(3x^2-9x+4)+(x^2+2x-10)

1+b²+b⁴ ​can be resolved into factors (1+b²+b),(1+b²- b).

We will evaluate  1+b²+b⁴​ with the help of algebraic identities,

We can write 1+b²+b⁴ as,

1+b²+b⁴ = 1+(b)²+(b²)²

             = 1+(b)²+(b)²+(b²)²-b² (Adding and subtracting b²)

             = 1+2(b²)+(b²)²-(b)²

             = (1)²+2(b²)(1)+(b²)²- (b)²

Now using the identity (a + b)²= a²+b²+2ab, we have,

1+b²+b⁴ = (1+b²)²- (b)²

             = (1+b²+b)(1+b²- b)  [By using identity a²-b²= (a+b)(a-b)]

Therefore, the correct answer is  1+b²+b⁴​= (1+b²+b)(1+b²- b).

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Answer:

P= (20+15)*2=35*2=70cm

Answer:

z = 83/(6-c-t)

Step-by-step explanation:

-cz +6z = tz +83

Subtract tz from each side

-cz +6z -tz = 83

Factor out z

z(6-c-t) = 83

Divide by (6-c-t)

z(6-c-t) /(6-c-t) = 83/(6-c-t)

z = 83/(6-c-t)

The correction option with regard to the above proportion prompt is Option A where AC/CE = BD/DF.

The rule of proportionality in geometry states that if two pairs of corresponding sides in two similar geometric figures are in proportion, then the figures are similar.

This rule applies to parallel lines as well. In a pair of parallel lines intersected by a transversal, the corresponding angles formed are in proportion.

Specifically, corresponding angles are congruent, alternate interior angles are congruent, and alternate exterior angles are congruent, maintaining the rule of proportionality.

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Answer:

  (a) AC/CE = BD/DF

  (d) CE/DF = AE/BF

Step-by-step explanation:

You have two transversals crossing three parallel lines, and you want to identify the correct proportions.

We can identify the correct proportions by first listing corresponding segment of the transversals.

A proportion can be formed by equating one pair of corresponding segments to another, or by equating a pair of segments from the left column to the corresponding pair from the right column. The segments need to be listed in the same order.

  AC/CE = BD/DF . . . . . . correct, first two of each column in correct order

  AC/BD = DF/CE . . . . . . incorrect. One of these is upside down

  AB/CD = CD/EF . . . . . . incorrect. Segments are not corresponding

  CE/DF = AE/BF . . . . . . correct, last two of each column in correct order

<95141404393>

It's not entirely clear what is meant by "5 Apples in 6 rows," so I will provide a general answer that could apply to a few different interpretations of the question.

If Johnny has 5 apples and places them in 6 rows, the answer to how many apples he will have left depends on how many apples are in each row and what Johnny does with them. For example, if he eats one apple from each row, he will be left with 5 - 6 = -1 apples, which doesn't make sense. If instead he rearranges the apples into one row, he will still have 5 apples. If he gives away 2 apples, he will have 3 apples left.

In summary, the number of apples Johnny will have left depends on the details of the scenario, including how many apples are in each row and what Johnny does with them.

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By organizing countless data points into comprehensible ranges or bins, the histogram, which resembles a bar graph in appearance, condenses a data series into an understandable visual. So Histograms based on data on housing, prices and salaries typically are skewed to the right.

A histogram in statistics is a graphic depiction of the data distribution. The histogram is shown as a collection of rectangles that are next to one another, where each bar represents a different type of data.

A branch of mathematics called statistics is used in many different fields. Frequency is the term for how often numbers appear in statistical data; it can be shown as a table and is known as a frequency distribution.

A histogram is a bar graph-like data visualization that groups various class levels into columns along the horizontal x-axis. The numerical count or percentage of occurrences for each column in the data are shown on the vertical y-axis.

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The solution of the quadratic equation is z₁ = -2 + 3.46i and z₂ = -2 - 3.46i.

The solution of the quadratic equation is calculated as follows;

The given quadratic equation;

z² + 4z + 16 = 0

We will solve the quadratic equation using the formula method as follows;

a = 1, b = 4, c = 16

The general formula for the quadratic equation is given as;

z = [ - b ± √ (b² - 4ac) ] / ( 2a )

From the given parameters, we will substitute the appropriate values and solve for z;

z =  [ - 4 ± √ (4² - 4 x 1 x 16) ] / ( 2 x 1)

z = [ - 4 ± √ ( - 48) ] / 2

z₁ = -2 + 3.46i

z₂ = -2 - 3.46i

Thus, the Argand diagram of the solution of the quadratic equation is in the diagram attached.

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Answer:

The cost when the two companies charge the same is $7,703.

Step-by-step explanation:

Let 'x' represent the number of tons.

