1/2(12k-6) i don't know what this answer is!!!

The total derivative of a function is not necessarily one-to-one. The total derivative represents the change in a function with respect to all of its input variables.

If a function has multiple input variables, the total derivative is a matrix, called the Jacobian matrix, whose entries represent the partial derivatives of the function with respect to each input variable.

A function with a non-invertible Jacobian matrix is not one-to-one, since multiple input values can result in the same output value. For example, consider the function f(x,y) = (x^2, y^2). The total derivative of f is given by the Jacobian matrix:

| 2x 0 |

| 0 2y|

This matrix is non-invertible when x=0 or y=0, since it has a determinant of zero. Thus, the function f is not one-to-one when x=0 or y=0.

In terms of polynomials, the total derivative is important for determining whether a polynomial has multiple roots. A root of a polynomial is a value of the input variable that causes the polynomial to equal zero. If a polynomial has multiple roots, it is not one-to-one, since different input values can result in the same output value.

The total derivative of a polynomial can be computed using the power rule of differentiation. For example, consider the polynomial p(x) = x^3 - 6x^2 + 11x - 6. The total derivative of p with respect to x is:

p'(x) = 3x^2 - 12x + 11

If p'(x) has multiple roots, then p(x) has multiple roots as well. In this case, p'(x) has roots at x=1 and x=11/3, so p(x) has multiple roots at x=1 and x=3. Thus, the total derivative is useful for identifying when a polynomial is not one-to-one.

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Is total derivative  is one-to-one? explain the significance of this result in terms of the derivative on polynomials.

Answer:

No

Step-by-step explanation:

As you probably know, triangles have 3 sides. The longest side is called the hypotenuse. In this case, the hypotenuse is 10.3. Now, you might or might not know the pythagorean theorem, which states that the a² + b² =c ².

In this case, we can say that 4.4 is a and 8.3 is b. Now if we square 4.4 and add it to 8.3 squared, we get 88.25. However, if you square 10.3, you get 106.09. Thus, the values cannot be this way. So, your answer is no.

Answer:

f(10) = -130

Step-by-step explanation:

f(x) = -x² - 3x

f(10) = -(10)² - 3(10)

f(10) = -100 - 30

f(10) = -130

Answer:

16

Step-by-step explanation:

Answer:

x = 120°

Step-by-step explanation:

We are given;

sec²x + 4secx = -4

Rearranging gives;

sec²x + 4secx + 4 = 0

Factorizing the left hand side gives;

(sec x + 2)(sec x + 2) = 0

This means that;

(sec x + 2) = 0

From trigonometry, we know that sec x = 1/cos x

Thus;

(1/cos x) + 2 = 0

1/cos x = -2

cos x = -1/2

cos x = -0.5

x = cos^(-1) -0.5

x = 120°

Answer:

18

Step-by-step explanation:

PEMDAS

3x4=12

12+6=18

Hope this helps.

The slope of the line which is perpendicular to the given line is (-6/5).

Describe the negative reciprocal.

The negative reciprocal of a number, let's say "n," is "- (1/n).

We are aware of a line's equation in slope intercept form, y = mx + b, as well as the fact that perpendicular lines have slopes that are reciprocal to each other's negative values.

The slope intercept form of the line 15x - 18y = -486 can be expressed as,

-18y = -15x - 486.

- y = (-15/18)x - (486/18).

- y = (-5/6)x - 27.

y = (5/6)x + 27.

The slope of the supplied line is (5/6), making the perpendicular line's slope (-6/5).

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The median, because the data distribution is skewed to the right.

Given that

The box plot with the following parameters:  

Minimum value at 11,

First Quartile, Q1 at 22.5,

Median at 34.5,

Third Quartile, Q3 at 36,

Maximum value at 37.5.

According to the question

When a distribution has a longer tail to one of its sides, then it is said to be skewed.

Since the tail is longer to the left, it is said to be left-skewed.

The data distribution is skewed to the left because the median (34.5) is closer to the third quartile (36) than to the first quartile  (22.5).

