triangle abc on a coordinate plane is dilated by a scale factor of ¾ to create triangle mno. what do you know about triangle abc and triangle mno?

Answer:

slope = \(-\frac{1}{3}\)

Step-by-step explanation:

1) Find the slope with the slope formula, \(m = \frac{y_2-y_1}{x_2-x_1}\) (in which \(m\) represents the slope). The \(x_1\) and \(y_1\) represent the x and y values of one point, and the \(x_2\) and \(y_2\) represent the x and y values of another point. Thus, substitute the x and y values of the given points (6, -2) and (-3, 1) into the appropriate places in the formula and solve:

\(m = \frac{(1)-(-2)}{(-3)-(6)} \\m = \frac{1+2}{-3-6} \\m = \frac{3}{-9} \\m = -\frac{1}{3 }\)

Thus, the slope is \(-\frac{1}{3}\).

Answer:

y = -3/4

Step-by-step explanation:

1. Simplify all terms - 8y + 6 = ?

2. Set to two sides - 8y = -6

3. Solve - y = -6/8 = -3/4

Hope this helps:)

Conservative vector fields have zero curl and the line integral of a conservative vector field along a closed curve is always zero.

To evaluate the line integral along the given positively oriented curve, we can use Greene's theorem.
First, let's rewrite the equation of the ellipse in standard form:

x^2 + y^2/4 + xy/2 = 4

We can now apply Greene's theorem, which states that for a vector field F = (P, Q) and a positively oriented, piecewise smooth curve C, the line integral of F along C is equal to the double integral of the curl of F over the region D enclosed by C.

In this case, we have F = (y, x), so P = y and Q = x. The curl of F is given by:

curl(F) = (dQ/dx - dP/dy) = (1 - 1) = 0

Since the curl of F is zero, the double integral over the region D is also zero. Therefore, the line integral of F along C is also zero.

In other words, the answer to the line integral along the given positively oriented curve is zero.

This may seem counterintuitive, but it is a consequence of the fact that the vector field F is conservative, which means that it can be expressed as the gradient of a scalar function (in this case, F = grad(f) where f = xy/2).

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Answer:

I guess the answer is 9.24

Answer:

ur screwed but the answer is 110.88

Step-by-step explanation:

:)

Answer:

0.625

Step-by-step explanation:

5÷8=0.625

This is equal to the number of pizzas Celia ate.

plz mark me as brainliest.

Answer:

0.625

Step-by-step explanation:

Fraction of pizza she ate = 5/8

5/8 x 125 =  625/100= 0.625

I hope im right!

The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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(A - 3I)v = | -2  2 | | v1 | = | 0 |
           | -5 -4 | | v2 |   | 0 |
Solving the system of equations, we obtain v1 = 1 and v2 = 1. The general solution of the given system of equations is: x(t) = C1 * e^(3t) * [1, 1]^T
where C1 is an arbitrary constant and T denotes the transpose operation.

(b) As a question-answering bot, I am unable to draw images. However, I can guide you on how to draw the direction field and sketch the trajectories. Plot the vector field F(x, y) = Ax, where A is the given matrix, and observe the behavior of the field. The eigenvector [1, 1] will provide the direction for the trajectories. Since the eigenvalue is positive, the trajectories will be moving away from the origin along the direction of the eigenvector.

(c) As t → ∞, the solutions of the system will grow exponentially in the direction of the eigenvector [1, 1]. Since the eigenvalue is positive (λ1 = 3), the trajectories will move away from the origin along the line y = x.

The given system of equations can be expressed as x' = Ax, where A is the coefficient matrix:
A =1 2
−5 −1
(a) The general solution of the system can be found by solving for the eigenvalues and eigenvectors of the matrix A. The eigenvalues of A can be found by solving the characteristic equation:
det (A - λI) = 0
⇒ det (1-λ 2-5  -1-λ) = 0
⇒ (1-λ)(-1-λ) - 2(-5) = 0
⇒ λ^2 + λ - 9 = 0
⇒ λ = (-1 ± sqrt(37)i)/2
Since the eigenvalues are complex, the general solution of the system can be expressed in terms of real-valued functions using Euler's formula:
x(t) = c1 e^(αt) cos(βt) v1 + c2 e^(αt) sin(βt) v2
where α = -1/2, β = sqrt(37)/2, v1 and v2 are the real and imaginary parts of the eigenvector corresponding to the eigenvalue (-1 + sqrt(37)i)/2, and c1 and c2 are arbitrary constants determined by the initial conditions.

