(3,-2) (4,6) what is the slope

The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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Answer:

Step-by-step explanation:

Perp. : -3/2

y + 8 = -3/2(x - 4)

y + 8 = -3/2x + 6

y = -3/2x - 2

Answer:

1/2(6*6)+3/2(6*4)

2*36 +72/2

144/2 =72

\(3^5 \cdot 2^{-6}=\dfrac{3^5}{2^6}=\dfrac{243}{64}\)

Answer: 350000

Step-by-step explanation: Hope this helps :) (if wrong please make sure next time add answer that can be picked from it better or if theres no answers maybe give some more detail?)

The future value of an annuity of $500 per year for 12 years, with an interest rate of 5%, can be calculated using the future value of an ordinary annuity formula. The future value is approximately $7,005.53.

To calculate the future value of an annuity, we can use the formula:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the annuity,

P is the annual payment,

r is the interest rate per compounding period,

n is the number of compounding periods.

In this case, the annual payment is $500, the interest rate is 5% (or 0.05), and the number of years is 12. As the interest is compounded annually, the number of compounding periods is the same as the number of years.

Plugging the values into the formula:

FV = $500 * [(1 + 0.05)^12 - 1] / 0.05

= $500 * [1.05^12 - 1] / 0.05

≈ $500 * (1.795856 - 1) / 0.05

≈ $500 * 0.795856 / 0.05

≈ $399.928 / 0.05

≈ $7,998.56 / 100

≈ $7,005.53

Therefore, the future value of the annuity of $500 per year for 12 years, with a 5% interest rate, is approximately $7,005.53.

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Answer:

Solutions below.

Step-by-step explanation:

This Question involves the concept of Function Substitution.

Function Substitution - As the name suggests, it is about substituting an input value (normally x) to find the value of y , or f(x) which is the range of the value.

Example: f(x) = 98x , f(2) = 98(2) = 196

We are given the following function:

\(p(t) = - 16 {t}^{2} + 1638\)

a) This part is asking us to find the height of the object when t = 2, which is the same as finding the value of P(2).

P(2) =

\( - 16 {(2)}^{2} + 1638 \\ = - 64 + 1638 \\ = 1574\)

Therefore at t = 2 seconds, the object is 1,574m above the river.

b) This part is asking us to find the height of the object when t = 6, which is the same as finding the value of P(6).

P(6) =

\( - 16 {(6)}^{2} + 1638 \\ = - 16(36) + 1638 \\ = - 576 + 1638 \\ = 1062\)

Therefore at t = 6 seconds, the object is 1,062m above the river.

The square root of 41 must lie between 6 and 7, as 6² = 36 and 7² = 49, and 41 lies between these two values.

The estimate of a non-exact square root of x is done finding two numbers, as follows:

For the number 41, these numbers are given as follows:

Hence we know that the square root of 41 lies between 6 and 7.

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Answer:

1. If x is under a square root then x cannot equal a negative number. If x is in the denominator of a fraction then x cannot equal zero.

2. ax2 + bx + c

Step-by-step explanation: Hope this helps :)

Answer:

.03

Step-by-step explanation:

1 pound = 16 ounces 2 pounds is 32

and 96/32 is 3

Answer:

$.03 per ounce

Step-by-step explanation:

1 pound = 16 ounces

2 pounds = 32 ounces

Take the price and divide by the number of ounces

.96 / 32 ounces

.03 per ounce

In part a), we can find E(Y) and Var(Y) using the laws of total expectation and total variance.

Let's denote the conditional expectation of Y given X = x as E(Y|X=x), and the conditional variance of Y given X = x as Var(Y|X=x).

a) To find the conditional expectation and conditional variance for each possible value of X, we need to consider the distribution of Y given X. Since Y is chosen uniformly from the interval (0, X), the distribution of Y given X = x is a uniform distribution on the interval (0, x). In this case, the conditional expectation E(Y|X=x) is equal to x/2 and the conditional variance Var(Y|X=x) is equal to x^2/12.

b) To find E(Y) and Var(Y) using the laws of total expectation and total variance, we need to consider the law of total expectation:

E(Y) = E[E(Y|X)]

Since X is chosen uniformly from the interval (0, 1), the marginal distribution of X is a uniform distribution on (0, 1). Therefore, E(Y|X) is a function of X, and we need to integrate E(Y|X) over the range of X to find E(Y).

Similarly, the law of total variance gives:

Var(Y) = E[Var(Y|X)] + Var[E(Y|X)]

We need to calculate Var(Y|X) and E(Y|X) and then integrate them accordingly.

By evaluating the integrals using the conditional expectation and variance values obtained in part a), we can find E(Y) and Var(Y) using the laws of total expectation and total variance.

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La esculturas triangulares tendrán las siguientes medidas 16.66 cm, 40 cm y 23.32 cm.

Es la suma total de los lados del triángulo, en este caso el perímetro total es de 80.

