A line has a slope of -1 and passes through the point (-19, 17). Write its equation in slope- intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.​

Answer:

The new points to the triangle will be:
\(A(1,4)\\ B(1,1)\\ C(-1,1)\)

Step-by-step explanation:

Because the reflection point is at \(x=2\), all x values will subtract their distances from \(x=2\) to get their new values. The y values remain the same.

The starting values are:

\(A(3,4)\\ B(3,1)\\ C(5 ,1)\)

Point \(A\) is 1 unit away from \(x=2\), so we'll subtract 1 from 2 to get the new x value: \(2 - 1 = 1\), so \(A(1,4)\).

 

Point \(B\) is also 1 unit away from \(x=2\), so we'll subtract 1 from 2 to get the new x value: \(2 - 1 = 1\), so \(B(1,1)\).

Point \(C\) is 3 units away from \(x=2\), so we'll subtract 3 from 2 to get the new x value: \(2 - 3 = -1\), so \(C(-1,1)\).

(1) f(x) = (1 - x³) / (x - 1)

(a) The domain is the set of values that this function can take on. If x = 1, the denominator becomes 0 and the function is undefined. Any other value of x is okay, though, since for x ≠ 1, we have

f(x) = (1 - x³) / (x - 1) = - (1 - x³) / (1 - x) = -(x² + x + 1)

which is defined for all x. This also tells us that the plot of f(x) is a parabola with a hole at x = 1. So, the domain is the interval (-∞, 1) ∪ (1, ∞).

(b) The range is the set of values that the function actually does take on. Taking the simplified version of f(x), we can complete the square to write

-(x² + x + 1) = -(x² + x + 1/4 - 1/4) - 1 = -(x + 1/2)² - 3/4

which is represented by a parabola that opens downward, with a maximum value of -3/4. So the range is the interval (-∞, -3/4).

(c) Judging by the plot of f, the limits at both negative and positive infinity are -∞.

(d) Same answer as part (a).

(2) f(x) = x³ - x

(a) The derivative of f at x = 3, and hence the slope of the tangent line to this point, is

\(f'(3)=\displaystyle\lim_{h\to0}\frac{f(3+h)-f(3)}h\)

\(f'(3)\displaystyle=\lim_{h\to0}\frac{((3+h)^3-(3+h))-24}h\)

\(f'(3)=\displaystyle\lim_{h\to0}\frac{(27+27h+9h^2+h^3)-(3+h)-24}h\)

\(f'(3)=\displaystyle\lim_{h\to0}\frac{26h+9h^2+h^3}h\)

\(f'(3)=\displaystyle\lim_{h\to0}(26+9h+h^2)=\boxed{26}\)

(b) The tangent line at x = 3 has equation

y - f (3) = f ' (3) (x - 3)

y - 24 = 26 (x - 3)

y = 26 x - 54

We also want to find any other tangent lines parallel to this one, which requires finding all x for which f '(x) = 26. We could use the same limit definition as in part (a), but to save time, we exploit the power rule to get

f '(x) = 3 x² - 1

Then solve for when this is equal to 26:

3 x² - 1 = 26   ==>   x² = 9   ==>   x = ±3

The other tangent line occurs at x = -3, for which we have f (-3) = -24, and so the equation for the tangent is

y - f (-3) = 26 (x - (-3))

y + 24 = 26 (x + 3)

y = 26 x + 54

Answer:

Length of line AC = 24 cm

Step-by-step explanation:

Given:

Length of line AB = 10 cm

Length of line BC = 14 cm

Find:

Length of line AC

Computation:

We know that line AB and BC are two part of line AC

So,

AC = AB + BC

Length of line AC = Length of line AB + Length of line BC

Length of line AC = 10 + 14

Length of line AC = 24 cm

Statement Problem: A drama club is planning a bus trip to New York City to see a Broadway play. The cost per person for the bus rental varies inversely to the number of people going on the trip. It will cost $30 per person if 44 people go on the trip. How much will it cost per person if 20 people go on the trip?

Solution:

Let the cost per person for the bus rental be c;

Let the number of people going on the trip be n;

Then, we have;

If 20 people go on the trip, the cost per person is;

The probability that the student scores an 85 or better and he receive an A in the score is 0.45.

In the question it is given that the professor tells that the student has 90% chance of getting A, if he gets 85 or better in mid term exam.