(b) To draw a direction field, we can plot arrows on a grid that indicate the direction of the vector x' = Ax at various points in the xy-plane. The direction of the vector at each point (x,y) can be found by evaluating Ax at that point and plotting an arrow with a slope equal to the components of Ax. To sketch a few trajectories, we can use the general solution and choose different initial conditions to plot several curves in the xy-plane. The trajectories will follow the direction of the arrows in the direction field.

(c) As t → infinity, the behavior of the solutions depends on the eigenvalues of A. Since the real part of the eigenvalue with a larger magnitude is negative (-1/2), the solutions will approach the origin as t → infinity. The imaginary part of the eigenvalue will cause oscillations in the trajectories, which become more and more damped as t increases.

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The volume of the solid generated when the region in the first quadrant is: V ≈ 183.78

The disc method, the shell method, and Pappus' centroid theorem can all be used to calculate volume. In many academic disciplines, such as engineering, medical imaging, and geometry, revolution volumes are used. Integration can be used to determine the area of a region bounded by a known curve.

Because we are only revolving the region in the first quadrant, the x values range from x = 0 to x = 3.

Because of the rotation is about the vertical line x = -1, the radius of the cylindrical shell at x is r = x + 1.

The height of the cylindrical shell at x is h = \(x^{2}\)

We can now create our integral equation to find the volume:

\(V =2\pi\int\limits^a_b {rh} \, dx =2\pi\int\limits^3_0 {(1+x)x^2} \, dx \\\\V =2\pi\int\limits^3_0 {(x^{2} +x^3)} \, dx\)

We can now integrate and evaluate to find the volume of the solid.

\(V=2\pi(\frac{x^3}{3}+\frac{x^4}{4} )|^3_0\\\\V = 2\pi(\frac{27}{3}+\frac{81}{4} )\\\\V=\frac{117\pi}{2}\)

V ≈ 183.78

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The given question is incomplete, complete question is:

Find the volume of the solid generated by revolving the region in the first quadrant bounded above by the curve y =\(x^{2}\), below by the x-axis, and on the right by the line x = 3, about the line x = −1

The truth value of proposition 2a, [(x ⊃ a) • (b ⊃ ∼ y)] ⊃ [(b ∨ y) • (a ⊃ x)], given that a and b are true and x and y are false, is TRUE.

In the provided scenario where a and b are true while x and y are false, proposition 2a, [(x ⊃ a) • (b ⊃ ∼ y)] ⊃ [(b ∨ y) • (a ⊃ x)], is evaluated to be true. Let's break it down to understand why.

The proposition is in the form of an implication (⊃), where the antecedent is [(x ⊃ a) • (b ⊃ ∼ y)] and the consequent is [(b ∨ y) • (a ⊃ x)]. To determine the true value, we need to examine both the antecedent and the consequent.

In the antecedent, we have two conditions connected by a conjunction (∧): (x ⊃ a) and (b ⊃ ∼ y). Since x and y are false, the condition (x ⊃ a) is vacuously true because false implies anything. Similarly, (b ⊃ ∼ y) is also true because b is true, and ∼ y (not y) is true since y is false. Therefore, the antecedent is true.

Moving on to the consequent, we have two conditions connected by a conjunction (∧): (b ∨ y) and (a ⊃ x). In this case, b is true, so (b ∨ y) is true regardless of the truth value of y. Additionally, a is true, and since x is false, (a ⊃ x) is false. Therefore, the consequence is false.

Now, when we evaluate the entire proposition, [(x ⊃ a) • (b ⊃ ∼ y)] ⊃ [(b ∨ y) • (a ⊃ x)], we find that a true antecedent implies a false consequent, which results in a true overall proposition. Hence, the truth value of proposition 2a is TRUE in the given scenario.

In conclusion, proposition 2a holds true when a and b are true, and x and y are false. Understanding the evaluation of logical propositions like these can help in reasoning and problem-solving tasks.

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After 3 months, the tree will reach a height of 12 feet.

Imagine you plant a tree that is initially 6 feet tall. Every month, it grows by 2 feet.

Let's denote the height of the tree at the start as H₀ = 6 feet. Since the tree grows 2 feet each month, we can express its growth rate as "2 feet per month." To calculate how tall it will be over time, we need to consider the number of months it has been growing.

After 1 month, the height of the tree will be:

H₁ = H₀ + (growth rate * number of months) = 6 + (2 * 1) = 8 feet.

After 2 months, the height of the tree will be:

H₂ = H₀ + (growth rate * number of months) = 6 + (2 * 2) = 10 feet.

After 3 months, the height of the tree will be:

H₃ = H₀ + (growth rate * number of months) = 6 + (2 * 3) = 12 feet.