Se pueden calcular usando el total y la información sobre cada lado:

Finalmente calcule cada lado:

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Answer:

  39, 40, 41

Step-by-step explanation:

Let x represent the middle integer. The sum of the three integers will be ...

  (x -1) +x +(x +1) = 3x

This is 40 more than 2 times the middle integer, so we have ...

  3x = 40 +2x

  x = 40 . . . . . . . subtract 2x

The three integers are 39, 40, 41.

_____

Additional comment

It often works well to solve consecutive integer problems by letting a variable represent the middle value, or the average of the integers.

Answer:

In physics, the line of action (also called line of application) of a force F is a geometric representation of how the force is applied. It is the line through the point at which the force is applied in the same direction as the vector F→.[1][2]

The line of action is shown as the vertical dotted line. It extends in both directions relative to the force vector, but is most useful where it defines the moment arm.

The concept is essential, for instance, for understanding the net effect of multiple forces applied to a body. For example, if two forces of equal magnitude act upon a rigid body along the same line of action but in opposite directions, they cancel and have no net effect. But if, instead, their lines of action are not identical, but merely parallel, then their effect is to create a moment on the body, which tends to rotate it.

Calculation of torque

References

Last edited 20 days ago by Belomaad

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Torque

Physics concept

Net force

The overall force acting upon an object. In order to calculate the net force, the body is isolated and interactions with the environment or other constraints are represented as forces and torques in a free-body diagram

Step-by-step explanation:

Formula

F=G{\frac{m_1m_2}{r^2}}

F = force

G = gravitational constant

m_1 = mass of object 1

m_2 = mass of object 2

r = distance between centers of the masses

Answer:

  (a)  15 -18i

Step-by-step explanation:

You want the simplified form of the expression -2i(5- i) + (17- 8i).

For many purposes, the value i in a complex number can be treated in the same way a variable would be treated. When simplifying an expression involving i, any instances of i² can be replaced with the real value -1.

  -2i(5- i) + (17- 8i) = -10i +2i² +17 -8i

  = -2 +17 +(-10 -8)i

  = 15 -18i

__

Additional comment

Your scientific or graphing calculator can probably help you evaluate such expressions.

"The mean will be higher than the median in any distribution that" ;

has a positively skewed distribution

A positively skewed distribution is one in which the majority of data values are clustered towards the lower end of the range, while the rest of the values are spread out towards the higher end of the range. As a result, the mean (the average of all the data values) will be higher than the median (the middle value of the data set).

This is because the mean is affected by the higher values in the distribution, while the median is not.

Positively skewed distributions are common in real-world data sets and are often seen in income distributions, stock market returns, and other economic data.

For example, a distribution of incomes may have a few very high earners pushing up the mean, while the majority of people make much lower amounts, resulting in a median that is lower than the mean.

Similarly, stock market returns may have a few very large returns that pull the mean up, while the majority of returns are much lower, resulting in a median that is lower than the mean.

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Any function whose graph is NOT a line is said to be nonlinear. It has the equation f(x) = ax + b. With the exception of the form f(x) = ax + b, its equation can take any form. Any two points on the curve have the same slope.

To ascertain whether a table of values is a linear function, follow these steps:

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Step 1

Given;

Required; To find the price per ounce

Step 2

State the ratio that can be used to find the price per ounce of the candy bars.

The square of the length of the chord that is a common external tangent of the other two circles with radii of 3 and 6 is 45.

Given that circles of radii 3 and 6 are externally tangent to each other and internally tangent to a circle of radius 9. The circle of radius 9 has a chord that serves as a common external tangent for the other two circles. The task is to find the square of the length of this chord.

The distance between the centers of the circles of radii 3 and 6 can be found by adding their radii: d1 = 3 + 6 = 9 units.

Since the circles are internally tangent to the circle of radius 9, the distance between their centers can be found by subtracting their radii from the radius of the larger circle: d2 = 9 - 3 - 6 = 0 units.

The chord is a common external tangent of the circles, and its length can be found by doubling the distance between the center of the circle of radius 9 and the chord: Chord length = 2 × h.

To find the height (h) of the triangle formed by the chord and the center of the circle of radius 9, we can use the formula h = (r1 + r2 - R) / 2, where r1 and r2 are the radii of the smaller circles, and R is the radius of the larger circle. In this case, h = (3 + 6 - 9) / 2 = 0.
Since h is zero, it means that the chord passes through the center of the circle of radius 9. Therefore, its length will be the diameter of the circle of radius 9.

The square of the length of the chord can be found using the Pythagorean theorem. Let's denote the length of the chord as d.

- We know that r1 + h = R, so h = R - r1 = 9 - 3 = 6.

- Using the Pythagorean theorem: d = sqrt(R² - h²) = √(9² - 6²) = √(81 - 36) = √(45).

Therefore, the square of the length of the chord is d^2 = 45.

In summary, the square of the length of the chord that serves as a common external tangent for the circles of radii 3 and 6, and is internally tangent to a circle of radius 9, is 45.