For skewed data, we always prefer the median because it is less affected by the outliers and if the mean is chosen, the value of the mean is biased towards the side that has larger values while the median does not get affected by it. So, we choose the median.

For skewed distributions, the median is the best measure of center.

Hence, the median, because the data distribution is skewed to the right.

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The probability of both rice and carrots being served with dinner is 23.4%.

The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.

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Hey friend!

The slope of your line is gonna be \(\frac{2}{3}\).

The rise from one point to the next is 2, and the run is three.

I hope this answer helped you,

Yours Truly,

~TheQueenOfBrainly

Explanation:

x = max number of gallons the tank can hold

Greg's car starts off 1/3 full, so (1/3)x = x/3 number gallons is in the car.

Add on 11 more gallons to get (x/3) + 11 = x/3+33/3 = (x+33)/3

The expression (x+33)/3 represents the number of gallons he has after buying 11 gallons of gas. This is equal to (5/6)x since this represents the idea of the tank being 5/6 full

The equation we need to solve is (x+33)/3 = (5/6)x

Let's do so to get...

(x+33)/3 = (5/6)x

(x+33)/3 = (5x)/6

6(x+33) = 3*5x

6x+198 = 15x

198 = 15x-6x

198 = 9x

9x = 198

x = 198/9

x = 22

His tank can hold up to 22 gallons.

The approximate circumference of a circle with a diameter of 10 inches is 31.42 inches.

To determine the circumference of a circle, we can use the formula C = πd, where C represents the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and d is the diameter of the circle. Given that the diameter is 10 inches, we substitute this value into the formula:

C = 3.14 * 10

Calculating this expression, we find:

C ≈ 31.42 inches

Therefore, the approximate circumference of the circle is 31.42 inches. It is important to note that the units of measurement are crucial in providing an accurate answer, so we include "inches" to denote the unit of measurement.

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Answer:

It started on the 55th floor.

Step-by-step explanation:

We can work backwards from the 54th floor. Since we are working backwards, if the elevator goes up, we will subtract and if it goes down, we will add. Starting with 54, we get 54 + 5 = 59, then 59 - 9 = 50, then 50 + 2 = 52, then 52 - 6 = 48, then 48 + 14 = 62, then 62 - 7 = 55.

Answer: 10^-5 = 1/10^5

Step-by-step explanation: Every time you see a negative exponent, it would be 1/10^ (exponent number)

\(\huge\text{Hey there!}\)

\(\mathsf{10^{-5}}\\\\\mathsf{= \dfrac{1}{10\times10\times10\times10\times10}}\\\\\mathsf{= \dfrac{1}{100\times100\times10}}\\\\\mathsf{= \dfrac{1}{10,000\times10}}\\\\\mathsf{= \dfrac{1}{100,000}}\\\\\mathsf{= \dfrac{1}{10^5}}\)

\(\huge\text{Thus, your answer should be: \boxed{\mathsf{\dfrac{1}{10^5}}}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The  reduced exact values for the root of f(x) = x² + 10·x - 5, obtained using the quadratic formula are; x = (-5 + √(30)) and x = (-5 - √(30))

The quadratic formula is a formula that is used to find the roots of a quadratic equation, by plugging in the coefficients of a quadratic equation into the formula.

The roots of the quadratic function, f(x) = x² + 10·x - 5, can be obtained using the quadratic formula as follows;

The quadratic formula, which can be used to find the roots of the quadratic function, f(x) = a·x² + b·x + c is; x = (-b ± √(b² - 4·a·c))/(2·a)

The function f(x) = x² + 10·x - 5, indicates;

a = 1, b = 10, and c = -5, therefore;

x = (-10 ± √(10² - 4 × 1 × (-5)))/(2 × 1) = (-10 ± √(120))/2

(-10 ± √(120))/2 = (-5 × 2 ± 2 × √(30))/2

(-5 × 2 ± 2 × √(30))/2 =  (-5 ± √(30))/2

The roots of the quadratic function are;

x = (-5 + √(30))/2, and x = (-5 - √(30))/2

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The given statement, "the margin-of-error refers to the number of percentage points by which survey results may vary" is true because the margin of error is an important factor to consider when interpreting the results of a poll.