So, after 3 months, the tree will be 12 feet tall.

We can also represent this growth pattern using a mathematical equation. Let "t" be the number of months the tree has been growing, and "Hₜ" be its height at time "t."

The equation for the height of the tree over time is given by:

Hₜ = H₀ + (growth rate * t).

Using this equation, you can plug in the value of "t" as 3 to find the height after 3 months:

H₃ = 6 + (2 * 3) = 12 feet.

In conclusion, the tree will keep growing 2 feet every month, and you can find its height at any given time using the formula Hₜ = H₀ + (growth rate * t). After 3 months, the tree will reach a height of 12 feet.

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Greetings from Brasil...

From potentiation properties:

Mᵃ ÷ Mᵇ = Mᵃ⁻ᵇ

division of power of the same base: I repeat the base and subtract the exponents

In our case

3² ÷ 3⁴

3²⁻⁴

We also know about another property: P⁻ⁿ = (1/Pⁿ) so

3⁻² = 1/3²

Answer:

1/9

Step-by-step explanation:

hope i helped

Mathematical approaches to aggregate planning involve using quantitative methods to determine the optimal production and resource allocation strategies over a specified planning horizon. These approaches utilize mathematical models to optimize various factors such as production costs, inventory levels, and customer demand.

One mathematical approach to aggregate planning is linear programming, which formulates the planning problem as a linear optimization model. Linear programming considers constraints such as capacity limits, labor availability, and demand variability to find the best allocation of resources and production levels. The objective is to minimize costs or maximize profit while meeting demand requirements.

Another approach is the use of mathematical forecasting techniques to predict future demand. Time series analysis, regression analysis, and other statistical methods can be employed to forecast demand patterns. These forecasts serve as inputs to mathematical models, such as inventory control models or production planning models, which determine the optimal production levels and inventory policies based on the anticipated demand.

Simulation modeling is another mathematical approach where computer-based simulations are used to evaluate different scenarios and make decisions about production levels, inventory levels, and workforce scheduling. These models consider various factors like demand variability, production capacity, and resource availability to simulate the system's behavior and analyze the impact of different planning strategies.

Overall, mathematical approaches to aggregate planning provide a systematic and quantitative way to optimize production and resource allocation decisions, considering factors such as demand, capacity, costs, and constraints. These approaches help organizations make informed decisions to meet customer demand efficiently while minimizing costs and maximizing operational performance.

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Answer:

X= 65

Y= 120

Step-by-step explanation:

3y +235 = y-5

2y +235 = - 5

2y = 240

Y = 120

2x - 60 = x-5

X - 60 = - 5

X = 65

Step-by-step explanation:

-9(1-10n)-2(3n+9)

-9+90n-6n-18

-9-18+90n-6n

-27+84n

3(-9+28n)

The null and the alternative hypotheses for "Test if the mean weight of cereal in a cereal box differs from 18 ounces." is H0: μ = 18; HA: μ ≠ 18. So the option 2 is correct.

We need more details about the particular test or experiment being undertaken in order to determine the null and alternative hypotheses.

The alternative hypothesis (HA) is a claim that disputes the null hypothesis and implies the existence of an effect or difference, whereas the null hypothesis (H0) asserts that there is no effect or difference.

The following alternative and null hypotheses are appropriate for the test:

H0: μ = 18 (A box of cereal typically contains 18 ounces of cereal.)

HA: μ ≠ 18 (The average amount of cereal in a box varies from 18 ounces.)

As a result, option 2 accurately reflects the null and alternative hypotheses:

H0: μ = 18; HA: μ ≠ 18

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Answer:

It is

Scale Factor = Ratio of Side Lengths

= 12/8 = 9/6 = 1.5.

Step-by-step explanation:

Hope this helped have an amazing day!

The two rectangles are similar and the scale factor is 3/2.

Given data:

The first rectangle is represented as ABCD

The second rectangle is represented as PQRS

Now, the dimensions of ABCD is 8 cm x 6 cm

The dimensions of PQRS is 12 cm x 9 cm

So, the scale factor is represented as k and the value of k is :

k = length of PQRS / length of ABCD

So, k = 12 / 8

k = 3/2

Hence , the similar rectangles have a scale factor of 3/2

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The simplified expression is 2187.

Given expression:

expression 3 with the exponent 4 multiplying  3 with the exponent of 3.

= \(3^{4} *3^{3}\)

we know that,

if base are equal exponents are added.

= \(3^{4+3}\)

= \(3^{7}\)

= 3*3*3*3*3*3*3

= 9*3*3*3*3*3

= 27*3*3*3*3

= 81*3*3*3

= 243*3*3

= 729*3

= 2187.

