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Which graph represents the function f(x) = -1x1 – 2?

Given statement solution is :- Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages: Simplification and abstraction, Prediction and simulation, Cost and time efficiency, Insight and understanding.

Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages:

Simplification and abstraction: Mathematical models allow complex systems or processes to be represented using simplified mathematical equations or algorithms. This simplification helps in understanding the underlying principles and relationships of the system, making it easier to analyze and predict outcomes.

Prediction and simulation: Models enable scientists to make predictions about the behavior of a system under different conditions. They can simulate scenarios that are difficult or impossible to observe in the real world, allowing researchers to explore various hypotheses and make informed decisions.

Cost and time efficiency: Models can be used to explore different scenarios and test hypotheses in a relatively quick and cost-effective manner compared to conducting real-world experiments. They can help guide experimental design by providing insights into the most relevant variables and parameters.

Insight and understanding: Mathematical models often reveal underlying patterns and relationships that may not be immediately apparent from experimental data alone. They provide a framework for organizing and interpreting data, leading to a deeper understanding of the system being studied.

However, mathematical models also have limitations and potential disadvantages:

Simplifying assumptions: Models are based on assumptions and simplifications, which may not fully capture the complexity of the real-world system. If these assumptions are incorrect or oversimplified, the model's predictions may be inaccurate or misleading.

Uncertainty and error: Models are subject to uncertainties and errors stemming from the inherent variability of the system, limitations in data availability or quality, and simplifying assumptions. It is crucial to assess and communicate the uncertainties associated with model predictions.

Validation and verification: Models need to be validated and verified against experimental data to ensure their accuracy and reliability. This process requires rigorous testing and comparison to real-world observations, which can be challenging and time-consuming.

Mathematical models are closely linked to the fields of chemistry, biology, and physics, providing valuable insights and predictions in these disciplines. Here are some examples:

Chemistry: Mathematical models are used to study chemical reactions, reaction kinetics, and molecular dynamics. One example is the use of rate equations to model the kinetics of a chemical reaction, such as the reaction between reactants A and B to form product C.

Biology: Mathematical models play a crucial role in understanding biological systems, such as population dynamics, gene regulation, and the spread of infectious diseases. For instance, epidemiological models like the SIR (Susceptible-Infectious-Recovered) model are used to simulate and predict the spread of diseases within a population.

Physics: Mathematical models are fundamental in physics to describe physical phenomena and predict outcomes. One well-known example is Newton's laws of motion, which can be mathematically modeled to predict the motion of objects under the influence of forces.

Quantum mechanics: Mathematical models, such as Schrödinger's equation, are used to describe the behavior of particles at the quantum level, providing insights into atomic and molecular structures and the behavior of subatomic particles.

Fluid dynamics: Mathematical models, such as the Navier-Stokes equations, are employed to study the behavior of fluids, including airflow, water flow, and weather patterns.

These examples demonstrate the wide range of applications for mathematical models in understanding, predicting, and simulating various phenomena in the fields of chemistry, biology, and physics.

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The height of the pile increasing when the pile is 6 ft high is 1.41ft/min (approx.)

Define Volume of cone?

A pyramid having a circular cross section is called a cone. A right cone is a cone with the vertex located above the base's middle. Right circular cone is another name for it. If you know the height and radius of a cone and plug those values into a formula, you can quickly get the volume of a cone. Formula is , V =  1/3 πr²h

We have, dV/dt = 40 ft³/min

h = diameter where, h = 2r

so r = 1/2h

The formula for regular circular cone is,

V =  1/3 πr²h

put the value of r,

V = 1/ 3 * π * (1/2h)² * h

   = 1/12 * π * h³

differentiate it, we get

dV/dt = 3/12 * π * h² * dh/dt

dh/dt = (dV/dt)/(3/12*π*h²)

we have, dV/dt = 40 ft³/min and h = 6

Put these values,

dh/dt = 40 / (3/12 * 22/7 * 6²)               (∵ π = 22/7)

After solving, we get

dh/dt = 1.41 ft/min

Therefore, The height of the pile increasing when the pile is 6 ft high is 1.41ft/min (approx.)

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The given expression represents the present value of a series of future cash flows discounted at a rate of 6.5% per year.

Each term in the expression represents a cash flow at a specific time in the future, and the denominator in each term represents the discount factor, which reflects the time value of money.

The first term, $250,000 / (1+0.065)^1, represents a cash flow of $250,000 that will be received in one year.

To determine its present value, we divide it by the discount factor (1+0.065)^1, which reflects the fact that the money will be received one year from now and is, therefore, less valuable than money received today.

Similarly, the second term, $37,500 / (1+0.065)², represents a cash flow of $37,500 that will be received in two years.

To determine its present value, we divide it by the discount factor (1+0.065)²,

which reflects the fact that the money will be received two years from now and is, therefore, less valuable than money received today.