For x tons the first company will charge:

5297 + 200.50x

For x tons the second company will charge:

6500 + 100.25x

We want to find x so that both companies charge the same, that is:

5297 + 200.50x = 6500 + 100.25x

x = 12 tons

For 12 tons both companies will charge the same.

The cost charged for 12 tones is:

5297 + 200.50*12 = $7,703

Hope this Helps! :)

Answer:

B.

Step-by-step explanation:

Mathematical modeling of surfaces is the representation of two-dimensional manifolds using mathematical techniques, particularly in the context of Digital Terrain Modeling (DTM) where surfaces refer to the Earth's terrain or physical objects.

Mathematical modeling of surfaces plays a crucial role in various fields, including computer graphics, engineering, and geosciences. Surfaces are fundamental objects that can be represented and analyzed using mathematical techniques.

In this section, we will delve into the concept of surfaces, particularly in the context of Digital Terrain Modeling (DTM). Additionally, we will explore the distinction between 3D and 2D DTM.

1. The Concept of Surfaces:

In the realm of mathematics, a surface is defined as a two-dimensional manifold, meaning it is a topological space that locally resembles Euclidean space.

In simpler terms, a surface is a geometrical entity that can be thought of as a continuous collection of points, forming a boundary between a solid and its surrounding space. In the context of DTM, surfaces typically refer to the representation of the Earth's terrain or any other physical object using mathematical models.

2. Digital Terrain Modeling:

Digital Terrain Modeling involves the creation of digital representations of the Earth's surface or any specific region using computer algorithms. It serves as a crucial tool in various applications, such as urban planning, environmental analysis, and military simulations. DTM utilizes mathematical models to represent the terrain accurately, allowing for detailed analysis and visualization.

3. 3D Digital Terrain Models:

A 3D Digital Terrain Model (DTM) is a representation of the Earth's surface that captures three-dimensional information. It provides a detailed depiction of the terrain, including elevation data, contours, and topographical features.

3D DTMs are typically generated using techniques such as LiDAR (Light Detection and Ranging) or photogrammetry. These models enable precise analysis of the landscape, volumetric calculations, and visualization from different perspectives.

4. 2D Digital Terrain Models:

In contrast to 3D DTMs, 2D Digital Terrain Models represent the Earth's surface in two dimensions. They provide a simplified view of the terrain, focusing primarily on elevation data and contour lines. 2D DTMs are commonly used in cartography, where the terrain is represented on a flat surface, such as a map or a computer screen. While they lack the depth information of 3D DTMs, 2D models are still valuable for many applications, including geographic information systems (GIS) and land surveying.

5. Differences between 3D and 2D Digital Terrain Models:

The main distinction between 3D and 2D DTMs lies in the level of detail and the dimensionality of the representation. 3D DTMs provide a more comprehensive and realistic view of the terrain, capturing not only the elevation but also the shape, slopes, and other three-dimensional features. These models are highly suitable for applications that require a precise understanding of the terrain's topography, such as hydrological analysis or landscape design.

On the other hand, 2D DTMs offer a simplified representation of the terrain, primarily focusing on elevation data and contour lines. They are more commonly used for general visualization and analysis purposes where the third dimension is not critical. 2D DTMs are easier to create and process, making them more accessible for applications that do not require intricate three-dimensional modeling.

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The type of statistical study that the researchers used is a randomized controlled trial (RCT). In a randomized controlled trial, participants are randomly assigned to two or more groups.

One group is the treatment group, which receives the intervention being studied. The other group is the control group, which does not receive the intervention.

The researchers in this study randomly assigned 200 full-time employees to two groups: a treatment group and a control group. The treatment group was instructed to meditate 10-20 minutes twice per day, and to participate in weekly 1-hour sessions. The control group was not given any special instructions.

After a period of 8 weeks, all participants were required to fill out the psychological strain questionnaire (PSQ). The PSQ is an accepted measure of work stress.

The researchers calculated the difference in questionnaire scores for all participants, where a positive change corresponds to a reduction in work stress. Then, they compared the average differences of each group.

The researchers found that the treatment group had a significantly lower average difference in PSQ scores than the control group. This suggests that meditation may be an effective way to reduce work stress.

Here are some other details about randomized controlled trials:

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The estimated cost of the new 3000-ft2 heat exchange system for the plant retrofit can be calculated using the power-sizing exponent and the price index. Based on the given information, the rough estimate for the cost of the new heat exchanger system is approximately $108,984.

To estimate the cost of the new heat exchange system, we need to consider the price index and the power-sizing exponent. The price index provides a measure of the change in prices over time. In this case, the price index 7 years ago was 1360, and the current price index is 1478.