Therefore the simplified expression is 2187.

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Answer:

3 r 2 +9 r − 120

Step-by-step explanation:

Write the problem as a mathematical expression.

3 r ^2 + 9 r− 120

Factor  3  out of  3 r ^2 + 9 r − 120 .

Factor  3 out of  3 r ^2 .

3 ( r ^2 ) + 9 r − 120

Factor  3  out of  9 r .

3 ( r^ 2 ) + 3( 3 r ) − 120

Factor  3  out of  − 120 .

3 r ^2 + 3( 3 r ) + 3 ⋅ − 40

Factor  3 out of  3 r 2 + 3 ( 3 r ) .

3 ( r^2 + 3 r )+ 3 ⋅ − 40

Factor  3 out of  3 ( r 2 + 3 r ) + 3 ⋅ − 40 .

3 ( r^ 2 + 3 r − 40 )

Factor.

Factor  r^ 2 + 3 r − 40 using the AC method.

3 ( ( r − 5 ) ( r + 8 ) )

Remove unnecessary parentheses.

3 ( r − 5 ) ( r + 8 )

Hope this helps! :)

Answer:

the item would cost $9000

function (f-1)(2) = 18 because the derivative of f at a = 2 is 18x2 + 10x.

We can find out how a function is changing at a specific point by looking at its derivative. We are required to calculate (f-1) in this scenario (2). We must first get the derivative of the given function, f(x) = 3x3 + 3x2 + 5x2, in order to perform this. The derivative of each term can be used to achieve this, giving us 9x2 + 6x + 10x. The derivative of f at a = 2 is equal to 18x2 + 10x when this is evaluated at a = 2. Now, by putting the derivative equal to 0 and finding x, we may calculate (f-1)(2). Thus, we obtain x = -1/9. Once this value has been entered, the original method returns (f-1)(2) = 18.

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Answer:

C. 32

Step-by-step explanation:

The shipment for 100 parts is received by a manufacturer. Shipment will be rejected if more than 5 parts are defective. The manufacturer selects a sample and based on that selected sample he accepts or rejects the whole shipment. The minimum size of the sample should be 32 based on the probability of less than 0.1 and then  decision should be made whether to accept or reject the shipment. If no defective part is found in the sample, shipment should be accepted.

Answer:

y=4x+23

Step-by-step explanation:

sorry  cant choose answer choice ..i ant tell which is which...bu i think you should by now....

i hope this stilled helped

The solutions of the inequality \(2x^{2} + x - 6 = 0\) are 3/2, -2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form \(ax^{2} +bx + c = 0\), the solutions are \(x = -b +/-\sqrt{b^{2} -4ac} /2a\).

Discriminant: b² - 4 a c = 1 - 4(2)(-6) = 1 + 48 = 49

Solution 1: x = \(-b + \sqrt{b^{2} -4ac} /2a\) = (-1 + √49)/(2×2) = (-1 +7)/4 = 6/4 = 3/2

Solution 2: x = \(-b-\sqrt{b^{2} -4ac} /2a\)= (-1 - √49)/(2×2) = -8/4 = -2

So, the two solutions are 3/2 and -2.

The equation can also be written as,

\(2x^{2} +4x -3x-6=0\)

\(2x(x+2) -3(x+2) = 0\)

\((2x-3)(x+2) = 0\)

x = 3/2, -2

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The coefficients `a`, `b`, `c`, `d`, `e`, and `f` are obtained from the user. The program then calculates the values of `x` and `y` using the determinant method. If the denominator (the determinant) is zero, it means that the system of equations has no unique solution. Otherwise, the program displays the solutions `x` and `y`.

Here's a C++ program that solves a system of linear equations with two unknowns (x and y) given the coefficients a, b, c, d, e, and f:

```cpp

#include <iostream>

using namespace std;

int main() {

   double a, b, c, d, e, f;

   // Accept input coefficients from the user

   cout << "Enter the coefficients for the linear equations:\n";

   cout << "a: ";

   cin >> a;

   cout << "b: ";

   cin >> b;

   cout << "c: ";

   cin >> c;

   cout << "d: ";

   cin >> d;

   cout << "e: ";

   cin >> e;

   cout << "f: ";

   cin >> f;

   // Calculate the values of x and y

   double denominator = a * e - b * d;

   if (denominator == 0) {

       // The system of equations has no unique solution

       cout << "No unique solution exists for the given system of equations.\n";

   } else {

       double x = (c * e - b * f) / denominator;

       double y = (a * f - c * d) / denominator;

       // Display the solutions

       cout << "Solution:\n";

       cout << "x = " << x << endl;

       cout << "y = " << y << endl;

   }

   return 0;

}

```

In this program, the coefficients `a`, `b`, `c`, `d`, `e`, and `f` are obtained from the user. The program then calculates the values of `x` and `y` using the determinant method. If the denominator (the determinant) is zero, it means that the system of equations has no unique solution. Otherwise, the program displays the solutions `x` and `y`.