This process is repeated for each term in the expression, representing cash flows that will be received in three, four, five, and six years, respectively.

The sum of these present values represents the total present value of the cash flows or the amount that they are worth today if they are discounted at a rate of 6.5% per year.

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\(\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=2x\\b=3\\r+1=4\Rightarrow r=3\\n=5\\T_4=\binom{5}{3}\cdot (2x)^{5-3}\cdot3^3\\T_4=\dfrac{5!}{3!2!}\cdot 4x^2\cdot27\\T_4=\dfrac{4\cdot5}{2}\cdot 4x^2\cdot27\\\\T_4=1080x^2\)

The correct options are- B. x = –4 – √2 and D. x = –4 + √2 are the roots of the given quadratic equation.

When a square is complete, a quadratic is written in the shape of a squared bracket, and if necessary, a constant is added. Finding the function's highest or minimum value and the time it happens is one use for the square-root method.

Given quadratic equation:

x² – 8x + 16 = 2

This can be written as:

x² – 2*4x + 4² = 2

(x + 4)² = 2

Taking square root both sides:

√(x + 4)² = √2

(x + 4) = ±√2

x = ±√2  - 4

Or x = -4 + √2 and x = -4 - √2

Thus, the roots of the quadratic equation found by using the method of completing the square are - x = -4 + √2 and x = -4 - √2

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Complete question:

Use completing the square to solve this quadratic equation. Check all that apply. x² – 8x + 16 = 2

A. x = 4 –√2

B. x = –4 – √2

C. x = 4 + √2

D. x = –4 + √2

Answer:

100 per

Step-by-step explanation:

The rate of change with respect to the number of deposit will be 100.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The graph of the linear function shown in the image.

Now,

Two points on the graph are (3, 350) and (2, 250).

Hence, Rate of change = (250 - 350) / (2 - 3)

                                    = -100/-1

                                    = 100

Thus, The rate of change with respect to the number of deposit will be 100.

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Alex's set of ordered pairs would no longer define a function if any of the following actions were taken:

A set of ordered pairs defines a function if, for every element in the domain (the set of first coordinates), there is exactly one element in the range (the set of second coordinates).

For example, if Alex's set of ordered pairs is {(1,2), (2,3), (3,4)}, it would no longer define a function if a new ordered pair of (2,5) is added to it, as it would mean that there are now two different second coordinates (3,5) for the first coordinate 2. This would violate the rule that every element in the domain must have exactly one corresponding element in the range. Similarly, removing one of the ordered pairs, changing the order of the ordered pair, or changing the domain or range would cause the set to no longer to define a function.

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Answer:

17168

Step-by-step explanation:

Answer:

x+8y+3

Step-by-step explanation:

Answer: 8y(3+x)

Step-by-step explanation: Correct me if this is wrong but I believe it’s right- Good luck!:)

Answer:

Step-by-step explanation:

its c

The statement that identifies and explains the mistake made by tamara was,

Her first mistake was in Step 2. She added 0.2 to each term instead of multiplying by 0.2.

The correct option is option A)

What is multiplication?

Multiplication is one of the basic arithmetic operation in which we take the product of two or more terms. The other basic operation is addition, subtraction and division.

We are given an expression 0.2(4+1.4y-2.1)

To compute simplify and find the value of y,

We multiply 0.2 inside we get the following,

(0.8+0.28y-0.42)

Instead of performing multiplication operation like this she added 0.2 in each and every term

This was the mistake made by her

Hence, The statement that identifies and explains the mistake made by tamara was,

Her first mistake was in Step 2. She added 0.2 to each term instead of multiplying by 0.2.

The correct option is option A)

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Answer:

square root of 6 +square root of two ÷4

simplified =0,9659258263

Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)

Answer:

f(x) = 51x

f(5) = 51(5)

f(5) = 255

Step-by-step explanation:

Answer:

a. mu_d = the true population mean difference in jump height

Step-by-step explanation:

In statistical parlance, observations used for a study could either be randomly chosen points or members of a large group or population, this small chosen observation obtained from a larger group is called the sample, the statistical measures or characteristic of such group is called statistic; while statistical characteristic, computations or measurement of the entire group of observations is called the parameter.

Mean of sample are usually represented with a bar sign on top such as (xbar) ; while mean of a population is represented as μ.

Answer:

(5 - (-1)) or 6

Step-by-step explanation:

Substitute the variables

= (x - y)

=(5 - (-1))

= 6

Hope this was simple enough for you to understand!

Answer: An implicit function is a function, written in terms of both dependent and independent variables, like y-3x2+2x+5 = 0. Whereas an explicit function is a function which is represented in terms of an independent variable.

Step-by-step explanation: To find the implicit derivative,

Differentiate both sides of f(x, y) = 0 with respect to x.