To calculate the cost estimate, we can use the following formula:

Cost estimate = (Cost of previous heat exchanger) × (Current price index / Previous price index) × (New size / Previous size) ^ power-sizing exponent

Using the given information, the cost of the previous heat exchanger was $75,000, the previous size was 1200 ft2, and the new size is 3000 ft2.

Plugging in these values into the formula, we get:

Cost estimate = ($75,000) × (1478 / 1360) × (3000 / 1200) ^ 0.55

Simplifying the calculation, we find:

Cost estimate ≈ $108,984

Therefore, a rough estimate for the cost of the new 3000-ft2 heat exchanger system for the plant retrofit is approximately $108,984. It's important to note that this is just an estimate and the actual cost may vary based on specific factors and market conditions.

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The points on the curve where the tangent line has a slope of -1 are (2/√3, -(2/√3)) and (-2/√3, 2/√3). None of the given answer choices matches this solution, so the correct option is (E) None of the above.

For the points on the curve where the tangent line has a slope equal to -1, we need to find the points where the derivative of the curve with respect to x is equal to -1. Let's find the derivative:

Differentiating both sides of the equation x^2 - xy + y^2 = 4 with respect to x:

2x - y - x(dy/dx) + 2y(dy/dx) = 0

Rearranging and factoring out dy/dx:

(2y - x)dy/dx = y - 2x

Now we can solve for dy/dx:

dy/dx = (y - 2x) / (2y - x)

We want to find the points where dy/dx = -1, so we set the equation equal to -1 and solve for the values of x and y:

(y - 2x) / (2y - x) = -1

Cross-multiplying and rearranging:

y - 2x = -2y + x

3x + 3y = 0

x + y = 0

y = -x

Substituting y = -x back into the original equation:

x^2 - x(-x) + (-x)^2 = 4

x^2 + x^2 + x^2 = 4

3x^2 = 4

x^2 = 4/3

x = ±sqrt(4/3)

x = ±(2/√3)

When we substitute these x-values back into y = -x, we get the corresponding y-values:

For x = 2/√3, y = -(2/√3)

For x = -2/√3, y = 2/√3

Therefore, the points on the curve where the tangent line has a slope of -1 are (2/√3, -(2/√3)) and (-2/√3, 2/√3).

None of the given answer choices matches this solution, so the correct option is:

E) None of the above.

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Answer:

21

Step-by-step explanation:

Answer: Side Angle Side

Answer:

B.

She can rotate triangle DEF 180and then compare the angles and sides. She will see that the triangles are congruent by the Side Angle Side theorem.

Step-by-step explanation:

The probability used in computing Butte's normal spoilage is the product of the probabilities of defective materials and defective workmanship, which is (10/1000) * (15/1000).

In this scenario, we have two independent events: defective materials and defective workmanship. The probability of defective materials is given as 10 units in 1,000, which can be expressed as 10/1000 or 0.01. Similarly, the probability of defective workmanship is given as 15 units in 1,000, which can be expressed as 15/1000 or 0.015.

Since these two events are independent, we can multiply their probabilities to find the joint probability. Therefore, the probability used in computing Butte's normal spoilage is (10/1000) * (15/1000), which simplifies to 0.00015 or 0.015%.

To understand this calculation further, we can consider the concept of independent events. When two events are independent, the occurrence of one event does not affect the probability of the other event occurring. In this case, the probability of defective materials and defective workmanship are independent of each other. By multiplying their probabilities, we find the joint probability of both events occurring simultaneously.

The resulting probability of 0.00015 or 0.015% represents the likelihood that a randomly selected unit will have both defective materials and defective workmanship. This probability is used in computing Butte's normal spoilage, which helps estimate the expected amount of defective units in a production process.

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The smallest positive integer which when divided by 10,9,8,7,6 leaves the remainder of 9,8,7,6,5 is 2519.

Given that,

We have to find what is the lowest positive number that, when divided by 10, 9, 8, 7, 6, yields a remainder of 9, 8, 7, 6, 5.

We know that,

The integers are

10,9,8,7,6

We have to find the LCM of the integers.

The lowest common multiple, or LCM, is another name for the least frequent multiple in mathematics. The least common multiple of two or more numbers is the number that is the smallest among all the multiples of the given numbers that are given.

The LCM 10,9,8,7,6 is 2520

In each example, the difference between the remainder and the divisor is 1.

The required number =2520−1=2519.

Therefore, The smallest positive integer which when divided by 10,9,8,7,6 leaves the remainder of 9,8,7,6,5 is 2519.

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If you incurred a $200,000 charge from the clinic and have an insurance plan with a $1,000 deductible and 80%/20% co-insurance, you would pay $40,800.