The student is 50% sure that he will get 85 or better in the examination.

To get the probability of the student scores an 85 or better and he receives an A grade, we use multiplication rule.

P( student getting A grade and 85 or better)= P(getting A) x P(getting 85 or better)

P(getting A)=0.9

P(getting 85 or better)=0.5

= 0.9x0.5

P( student getting A grade and 85 or better)=0.45

Therefore, probability that the student scores an 85 or better and getting A is 0.45.

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Answer:

\(\Huge \boxed{\mathrm{C. \ 1}}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

\(27 \cdot ((3^3)^{-1})\)

Multiplying exponents.

\(27 \cdot 3^{-3}\)

Rewriting 27 with base 3.

\(3^3 \cdot 3^{-3}\)

Adding exponents since bases are the same.

\(3^0 =1\)

\(\rule[225]{225}{2}\)

Answer:

C.  1

Step-by-step explanation:

27 * {(3³)⁻¹}

=      27    

       3³

=      27    

       27

= 1

Answer:

Option is the the. correct answer A

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 probability that state 1 changes to state 2 after three repetitions of the experiment is 0.052.

The first power of the transition matrix A is simply the matrix itself:

A1 = [ 0.3 0.1 0.6 ]

[ 0.5 0.2 0.3 ]

The second power of the transition matrix is obtained by multiplying A by itself:

A2 = A1 * A1 = [ 0.30.3+0.10.5 0.30.1+0.10.2 0.30.6+0.10.3 ]

[ 0.50.3+0.20.5 0.50.1+0.20.2 0.50.6+0.20.3 ]

= [ 0.19 0.06 0.33 ]

[ 0.29 0.08 0.33 ]

The third power of the transition matrix is obtained by multiplying A2 by A:

A3 = A2 * A = [ 0.190.3+0.060.5 0.190.1+0.060.2 0.190.6+0.060.3 ]

[ 0.290.3+0.080.5 0.290.1+0.080.2 0.290.6+0.080.3 ]

= [ 0.161 0.052 0.327 ]

[ 0.247 0.068 0.327 ]

To find the probability that state 1 changes to state 2 after three repetitions of the experiment, we need to look at the second element of the first row of A3. This element is 0.052, so the probability that state 1 changes to state 2 after three repetitions of the experiment is 0.052.

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Answer:

\(100-p^{16}=(10-p^{8})(10+p^{8})\)

Step-by-step explanation:

Factoring

Binomial factoring is a common task when solving a great variety of math problems.

One of the best-known formula that helps us to factor a binomial is:

\((a^2-b^2)=(a-b)(a+b)\)

It can easily be identified because the expression is the difference between two perfect squares.

The expression

\(100-p^{16}\)

can be factored with the formula above since it's the difference of two squares:

\(a=\sqrt{100}=10\)

\(b=\sqrt{p^{16}}=p^{8}\)

The expression is factored as follows:

\(\boxed{100-p^{16}=(10-p^{8})(10+p^{8})}\)

Answer:

Athena weighs 6 pounds. (Zeus weighs 3 pounds).

Step-by-step explanation:

We know that A (Athena) + Z (Zeus) = 9. And we know that Zeus weighs three pounds less than Athena. Knowing this we can do
1 + 8 = 9
2 + 7 = 9
3 + 6 = 9
We can see that 6 and 3 equal 9 and 6 is 3 away from 3, getting us the answer that Athena weighs 6 pounds. :) I hope this helps! ^^

The largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.

Suppose that the number is abcd.efg and belongs to the decimal numerical system. Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more. Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more. We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.

WE need to find the five-digit multiple of 15 whose digits are all distinct and nonzero.

Thus, we can see that the largest five-digit multiple of 15 could be ;

12345

Since it must be all distinct and nonzero. so the correct digit is 12345.

Hence, the largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.

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Answer:

Step-by-step explanation:

    A,  use  three_digite  rounding  arithmetic  to compute  13- 6 and determine  the absolute,relative ,and percentage errors.

tepeat part (b) using  three – digit chopping arithmetic.

Answer:

\(41\frac{2}{3}\)  

I hope this helps!

Answer:

41.66 repeating or 41.67

Step-by-step explanation: hope this helps

Answer:

g(x) has a +1 for it's b in y = mx+b, and f(x) has 0 for it's b (b is the y intercept)

Step-by-step explanation:

The range, in centimetres (cm), of the following lengths is 20.5 cm

What is the range?