Apply usual derivative formulas to differentiate the x terms.

Apply usual derivative formulas to differentiate the y terms along with multiplying the derivative by dy/dx.

Solve the resultant equation for dy/dx (by isolating dy/dx).

Answer:

\(3x^2+126x\)

Step-by-step explanation:

Solve For X.

3x(x+42)

Ans:

3x(x+42)

Use the distributive property to multiply 3x by x+42.

\(3x^2+126x\)

Answer:

\(x=4y^2-24y+30\)

\((x-4.5)^2+(y-2.5)^2=23\)

Step-by-step explanation:

Standard form of a sideways parabola:  \(x=ay^2+by+c\)

Given equation:

\(4y^2-x-24y+30=0\)

Add x to both sides:

\(4y^2-24y+30=x\)

\(\implies x=4y^2-24y+30\)

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

Standard form of circle equation

\((x-a)^2+(y-b)^2=r^2\)

(where (a,b) is the center and r is the radius)

Given equation:

\(2x^2+2y^2-18x-10y+7=0\)

Group like terms:

\(2x^2-18x+2y^2-10y+7=0\)

Divide by 2:

\(x^2-9x+y^2-5y+3.5=0\)

Factor by completing the square for each variable:

\((x-4.5)^2-20.25+(y-2.5)^2-6.25+3.5=0\)

Rearrange into standard form:

\((x-4.5)^2+(y-2.5)^2=23\)

Therefore, the circle has a center at (4.5, 2.5) and a radius of √23

Answer: B

Step-by-step explanation:

Since \(AB < AC < BC\), it follows that \(\angle C < \angle B < \angle A\)

Answer:

Screen record as your parent puts the password in or wipe off your screen and give the parent your phone to put the password in then look at the fingerprint circles and that where each number is, then try all the possible combinations

Step-by-step explanation:

You have the following polynomial:

2x⁴ - 3x³ + x² + 7x + 3 = 0

Based on the grade of the previous polynomial, you can conclude that there are 4 roots.

The complex roots are always present in pairs. Then, it's possible the given polynomial has 4 complex roots. In case there are 2 real roots, then, there are two comlpex roots.

Otherwise, there are 4 real roots.

Then, you can conclude for the possible roots of the polynomial:

- 4 real roots

- 4 complex roots

- 2 real roots and 2 complex roots

Answer:

15%

Step-by-step explanation:

Is means equals and of means multiply

60 = P * 400

Divide each side by 400

60/400 = P

.15 = P

Change to percent form

15%  is the percent

Answer:

the answer to the question you've asked is 15

To begin, let's find how much the book is including tax and the student discount.  Once we find this, we can see if Lara or Alex is correct and if they can afford it.

First, we want to compute the student discount. The student discount is 35%. Thus, we can do 0.65 x 28.50 = 18.525. With 10% tax, we have 18.525 x 1.1 = 20.3775. Which will round up to $20.38.

Now, lets see what Alex did and if he got the same answer. First he takes 35% of $28.50 and subtracts it from the normal price.

.35 x 28.50 = 9.975

28.50 - 9.975 = 18.525

Then he takes 10% of this number and adds it back.

.10 x 18.525 = 1.8525

18.525 + 1.8525 = 20.3775

Alex has the correct answer.

Next, we will see if Lara computed it correctly.

First she takes 65% of the normal price.

0.65 x 28.50 = 18.525

Then she computes 110% of the reduced price.

18.525 x 1.10 = 20.3775

Lara also gets the correct answer.

So, do they have enough money to purchase the book?

YES:

$20.38 < $21

Is Alex correct?

YES

Is Lara correct?

YES

Although they used different methods to get the answer, they both got the right one!

Answer:

D 98°

Step-by-step explanation:

180-82 = 98 or the long way

3x+5 = 180-82

3x = 93

x = 31

3(31) + 5 = 98

Answer:

comp=59º

sup=149º

Step-by-step explanation:

complement adds to 90º

supplement adds to 180º

90-31=59

180-31=149

Answer:

c = -11

expression value = 245

c = 0

expression value = 3

c = 15

expression value = 453

Step-by-step explanation:

Given expression = \(2c^2 + 3\)

for c = -11 , we put c in place of c in given expression

\(2(-11)^2 + 3 = 2(121) + 3 = 242 + 3 = 245\)

for c= 0

\(2(0)^2 + 3 = 2(0) + 3 = 0 + 3 = 3\)

for c = 15

\(2(15)^2 + 3 = 2(225) + 3 = 450 + 3 = 453\)

Answer:

80 degrees

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees so we can create the equation 70+30+x=180. This solves out to 80 so x=80 degrees.

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

Answer:

j = 9.65

Step-by-step explanation:

\(\frac{8}{cos(34)}\) = j

j = 9.649743588... (round as needed)