In a poll, the margin of error refers to the amount of random sampling error that is expected to be present in the results of the survey. It is a measure of the statistical uncertainty associated with using a sample of a population to make inferences about the opinions or characteristics of the entire population.

The margin of error is typically reported as a plus or minus percentage, such as "plus or minus 3 percentage points," and it represents the range of values within which the true population parameter is likely to fall with a certain level of confidence. For example, if a poll has a margin of error of plus or minus 3 percentage points with a 95% level of confidence, this means that if the poll were conducted 100 times, the results would be expected to fall within plus or minus 3 percentage points of the true population parameter in 95 of those surveys.

Therefore, the margin of error is an important factor to consider when interpreting the results of a poll and helps to provide a measure of the precision and reliability of the survey findings.

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The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.

What is Linear Function?

A straight line on the coordinate plane is represented by a linear function.

The linear function formulas are:

Here, we have

The given functions are f(0)=2 and f(3) = -1

For f(0) = 2

Coordinate: (0,2)

y-intercept, c: 2

For f(3) = -1

Coordinate: (3,-1)

gradient or slope, m when x₁ = 0, y₁ = 2, x₂ = 3, y₂ = -1

=( y₂-y₁)/(x₂-x₁)

= ( -1 -2)/(3 - 0)

= -3/3

= -1

The linear equation is in the slope-intercept form, y=mx+c

f(x) = -x+2, where -1 is the slope and 2 is the y-intercept.

Hence, The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.

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To solve the equation 2y - z = -6 for y, we isolate the variable y on one side of the equation.

2y - z = -6

Adding z to both sides:

2y = z - 6

Next, we divide both sides by 2 to solve for y:

y = (z - 6)/2

Now we can substitute the given values to find the corresponding y-values for the given ordered pairs:

For (-2, __):

y = (-2 - 6)/2

y = -8/2

y = -4

For (0, __):

y = (0 - 6)/2

y = -6/2

y = -3

For (__, -5):

-5 = (z - 6)/2

-5 * 2 = z - 6

-10 + 6 = z

z = -4

So the ordered pairs are: (-2, -4), (0, -3), and (-4, -5).To draw a line using two of the ordered pairs, we can plot the points (-2, -4) and (0, -3) on a coordinate plane and connect them with a straight line. The line will represent all the possible points that satisfy the equation 2y - z = -6.

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The range of possibilities for the third side of the triangle, after using the triangle inequality theorem is 13 < n < 25.

According to the theorem of triangle inequality, the sum of any two of a triangle's sides must exceed the length of the third side. When we know the lengths of two sides, x and y, we can apply the triangle inequality theorem to estimate the length of the third side, which will be between x + y and x - y.

As a result,

x – y < n < x + y

19 – 6 < n < 19 + 6

13 ft < n < 25 ft

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Answer:

es 357 ya que primero mutiplicas sumas restas y multiplicas

Step-by-step explanation:

pir esi se ilibi topi rrospe

Answer:

Diameter =16

Step-by-step explanation:

Chord theorem: When two chord intersect inside the circle, the product of the products of their segment are equal.

       4c * 6 = (2c +8)*4  

          24c = 2c*4 + 8*4  

           24c = 8c + 32  

Subtract 8c from both sides,

     24c - 8c = 32

             16c = 32

Divide both sides by 16,

                 c = 32 ÷ 16

                  \(\boxed{c = 2}\)

To find the horizontal diameter, add 2c +8 and 4.

   2c + 8 + 4 = 2c + 12

                    = 2*2 + 12

                   = 4 + 12

                    = 16

Diameter = 16

Answer:

- \(\frac{35}{6}\)

Step-by-step explanation:

The additive inverse is the opposite of 6, that is - 6 ( 6 - 6 = 0 )

The multiplicative inverse is the reciprocal of 6 , that is \(\frac{1}{6}\) ( 6 × \(\frac{1}{6}\) = 1 )

Thus their sum is

- 6 + \(\frac{1}{6}\) = - \(\frac{36}{6}\) + \(\frac{1}{6}\) = - \(\frac{35}{6}\)

Answer:

- 5 5/6 or you can write it as -35/6.