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Answer:

Distance (d) = 15

Step-by-step explanation:

The given requires the distance between the point of origin, (0, 0), and (-12, 9). We can use the following distance formula for this problem:

\(\displaystyle\mathsf{Distance(d)=\:\sqrt{(x_2-x_1)^2\:+\:(y_2-y_1)^2}}\)

Let (x₁, y₁) = (0, 0)

     (x₂, y₂) = (-12, 9)

Substitute these values into the distance formula.

\(\displaystyle\mathsf{Distance(d)=\:\sqrt{(x_2-x_1)^2\:+\:(y_2-y_1)^2}}\)

\(\displaystyle\mathsf{Distance(d)=\:\sqrt{(-12\:-\:0)^2\:+\:(9-0)^2}}\)

Perform the required subtraction within each parenthesis:

\(\displaystyle\mathsf{Distance(d)=\:\sqrt{(-12)^2\:+\:(9)^2}}\)

Next, take the squared values of -12 and 9 under the radical:

\(\displaystyle\mathsf{Distance(d)=\:\sqrt{144\:+\:81}}\)

Add 144 and 81:

\(\displaystyle\mathsf{Distance(d)=\:\sqrt{225}}\)

Distance (d) = 15

Therefore, the distance between the point of origin and (-12, 9) is 15.

1. The height of the cone is equal to

2. You can solve for the slant height, s by applying Pythagorean's theorem.

3. To get from the base of the cone to the top of the hill, an ant has to crawl 29 mm.

In Mathematics and Geometry, the volume of a cone can be calculated by using this formula:

Volume of cone, V = 1/3 × πr²h

Where:

By substituting the given parameters into the formula for the volume of a cone, we have the following;

8792 =  1/3 × 3.14 × 20² × h

26,376 =  3.14 × 400 × h

Height, h = 26,376/1,256

Height, h = 21 mm.

Question 2.

In order to solve for the slant height, s, we would have to apply Pythagorean's theorem since the height of the cone has been calculated above.

Question 3.

By applying Pythagorean's theorem, we have the following:

r² + h² = s²

20² + 21² = s²

400 + 441 = s²

s² = 841

Slant height, s = √841

Slant height, s = 29 mm.

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Answer:

This sequence is a geometric sequence.

The common ratio of the sequence is

3/9 = 1/3

Hope this helps

A 9' x15' tool room was enlarged to 11' x20', 85 square feet were added.

The tool room was enlarged from 9' x 15' to 11' x 20'. To solve the problem, we need to use the formula for finding the area of a rectangle which is,

A = l*w,

where A is the area of the rectangle, l is the length of the rectangle, and w is the width of the rectangle.

Area of the original tool room = 9' x 15' = 135 sq ft.

Area of the enlarged tool room = 11' x 20' = 220 sq ft.

Difference in area = 220 sq ft - 135 sq ft = 85 sq ft.

Therefore, 85 square feet of floor space were added.

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Answer:

-10 1/2

Step-by-step explanation:

Answer:

A + B = 24

16A + 20B = 434

Step-by-step explanation:

To write a system of equations for this scenario, let's say that A represents the number of hours machine A ran, and B represents the number of hours machine B ran.

The first equation will be:

A + B = 24

because the total number of hours ran is 24.

The second equation will be:

16A + 20B = 434

because the total number of items made is 434.

A + B = 24

16A + 20B = 434

First solve for one variable, and let's just do A.

Using the first equation, A + B = 24, A is equal to 24 - B.

Substitute this value to the second equation.

16 (24 - B) + 20B = 434

384 - 16B + 20B = 434

4B = 50

B = 12.5

Now use this value of B to find the value of A.

A + 12.5 = 24

A = 11.5

Machine A ran for 11.5 hours, and Machine B ran for 12 hours.

A parabola is a U-shaped curve that can be formed by intersecting a cone with a plane that is parallel to one of its sides.

To find an equation of a parabola given the vertex and focus, we can use the following formula:

For a parabola with vertex (h, k) and focus (h, k + p), the equation is:

(x - h)^2 = 4p(y - k)

where p is the distance from the vertex to the focus.

If the focus is at (h + p, k), then the equation is:

(y - k)^2 = 4p(x - h)

where p is the distance from the vertex to the focus.

what is distance?

In the context of a parabola, the distance is the distance between the vertex and the focus, which is also known as the focal length. It is a constant value that determines the shape and size of the parabola.

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Answer:

It's the fourth one y=-1/6x+2/3

Step-by-step explanation:

Step-by-step explanation:

sooooo hard

wysjamajaklansjsmz.zu

I'll be friend

Answer:

12

Step-by-step explanation:

1:2:4

let josh=1x

james=2x

john=4x

josh has nine sweets less than john

4x-1x=9

3x=9

x=3

john's sweet=4x

4(3)=12

Answer:

'\/(-_-)\/'

Step-by-step explanation: