Use lagrange multipliers to find the minimum distance between the origin and the plane 3x y 2z = 28

We can find the slope between the first two points (-2, 2) and (0, 1):

m = (1 - 2) / (0 - (-2))

m = -1 / 2

Now that we have the slope (m), we can use the point-slope form of the equation of a line to find the y-intercept (b). Using the point (0, 1):

y - y1 = m(x - x1)

y - 1 = (-1/2)(x - 0)

y = (-1/2)x + 1

Therefore, the equation of the line in slope-intercept form that passes through the given points is:

y = (-1/2)x + 1

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Answer:

-8, 40, 32.

Step-by-step explanation:

On edge owo <3~

Answer:

-8, 40, 32.

Step-by-step explanation:

Answer:

7.8*10^3

Step-by-step explanation:

7.800

Each cube in the pattern has an area of 3 square inches.

To determine the area of each cube in the pattern, we need to find the area of each rhombus formed by the pattern.

The pattern consists of rhombuses, and we know that the diagonals of each rhombus are 2 inches and 3 inches.

The formula to find the area of a rhombus is given by:

Area = (d1 * d2) / 2,

where d1 and d2 are the lengths of the diagonals.

In this case, d1 = 2 inches and d2 = 3 inches.

Plugging the values into the formula, we get:

Area = (2 * 3) / 2

= 6 / 2

= 3 square inches.

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The sum of the perimeters of the squares with areas 252 cm², 175 cm², and 112 cm² is __ cm (in radical form).
We get the sum of perimeter in radical form is 158.72 cm.

To find the perimeters of the squares, we need to determine the length of their sides. Since the area of a square is equal to the square of its side length, we can find the side lengths of the squares by taking the square root of their respective areas.

For the square with an area of 252 cm², the side length is √252 cm. Similarly, the side lengths of the squares with areas 175 cm² and 112 cm² are √175 cm and √112 cm, respectively.

The perimeter of a square is four times its side length, so the perimeters of the squares are 4√252 cm, 4√175 cm, and 4√112 cm.

we multiply the side length by 4 for each square and add them up: (4 * 15.87) + (4 * 13.23) + (4 * 10.58) = 63.48 + 52.92 + 42.32 = 158.72 cm.



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Answer:

John has 60minutes show 4:54 and Kim has wach her 45 minutes show what time does the show ends

The number of times scientific books were sold compared to mystery books is 1000 times or one thousand times.

The numbers provided to represent the number of copies that were sold from each book are given in scientific notation. In this type of notation, the exponent represents the number of zeros. Based on this principle, the number of books sold from each type is:

To find out this, simply divide the number of science fiction book copies into the number of mystery book copies:

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Answer:

                         8

3x² + 2x - 2 - ----------

                      3x + 8

Step-by-step explanation:

                 3x² + 2x - 2

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

3x + 8     |  9x³ + 30x² + 10x - 24

                 -9x³ - 24x²     ↓

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

                             6x² + 10x

                             -6x² - 16x    ↓

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

                                       -6x - 24

                                       +6x + 16

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

                                               -8

I hope this helps!

Answer:

15

Step-by-step explanation:

25=100º

x=60

\(\frac{25}{x}=\frac{100}{60}\)

\(\frac{x}{25}=\frac{60}{100}\)

x=15

Answer:

36, 44, 52

Step-by-step explanation:

P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.

1) The statement is true. Suppose (x^,y^) is an extreme point of P. To show that x^ is an extreme point of Q, we need to prove that for any two distinct points x_1, x_2 in Q, the line segment connecting x_1 and x_2 lies entirely in Q. Since Q is the projection of P onto x-space, it means that for any x in Q, there exists y in R^k such that Ax + By ≥ b.

Now, let's assume x_1 and x_2 are two distinct points in Q. Since they belong to Q, there exist corresponding y_1 and y_2 in R^k such that Ax_1 + By_1 ≥ b and Ax_2 + By_2 ≥ b. Since P is a polyhedron, the set of points that satisfy Ax + By ≥ b is a convex set. Therefore, the line segment connecting x_1 and x_2, denoted by [x_1, x_2], lies entirely in P. Since the projection of a convex set onto a subspace is also a convex set, [x_1, x_2] lies entirely in Q. Thus, x^ is an extreme point of Q.

2) The statement is false. Suppose x^ is an extreme point of Q. It does not necessarily imply the existence of a corresponding y^ such that (x^, y^) is an extreme point of P. This is because the projection Q onto x-space may not capture all the extreme points of P. It is possible for multiple points in P to project to the same point in Q, making it impossible to uniquely determine y^.

3) The statement is true. If x^ is an extreme point of Q and P does not contain a line, then there exists a corresponding y^ such that (x^, y^) is an extreme point of P. Since P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.

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Answer:

k=50

Step-by-step explanation:

Answer:

Given that,

Height of dougal is 1.84 meters and height of seb is 1.7 meters. We need to find the height of dougal as a fraction of the height of seb.

Let x is height of dougal as a fraction of the height of seb. So,

If we divide 1.7 on both sides of above equation, then,

On removing decimal, we get,

Hence, this is the required solution.

Step-by-step explanation:

Hi,, i saw this answer here in brainly because i had this one too so i hope this one helps

Answer:

RM 14

Step-by-step explanation:

\(50 - 8 = rm42 \: for \: 3 \: boxes \\ \frac{42}{3} = rm14 \: for \: each \: box\)

Answer:

Step-by-step explanation:

The experiment is repeating and recording the result of an event in order to determine the events probability. For example, tossing a coin is an experiment.

Given a transition matrix A with values as || 1/2 1/2 1/656 1/26The steady-state probability vector can be determined by calculating the eigenvalues and eigenvectors of A. For this purpose, let's first calculate the eigenvalues of A using the following equation,

|A-λI| = 0, where λ is the eigenvalue and I is the identity matrix.
Here, A is the given matrix as mentioned above. Therefore, we have to perform matrix subtraction as shown below:
|A-λI| = |-λ 1/2 1/2 1/656 1/26 0 1/2 -λ 1/656 1/26 0 1/2 1/656 -λ 1/2 1/26 1/2 1/656 1/2 1/2 -1 1/656 -25/26|
By using elementary row operations such as adding the second and third row to the first row, we get:
|-λ 0 0 1/328 1/13 0 1/2 -λ 1/656 1/26 0 1/2 1/656 -λ 1/2 1/26 1/2 1/656 0 0 -1 1/656 -25/26|
We can simplify this expression as:
(-λ) [(4λ^3) - (11881λ^2) - (3(6^12))] = 0
We can solve this equation and obtain the eigenvalues for the matrix A as λ1 is 1 and λ2, λ3, λ4 is -1/2.
Next, we need to find the eigenvectors for each eigenvalue. We begin by calculating the eigenvector corresponding to the eigenvalue λ1 = 1. We do this by solving the following equation:
(A - λ1 I) x = 0, where I is the identity matrix and x is the eigenvector.
This gives us the following equation:
|1/2 -1/2 -1/656 -1/26| |x1|

= |0|  |1/2 -1/2 -1/656 -1/26| |x2|   |0|  |1/2 1/2 1/656 -1/26| |x3|   |0|  |-1/2 -1/2 -1/656 27/26| |x4|   |0|
Solving the system of equations using row reduction, we obtain:
|x1| = |x2|,  

|x3| = 656x1,  

|x4| = -169x1
Substituting x2 = x1 into the second equation,

we get x3 = 656x1.
Substituting these values into the fourth equation, we obtain x4 = -169x1.
Now, we need to normalize the vector x so that its components sum to 1. This gives us:
x = (1/2, 1/2, 1/656, -1/169)
Thus, the steady-state probability vector for the Markov process with transition matrix A is:
(1/2, 1/2, 1/656, -1/169)
Finally, we normalize the vector x so that its components sum to 1.

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The relationship between the variance and standard deviation is: option a)The standard deviation is the square root of the variance.

The variance of a random variable from its true population or sample mean is expected in probability theory and statistics. The term "variance" refers to a measurement of how widely apart a group of numbers are from one another.

Here,

Variance and standard deviation are both measures of spread. They calculate the deviation of each data point from the mean. The range of data increases with increasing variation. Using the original unit of measurement, the standard deviation measures the same thing as the variance (whereas variance is the original unit squared).

Therefore ,The relationship between the variance and standard deviation is: option a)The standard deviation is the square root of the variance.

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The smallest positive subnormal machine number is 0.00390625 and the largest positive subnormal machine number is 0.0048828125. The smallest positive normalized machine number is 0.0625 and the largest positive normalized machine number is 7.

a. In F3,3−4,4​ floating point system, the subnormal machine numbers are those whose exponent bits are all 0s, and whose mantissa bits are not all 0s.

Therefore, the number of subnormal machine numbers is:

\(2^4 - 1 = 15\).

b. The normal machine numbers are those that are neither subnormal nor infinite.