Step-by-step explanation:

The additive inverse of 6 is -6 because 6 + (-6) = 0 while the multiplicative inverse is 1/6 because 6 * 1/6 = 1.

So the answer is  - 6 + 1/6 = - 5 5/6.

Cameron has a total of 48 books. Of them, 24 are fantasies, 12 are biographies and 6 are mysteries.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Let x be the total number of books that Cameron has.

Number of fantasy books = x/2

Number of biographies = x/4

Number of mysteries = x/8

Number of sports books = 6

x/2 + x/4 + x/8 + 6 = x

x(1/2 + 1/4 + 1/8) + 6 = x

7/8 x + 6 = x

x - 7/8 x = 6

1/8 x = 6

x = 6 × 8 = 48

Number of fantasy books = x/2 = 48 / 2 = 24

Number of biographies = x/4 = 48 / 4 = 12

Number of mysteries = x/8 = 48 / 8 = 6

Hence there are a total of 48 books of which 24 are fantasies, 12 are biographies and 6 are mysteries.

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Answer:

a) 210×0.10=21

b) 48×0.10=4.8

Step-by-step explanation:

210-21=189

48-4.8=43.2

Answer:

A answer is: m = (626 - 27 x 6)/8

The height of the tree is 16 feet if it casts a 24 feet shadow at the same time of the day when 4 feet wall casts a 6-foot shadow.

The shadows at the same time of the day can be compared for the garden wall and a tree as follows;

tree shadow / tree height = wall shadow / wall height

As the height of the wall is given to be 4 feet and it has a 6-foot shadow, and the tree casts a 24-foot shadow, substituting these values in the equation;

24 / x = 6 / 4

Here x represents the height of the tree

Solving for x;

24 / x = 1.5

24 = 1.5 x

x = 24 / 1.5

x = 16

Therefore the height of the tree is calculated to be 16 feet.

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The height of the tree is 16 feet when it casts a 24 feet shadow at the same time of the day when 4 feet wall casts a 6-foot shadow.

An equation is an expression that shows the relationship between two or more numbers and variables.

The shadows at the same time of the day can be compared for the garden wall and a tree is given by;

tree shadow / tree height = wall shadow / wall height

Since we know that the height of the wall is given to be 4 feet and it has a 6-foot shadow, and the tree casts a 24-foot shadow, substituting these values in the equation;

24 / x = 6 / 4

Here x represents the height of the tree

Solving for x,

24 / x = 1.5

24 = 1.5 x

x = 24 / 1.5

x = 16

Therefore, the height of the tree is calculated to be 16 feet.

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(a) The set N₁ is convex.
(b) The set ₂ is not convex.
(c) The set N₃ is convex.
(d) The set ₄ is not convex.
(e) The set ₅ is not convex.

(a) The set N₁ is defined as {(x₁, x₂) ∈ R² | x₁² + x₂² ≤ 1}. This represents a closed disk of radius 1 centered at the origin. Any two points within or on the boundary of this disk can be connected by a straight line segment that lies entirely within the disk. Therefore, the set N₁ is convex.
(b) The set ₂ is defined as {(x, ₂) ∈ R² | x² + x² = 1}. This represents the unit circle in the xy-plane. If we consider two points on the circle, we can find a line segment connecting them that lies outside the circle. Hence, the set ₂ is not convex.
(c) The set N₃ is defined as {(x₁, x₂, x₃) ∈ R³ | x₁ + x₂ + x₃ ≥ 1}. Any two points within this set can be connected by a straight line segment, and the segment will lie entirely within the set. Thus, the set N₃ is convex.
(d) The set ₄ is defined as {(x, A) ∈ R² | A ≥ e²}. If we take two points in this set, their convex combination will not necessarily satisfy the condition A ≥ e². Hence, the set ₄ is not convex.
(e) The set ₅ is defined as {(x, A) ∈ R² | A ≥ sin(x)}. Taking two points in this set, their convex combination will not necessarily satisfy the condition A ≥ sin(x). Therefore, the set ₅ is not convex.

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