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Answer:

-24

Step-by-step explanation:

The common difference (D) is -2. And A1 is -2. so if you just add -2 to the geometric sequence until A12, you would get -24.

The normal probability plot suggests the data is approximately normally distributed. The sample standard deviation of given data is 3.13. The 95% confidence interval for the population standard deviation is (1.85, 6.28). The investment manager's desire for a population standard deviation below 6% is validated by the confidence interval.

To construct a normal probability plot, we first need to sort the data in ascending order:

6.6, 6.7, 8.7, 9.6, 10.0, 10.3, 11.3, 12.4, 12.4, 13.8, 14.9, 15.9

Then we can plot the ordered data against the expected values of a normal distribution with the same mean and standard deviation as the sample. The plot shows that the points follow a roughly straight line, which suggests that the data is roughly normally distributed.

To determine the sample standard deviation, we can use the formula:

s = sqrt[(∑(xi - x)²) / (n - 1)]

where xi is the rate of return for each year, x is the sample mean, and n is the sample size.

Sample mean:

x = (13.8 + 15.9 + 10.0 + 12.4 + 11.3 + 6.6 + 9.6 + 12.4 + 10.3 + 8.7 + 14.9 + 6.7) / 12 = 11.433

Sample standard deviation:

s = sqrt[((13.8 - 11.433)² + (15.9 - 11.433)² + ... + (6.7 - 11.433)²) / (12 - 1)]

= 3.059

Therefore, the sample standard deviation is 3.059.

To construct a 95% confidence interval for the population standard deviation of the rate of return, we can use the formula:

CI = [(n - 1) * s² / χ²(α/2, n-1), (n - 1) * s² / χ²(1-α/2, n-1)]

where n is the sample size, s is the sample standard deviation, χ² is the chi-square distribution, and α is the level of significance (1 - confidence level).

For a 95% confidence level and 11 degrees of freedom (n - 1), α = 0.05/2 = 0.025. From the chi-square distribution table with 11 degrees of freedom, we can find the critical values as follows:

χ²(0.025, 11) = 2.201 and χ²(0.975, 11) = 23.337

Plugging in the values, we get:

CI = [(12 - 1) * 3.059² / 23.337, (12 - 1) * 3.059² / 2.201]

= [1.946, 26.557]

Therefore, we can say with 95% confidence that the population standard deviation of the rate of return is between 1.946 and 26.557.

The investment manager wants to have a population standard deviation for the rate of return below 6%. The confidence interval (1.946, 26.557) does not validate this desire, as it includes values above 6%. Therefore, based on the sample data, the investment manager cannot be confident that the population standard deviation is below 6%.

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If linear function can be modeled using the equation 2x-y=2. Then x=1 is the Zero of this function

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

2x-y=2

We need to write this in slope intercept form

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

y=2x-2

m=2 and y intercept is -2

Now take the values of x and y

x       0       1         2         3

y       -2      0         2         4

Hence the zero of this function is x=1

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The distribution for the random variable follows the binomial distribution with p = 0.5.

The random variable representing the number of red cards observed in these four trials follows the binomial distribution with a probability of success of 0.5. Therefore, the correct answer is (b) the binomial distribution with p = 0.5.

Each trial consists of choosing one card from the set of 10 cards, and the probability of selecting a red card is 0.5 since there are 5 red cards out of 10 total cards. The trials are independent because after each selection, the chosen card is replaced, so the probability of selecting a red card remains the same for each trial.

The binomial distribution is suitable for situations where there are a fixed number of independent trials, and each trial has two possible outcomes (success or failure) with a constant probability of success. In this case, the random variable represents the number of successes (red cards) observed in four trials.

The probability mass function (PMF) for the binomial distribution is given by:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where X is the random variable, k is the number of successes, n is the number of trials, p is the probability of success, and C(n, k) represents the binomial coefficient.

n = 4 (four trials), p = 0.5 (probability of selecting a red card), and we are interested in finding P(X = k) for different values of k (0, 1, 2, 3, 4) representing the number of red cards observed in the four trials.

The distribution for the random variable follows the binomial distribution with p = 0.5.

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