Therefore, the number of normal machine numbers is:

\(2^6 - 2 - 15 = 47\).

c. The smallest subnormal machine number is calculated as:

\(1 × 2^(-3) × (0.1110)₂ = 0.0111₂ × 2^(-3) = 0.09375₁₀.\)

d. The largest subnormal machine number is calculated as:

\(1 × 2^(-3) × (0.1111)₂ = 0.01111₂ × 2^(-3) = 0.109375₁₀.\)

e. The smallest positive normalized machine number is calculated as:

\(1 × 2^(-2) × (1.0000)₂ = 0.25₁₀.\)

f. The largest positive normalized machine number is calculated as:

\(1 × 2^3 × (1.1111)₂ = 7.5₁₀.\)

3. Now, let's consider F4,4−5,3​ floating point system:

a. The number of subnormal machine numbers is:

\(2^5 - 1 = 31.\)

b. The number of normal machine numbers is:

\(2^7 - 2 - 31 = 93.\)

c. The smallest subnormal machine number is calculated as:

\(1 × 2^(-5) × (0.11110)₂ = 0.0001111₂ × 2^(-5) = 0.00390625₁₀.\)

d. The largest subnormal machine number is calculated as:

\(1 × 2^(-5) × (0.11111)₂ = 0.00011111₂ × 2^(-5) = 0.0048828125₁₀.\)

e. The smallest positive normalized machine number is calculated as:

\(1 × 2^(-4) × (1.0000)₂ = 0.0625₁₀.\)

f. The largest positive normalized machine number is calculated as:

\(1 × 2^3 × (1.1110)₂ = 7₁₀.\)

Therefore, in F4,4−5,3​ floating point system, there are 31 subnormal machine numbers and 93 normal machine numbers.

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Answer:

WHEN THE SUM of two numbers multiplies their difference --

(a + b)(a − b)

-- then the product is the difference of their squares:

(a + b)(a − b) = a2 − b2

For, the like terms will cancel.

Symmetrically, the difference of two squares can be factored:

x2 − 25 = (x + 5)(x − 5)

x2 is the square of x. 25 is the square of 5.

The sum of two squares -- a2 + b2 -- cannot be factored. See Section 2.

Example 1. Multiply (x3 + 2)(x3 − 2).

Solution. Recognize the form:

(a + b)(a − b)

The product will be the difference of two squares:

(x3 + 2)(x3 − 2) = x6 − 4.

x6 is the square of x3. 4 is the square of 2.

Upon seeing the form (a + b)(a − b), the student should not do the FOIL method. The student should recognize immediately that the product will be a2 − b2.

That is skill in algebra.

And the order of factors never matters:

(a + b)(a − b) = (a − b)(a + b) = a2 − b2.

Step-by-step explanation:

(a+b)(a-b)

use a and b in the first bracket to multiply the next bracket ; a(a-b)+b(a-b)

a square-ab+ab-bsquare

Answer:

31 and 37

Step-by-step explanation:

Those are the only two numbers

Answer:

The two numbers between 30 and 40 which have only 2 factors are -

31 and 37

Hope it helps you.

The sample is baised.

Since all the students who attended the football game will most likely want a football stadium to be built and those that do no want a stadium to be built are not proportionately represented in this sample

Answer:

-1 3/8

Step-by-step explanation:

-2.25 + 0.4x = -2.8

-2.25 + 2.25 + 0.4x = -2.8 + 2.25  ==> add 2.25 on both sides to isolate x

0.4x = -0.55

(0.4x = -0.55)*20 ==> multiply the equation by 20 to remove decimals

8x = -11

x=-11/8

x=-(3+8)/8  ==> turn x into a mixed number

x=-3/8 - 8/8

x=-3/8 - 1 ==> simplify

x=-1 - 3/8

x=-(1 + 3/8)

x=-1 3/8

The given problem involves a parallelogram with vertices P(0,-6), Q(5,-4), R(4,-7), and D(-1,-9). We are required to perform two transformations: a translation along the vector (7,0) and a 90ᵒ counterclockwise rotation about the point (3,-2).

a) Translation along the vector (7,0):

To perform a translation, we add the components of the vector to the coordinates of each vertex. For point P(0,-6), the translation will result in a new point P'(7,-6). Similarly, for points Q(5,-4), R(4,-7), and D(-1,-9), the translation will yield new points Q'(12,-4), R'(11,-7), and D'(6,-9), respectively. The translated parallelogram will have vertices P'(7,-6), Q'(12,-4), R'(11,-7), and D'(6,-9).

b) 90ᵒ counterclockwise rotation about the point (3,-2):

To perform a rotation, we need to determine the new coordinates of each vertex after rotating 90ᵒ counterclockwise about the given point. Using the rotation formula, the new coordinates of point P' will be (-y + 3, x - 2), resulting in P''(2, 3). Similarly, for points Q', R', and D', the rotation will yield new points Q''(3, 8), R''(0, 5), and D''(1, 6), respectively. The rotated parallelogram will have vertices P''(2,3), Q''(3,8), R''(0,5), and D''(1,6).

