanation:

Answer: We know that for any circle with radius r the formula for the area and circumference of the circle is given as: Area of circle=πr². ... Hence, to describe the relationship between the area of a circle and its circumference. The Area of circle is 1/2 times the radius times the circumference.

Step-by-step explanation:

Answer:

=5

Step-by-step explanation:

6-2=5

Answer:

1,

Step-by-step explanation:

now z also a dk4k ak4 smka 4ml 4 LL

Answer:

Step-by-step explanation:

$ 3750 = truck rental; $125 per ton of sugar transported

C is cost; S is number of tons transported

Equation relating C to S would be a linear equation like y = mx + b

C = 125S + $3750

This equation would be graphed in the first quadrant only

you would start with your y-intercept at (0, 3750)

As x increases by 1, your y increases by 125 yielding these points:

(1, 3875) (2, 4000) (3, 4125) etc.

This shows that for each increase by one ton of sugar, the cost goes up $125

1)Cost of 1 ton = $ 2000

Cost of 2 ton = $3500

Cost of 3 ton = $5000

$ 1500 increase for each of ton of sugar being transported.

2) (1 , 2000) ; (2 , 3500)

Slope =

= 1500

The data structures are true:  Option (1,3)

Data structures are ways of organizing and storing data in a computer so that it can be accessed and manipulated efficiently. There are several types of data structures, including arrays, linked lists, stacks, queues, trees, and graphs. Each structure has its own unique features and advantages, making it suitable for different scenarios.

For example, arrays are used for storing and accessing data in a linear fashion, while trees and graphs are used for representing hierarchical relationships between data. Data structures are a fundamental concept in computer science and are used in many applications, including databases, compilers, and operating systems. Understanding and implementing data structures is essential for efficient programming and software development

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Full Question: Which of the following statements about the data structures are true? Select ALL CORRECT answers.

Answer:

the next two are 65, and 257

Answer:

65 and 257

Step-by-step explanation:

17x4=68   68-3=65.      65x4=260   260-3=257

1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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Answer:

4 is the correct answer.

Number "4" can each term of the equation be multiplied by to eliminate the fractions before solving.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

To eliminate the fractions in the equation -3/4m -1/2m=2+1/4m, we need to find the least common multiple (LCM) of the denominators of the fractions, which is 4.

We can then multiply each term of the equation by 4 to eliminate the fractions.

So, multiplying both sides of the equation by 4, we get:

-3m - 2m = 8 + m

To simplifying, we have:

-5m = 8 + m

To solve for m, we can isolate the variable on one side of the equation. Adding 5m to both sides, we get:

4m = 8

Finally, dividing both sides by 4, we get:

m = 2

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Answer:

Step-by-step explanation:

(2x-5)(x+6)=0

either 2x-5=0               Or, x+6=0

2x-5=0

2x=0+5

x=5/2

x+6=0

x=0-6

x=-6

so x=5/2 , x=-6

Answer:

ok sooo

Step-by-step explanation:

2x - 5 + - x - 2

Take the square root of each side.

\(\sf \sqrt{x^{2} } =\sqrt{25} \\\\\\ x=\± 5\)

The radius of the given circle is 3x+8.

First, we need to simplify the expression inside the parentheses:

pi (9x² + 48x + 64) = pi [(3x + 8)(3x + 8)]

Now, we can equate this expression to the formula for the area of a circle:

\(\pi r^2 = \pi [(3x + 8)(3x + 8)]\)

Simplifying this equation by canceling out pi from both sides, we get:

\(r^2 = (3x + 8)(3x + 8)\)

Expanding the right-hand side of the equation, we get:

\(r^2 = 9x^2 + 48x + 64\)

Taking the square root of both sides, we get:

\(r = \sqrt{(9x^2 + 48x + 64)\)

Therefore, the answer is (C) 3x+8.

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Given:

The inequality is

\(5.25-b\geq 6.5\)

To find:

The solution of the given inequality on the number line.

Solution:

We have,

\(5.25-b\geq 6.5\)

Subtract 5.25 from both sides.

\(5.25-b-5.25\geq 6.5-5.25\)

\(-b\geq 1.25\)

Multiply both sides by -1 and change the sign of inequality.

\(b\leq -1.25\)

The value of b always less than or equal to -1.25. Since -1.25 included in the solution set, therefore there is a solid circle on -1.25.

-1.25 lies between -2 and -1. It means the solid circle lies between -1 and -2.

\(b\leq -1.25\), so the number line is shaded from the circle to negative 5.

A number line going from negative 5 to positive 5 is the required solution if a solid circle appears between negative 1 and negative 2. The number line is shaded from the circle to negative 5.

Therefore, the correct option is A.

Answer:

the correct answer is option C

Step-by-step explanation:

I fixed my mistake from choosing option A

Answer:

Step-by-step explanation:

We can classify the graph of the equation 25x² − 10x − 200y − 119 = 0 as a hyperbola.

The given equation is 25x² − 10x − 200y − 119 = 0.

Let's see how we can classify the graph of this equation.

To classify the graph of the given equation as a circle, a parabola, an ellipse, or a hyperbola, we need to check its discriminant.

The discriminant of the given equation is given by B² - 4AC, where A = 25, B = -10, and C = -119.

The discriminant is:(-10)² - 4(25)(-119) = 100 + 11900 = 12000

Since the discriminant is positive and not equal to zero, the graph of the equation is a hyperbola.

Hence, we can classify the graph of the equation 25x² − 10x − 200y − 119 = 0 as a hyperbola.

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The cost of materials for the cheapest container is $184.67.

Suppose the width is x and it is given that the length of its base is twice the width, so the length of the base is 2x.

The base area is 2x².

Since the volume is $12m³

The height has to be 12/ 2x² = 6/ x²

The cost of making such a container is.

cost of base = 2x² × 10

= 20x²

The cost of sides =( 2 × 2x 6/x² + 2 × x × 6 / x²) 6

= (24/x + 12/x )6

= 36/x × 6

216/x

The overall cost is hence the sum of the base and the sides = f(x)

= 20x² + 216/x

To get the minimum,

df(x) / dx = 20x² + 216/x = 0

= 40x - 216/x² = 0

x³ = 216/40

= 54/10

= 27/5

x = 3/∛5

= 3/ 1.70

= 1.76

f(x) = 20(1.76)² + 216/ 1.76

= 61.952 + 122.72

= 184.67

Therefore we get the cost of the materials to be $184.67.

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