The difference between the lowest and highest numbers is referred to as the range. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.

As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

Given, 15 cm, 0.5 cm, 10.3 cm, 16.7 cm, 21 cm, 8.6 cm

So, the highest value of length = 21 cm

the lowest value of length = 0.5 cm

Then, range = the highest value - the lowest value

                    = 21 - 0.5 = 20.5 cm

Hence, the range, in centimetres (cm), of the following lengths is 20.5 cm

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Answer:

4 19/24

Step-by-step explanation:

3 5/12 + 1 3/8

denominators multiplied by 3 and the numerators

= 3 10/24 + 1 9/24=4 19/24

The values of the given trigonometric functions are 240° and 60° respectively.

What are trigonometric functions?

Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle.

The three primary trigonometric functions are sine, cosine, and tangent.

The sine function (sin) relates the length of the opposite side of an angle to the length of the hypotenuse of a right triangle. It is defined as sin(θ) = opposite/hypotenuse.

The cosine function (cos) relates the length of the adjacent side of an angle to the length of the hypotenuse of a right triangle. It is defined as cos(θ) = adjacent/hypotenuse.

The tangent function (tan) relates the length of the opposite side of an angle to the length of the adjacent side of a right triangle.

Now To find

(a.)  sin⁻¹(-√3/2)

(b.)  cos⁻¹ (1/2)

For a

sin⁻¹(-√3/2)=sin⁻¹(-0.8660)=-⁻60° or 240°

and

For b

cos⁻¹ (1/2)=cos⁻¹ (0.5)=60°

Hence,

             the values of the given trigonometric functions are 240° and 60° respectively.

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Answer:

9180 (cm³)

Step-by-step explanation:

area of cross-section (trapezium) = 0.5 X (12 + 22) X 9

= 0.5 X 34 X 9 = 153 cm²

then multiply that by the length (60)

153 X 60 = 9180 (cm³)

cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.

To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:

cos(tan^(-1)(x)) = 1 / √(1 + x^2)

In this case, x is -2/3. Substituting the value into the identity:

cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)

Now, let's calculate the value:

cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)

                   = 1 / √(13/9)

                   = 1 / (√13/3)

                   = 3 / √13

                   = 3√13 / 13

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The statement that describes the second stage of the repeated-measures ANOVA is: it removes individual differences from the denominator.

The repeated-measures ANOVA is a two stage process that is described as analysis of dependencies. This test is used to prove an assumed cause-effect relationship between varaibles (dependent and independent).

The means across one or more variables which have repeated observations are compared using the repeated-measures ANOVA.

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The weight of the 0.8-meter piece is 19.6 kilograms.

We can use the ratio of length to weight to determine the weight of the 0.8-meter piece.

Let's call the weight of the 2.8-meter piece "W₁" and the weight of the 0.8-meter piece "W₂". Then we have:

W₁/2.8m = 24.5kg/1m

Solving for W₁, we get:

W₁ = (24.5kg/1m) x 2.8m = 68.6kg

Now we can use the same ratio to find W₂:

W₂/0.8m = 24.5kg/1m

Solving for W₂, we get:

W₂ = (24.5kg/1m) x 0.8m = 19.6kg

Therefore, the weight of the 0.8-meter piece is 19.6 kilograms.

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Answer:

6 months

Step-by-step explanation:

We can set up an equation based on his monthly savings to find out how long it will take for Hatif to reach $630 in his account.

Let's assume it takes Hatif "n" months to reach $630 in his account. Each month, he saves $80.

The equation representing the situation is:

$150 + $80n = $630

Now, let's solve for "n":

$80n = $630 - $150

$80n = $480

n = $480 / $80

n = 6

Therefore, it will take Hatif 6 months to reach $630 in his account.

The required, each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.

here,
To divide the 2 cakes equally among 7 people, we can use division. We can think of the total amount of cake as 2 whole cakes or 2/1 cakes. To find out how much cake each person can have, we can divide the total amount of cake by the number of people:

2/1 cakes ÷ 7 people = 2/1 × 1/7 = 2/7 cakes per person

So each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.

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Answer:

-85º

Step-by-step explanation:

275 - 360 = -85

In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.

Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.

Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.

Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.

Alternate interior angles are congruent, as well as alternate exterior angles.

By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.

It is important to measure angles systematically and compare them to find congruent or equal measures.

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