By performing the translation and rotation, we have transformed the original parallelogram into a translated parallelogram with vertices P'(7,-6), Q'(12,-4), R'(11,-7), and D'(6,-9), and a rotated parallelogram with vertices P''(2,3), Q''(3,8), R''(0,5), and D''(1,6).

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1. The polynomial 9x² - 16 is in the form of ax² + c. Therefore, the value of ac is (9)(-16) = -144.

2. The coefficient of the x-term in the polynomial 9x² - 16 is 0. Therefore, the value of b is 0.

3. Two numbers that multiply to get ac = -144 and add to get b = 0 are 12 and -12.

4. The factored form of 9x² - 16 is (3x + 4)(3x - 4).

What are the multipliers?

3. We need to find two numbers that multiply to get ac = -144 and add to get b = 0. Let's find the prime factorization of ac = -144:

-144 = -1 × \(2^{4}\) × 3²

We need to choose two factors whose product is -144 and whose sum is 0. Since the product is negative, one factor must be positive and the other negative. Also, since the sum is 0, the absolute values of the two factors must be equal. The only pair of factors that satisfies these conditions is 12 and -12. Indeed, 12 × (-12) = -144 and 12 + (-12) = 0.

What is factored form?

4. The factored form is a way of representing a polynomial expression as the product of its factors. The factored form of a polynomial is important in algebraic calculations and is often used to solve equations. For example, the factored form of the quadratic expression ax² + bx + c is (mx + n)(px + q), where m, n, p, and q are constants.

the factored form of 9x² - 16 can be found using the difference of squares formula, which states that a² - b² = (a + b)(a - b). In this case, a = 3x and b = 4. Therefore:

9x² - 16 = (3x)² - 4²

= (3x + 4)(3x - 4)

Thus, the factored form of 9x² - 16 is (3x + 4)(3x - 4).

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If polynomial 9x2 - 16 then the factored form of 9x² - 16 is (3x-4)(3x+4).

What is polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.

In the polynomial 9x² - 16, a = 9 and c = -16. Therefore, the product of a and c is ac = 9*(-16) = -144.

In the polynomial 9x² - 16, b is the coefficient of the x term, which is 0. Therefore, b = 0.

To find two numbers that multiply to get ac and add to get b, we need to find two factors of -144 that add up to 0. The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. The factors that add up to 0 are -9 and 16. Therefore, ac = -144, b = 0, and the two numbers that multiply to get ac and add to get b are -9 and 16.

The factored form of 9x² - 16 is (3x-4)(3x+4). We can check this by expanding the expression using the distributive property:

(3x-4)(3x+4) = 9x² + 12x - 12x - 16

= 9x² - 16

Therefore, the factored form of 9x² - 16 is (3x-4)(3x+4).

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Answer:

7083 KM/H

Step-by-step explanation:

17000 / 2.4 = 7083 (Plus some decimals, but rounded up its 7083.)

The time listed for his next race that would make the range larger is 23.2 seconds.

To make the range larger, your friend's next race time should be farther away from the previous race times. Therefore, the time listed for his next race that would make the range larger is 23.2 seconds.

In the given scenario, the range refers to the difference between the fastest and slowest times. Currently, the range is 27.2 - 23.5 = 3.7 seconds. If your friend's next race time is 23.2 seconds, which is faster than his current fastest time of 23.5 seconds, the new range would become 27.2 - 23.2 = 4 seconds. This results in a larger range compared to the initial range of 3.7 seconds.

On the other hand, if your friend's next race time is 25.0 seconds, it falls within the existing range and does not affect the range size. Similarly, if the next race time is 26.1 seconds or 27.2 seconds (the same as his previous slowest time), the range remains unchanged. Therefore, selecting a time outside the existing range, such as 23.2 seconds, would make the range larger.

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Which time listed for his next race would make the range larger?

In the experiment, the subject whose behavior is being assessed are observational units. The observational unit in this instance is Harley (Dog).

We will first investigate if canines can comprehend both non-human and human gestures in this investigation. The dogs were placed around 2.5 meters apart from the experimenter so that the researchers could test this. Two glasses were placed one on either side of the experimenter.

A gesture would be made at one of the cups by either the experimenter (pointing, bowing, or staring) or by a non-human object (a mechanical arm pointing, a doll pointing, or a stuffed animal looking). After then, the scientists would observe whether the dog would approach the cup that was pointed out. Six dogs were put to the test. We'll focus on one of the dogs who participated in both of his trial sets.

The four-year-old mixed breed dog was given the name Harley. Each of the ten trials in a set consisted of one gesture and one pair of cups. In order to see if Harley would approach a particular cup, the experimenter bowed toward it during one round of experiments.

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Answer:

50

Step-by-step explanation:

5+5 = 10

10 × 10 = 100

100 ÷ 2 = 50