With a $1,000 deductible, you are responsible for paying the first $1,000 of the medical expenses out of pocket. After meeting the deductible, the co-insurance comes into effect. In this case, the co-insurance is 80%/20%, which means that the insurance company will cover 80% of the remaining expenses, while you are responsible for paying the remaining 20%.

For a $200,000 charge from the clinic, here's how the calculation works:

Amount after deductible: $200,000 - $1,000 = $199,000

Co-insurance: You pay 20% of $199,000 = $39,800

The total amount you would pay is the sum of the deductible and the co-insurance:

$1,000 + $39,800 = $40,800

Therefore, the correct answer is B) $40,800, as this represents the amount you would pay if you incurred a $200,000 charge from the clinic with a $1,000 deductible and 80%/20% co-insurance.

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there's actually no problem or link here, but if you put something here then maybe we can help!

Answer

Thanks lol i just started and its getting fun

Step-by-step explanation:

Answer:

105 teachers

Step-by-step explanation:

15:1  --> 1575:105

1575/15=105

Hope this helps :)

Answer:

x = 20

Step-by-step explanation:

\(\frac{10}{x}\) = \(\frac{x}{40}\)

We cross-multiply and get

400 = \(x^{2}\)

\(\sqrt{400}\) = \(\sqrt{x^{2} }\)

x = 20

So, the answer is x = 20

Answer:

n = 18

Step-by-step explanation:

Corresponding parts of similar triangles are in same ratio

\(\frac{FG}{XY}=\frac{HG}{YZ}\\\\\frac{n}{6}=\frac{15}{5}\\\\n=\frac{15}{5}*6\\\\n=3*6\\\\n=18\)

Answer:

See below

Step-by-step explanation:

(a+11)9

a*9=9a

11*9=99

a+11 is the simplified version.

-hope it helps

Answer:

So we must create 4-digit numbers with the 5 odd digits in the image.

First, a number is only divisible by 5 if the last digit is 0 or 5, and we only can use the last digit equal to 5 (because 0 is not in the image).

if each odd number can be used only once, we have:

Now, for the other 3 digits we have 4 options.

So for the first one we have 4 options,

for the second we have 3 options (because one is already taken)

for the last one we have only 2 options

then the number of combinations is:

C = 4*3*2 = 24.

If the numbers can be repeated (for example, 5555 is allowed, then)

we still have our last digit fixed in 5, and for the first digit we have 5 options, for the second we also have 5 options, and for the third we also have 5 options, then we have a total of:

C = 5*5*5 = 25*5 = 125 combinations.

Answer:

Discrete

Step-by-step explanation:

Discrete is the type of variable in which the number of auto accidents reported in a given month q

Discrete data is a count that uses integers and has a finite number of potential values. This sort of information can't be broken down into smaller chunks. Discrete data consists of finite, numeric, countable, and non-negative integers with discrete variables.

As we know that the number of auto accidents that can be reported in a month will be always a whole number, therefore, the number of accidents can be represented as 0, 1, 2,..., 1000, etc.

Thus, the type of variable is the number of auto accidents reported in a given month is Discrete.

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The answer is 3258 please give me brainliest.

The solution to the system is x1 = 8, x2 = 1, and x3 = -1.

To solve the systems, we will use the method of elimination. This method involves multiplying one or both equations by a constant in order to eliminate one of the variables.

First, we will eliminate x1 from the first and second equations by multiplying the first equation by -1 and then adding the two equations together:
-1(x1 - 3x2) = -1(5)
-x1 + 3x2 = -5

-x1 + x2 + 5x3 = 2
2x2 + 5x3 = -3
Next, we will eliminate x2 from the second and third equations by multiplying the second equation by -1 and then adding the two equations together:
-1(-x1 + x2 + 5x3) = -1(2)

x1 - x2 - 5x3 = -2
x2 + x3 = 0
x1 - 6x3 = -2

Finally, we will eliminate x3 from the second and third equations by multiplying the third equation by -5 and then adding the two equations together:

-5(x2 + x3) = -5(0)
-5x2 - 5x3 = 0

2x2 + 5x3 = -3
-3x2 = -3
x2 = 1

Now that we know the value of x2, we can substitute it back into the third equation to find the value of x3:
x2 + x3 = 0
1 + x3 = 0
x3 = -1
And finally, we can substitute the values of x2 and x3 back into the first equation to find the value of x1:
x1 - 3x2 = 5
x1 - 3(1) = 5
x1 = 8
So the solution to the system is x1 = 8, x2 = 1, and x3 = -1.

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Answer: 48

Step-by-step explanation:

By the geometric mean theorem,

\(\frac{x}{36}=\frac{64}{x}\\\\x^{2}=36 \cdot 64\\\\x=\sqrt{36 \cdot 64}\\\\x=\sqrt{36} \sqrt{64}=48\)