Which functions are not linear? select three such functions.

a. = 2 b. = 5 ―2 c. ―3+ 2= 4

d. = 32 +1 e. = ―5―2 f. = 3

If we change x by -0.7, we can expect the value of f(x) to decrease by approximately 2.1 units.

Assuming you meant to say "let f be a differentiable function where f(9) = 4 and f'(9) = 3. If we change x by -0.7 and we change y by 0.3, then we can expect the value of f(x) to change by approximately what amount?"

Using the linear approximation formula, we have:

\(Δf(x) ≈ f'(9) Δx\)

where Δx = -0.7 and we want to find Δf(x) when Δy = 0.3.

We can rearrange the formula to solve for Δf(x):

\(Δf(x) ≈ f'(9) Δx\)

Δf(x) ≈ 3(-0.7)

Δf(x) ≈ -2.1

This means that if we change x by -0.7, we can expect the value of f(x) to decrease by approximately 2.1 units. However, this is only an approximation based on the linear behavior of the function near x = 9, so it may not be exactly accurate for large changes in x.

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Complete question :

Last year there were 221 students and 13 teachers at Hillard School. This year there are 272 students. The principal wants to keep the same student-to-teacher ratio as last year. Which proportion can the principal use to find x, the number of teachers needed this year?

Answer:

221 / 13 = 272 / x

Step-by-step explanation:

Given that :

Last year:

Number of students = 221

Number of teachers = 13

Last year:

Number of students = 272

Number of teachers = x

To keep the same student to teacher ratio :

We equate the ratio for both years :

221 / 13 = 272 / x

221x = 272 * 13

221x = 3536

x = 3536 / 221

x = 16

Answer: 111 ft tall. Thats a big tree!

Step-by-step explanation: if its seven more than two times the height of the house, do 52 X 52 + 7 which equals 111 ft.

Step-by-step explanation:

here, 4 days = 20 miles

so, 1 day = 5 miles

hence, x miles = 5x miles

To determine if a matrix is diagonalizable, you first need to check if it is a square matrix. If it is not a square matrix, it cannot be diagonalized.

If it is a square matrix, you will then need to check the eigenvalues of the matrix to determine if there is a basis of eigenvectors. If the matrix has at least n linearly independent eigenvectors, where n is the number of columns of the matrix, then the matrix is diagonalizable.

For example, if a matrix is 2x2, it will need two linearly independent eigenvectors in order to be diagonalizable.

If the matrix is diagonalizable, then it can be transformed into a diagonal matrix by the product of a matrix composed of the eigenvectors and its inverse.

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To determine if a matrix is diagonalizable, we need to find the eigenvalues and eigenvectors, and check if the eigenvectors form a basis for the space. If they do, then the matrix is diagonalizable.

1. Find the eigenvalues of the matrix. The eigenvalues are the values of λ that satisfy the equation det(A - λI) = 0, where A is the matrix, I is the identity matrix, and det is the determinant.

2. Find the eigenvectors of the matrix. The eigenvectors are the vectors x that satisfy the equation (A - λI)x = 0, where A is the matrix, λ is an eigenvalue, and I is the identity matrix.

3. Check if the eigenvectors form a basis for the space. If the eigenvectors form a basis, then the matrix is diagonalizable. If the eigenvectors do not form a basis, then the matrix is not diagonalizable.

4. If the matrix is diagonalizable, then we can find a matrix P such that P^-1AP = D, where D is a diagonal matrix with the eigenvalues on the diagonal.

So, a matrix is diagonalizable, if it has eigenvalues and eigenvectors, and  if the eigenvectors form a basis for the space. If they do, then the matrix is diagonalizable, and we can find a matrix P that diagonalizes the matrix.

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Answer:

first one linear

second one quadratic

linear

Step-by-step explanation:

Answer:

f(x)=2x+3 is linear and polynomial

f(x)=x^2+2x= -3 quadratic and polynomial

f(x)=3^3 - 2 is exponential

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

4175.40384   Dutch guilders

Step-by-step explanation:

The main objective here is to convert the currency at hand (2,000 swiss francs) to Dutch guilders. In order to achieve that ; we need first require to convert the currency at hand into United states dollars

So ; if 1 swiss francs  =  1.0328 united states dollars  (as at Wednesday)

Then 2000 swiss francs  will be = 2000  ×  1.0328 united states dollars  = 2065.6 united states dollars

SO; if  1 united states dollars = 2.0214 Dutch guilders ( as at Wednesday)

Then 2065.6 united states dollars will be = 2065.6 × 2.0214

= 4175.40384   Dutch guilders

Answer:

closest would be 3,500

Step-by-step explanation:

Answer:

b=20

a=14

I hope this helps!

a is 15,b is 9 do u understnd

Answer:

70

Step-by-step explanation:

40/28=1.42,

100/1.42=70, thus

28 is 70% of 40

the probability that the randomly chosen athlete is either a football player or a basketball player is 99%.

To find the probability that the randomly chosen athlete is either a football player or a basketball player, we need to calculate the union of the probabilities.

Let's denote the probability of being a football player as P(F) and the probability of being a basketball player as P(B). We are given the following information:

P(F) = 43% = 0.43

P(B) = 56% = 0.56

P(F ∩ B) = 4% = 0.04 (since 4% play both football and basketball)

The probability that an athlete is either a football player or a basketball player can be calculated using the formula:

P(F or B) = P(F) + P(B) - P(F ∩ B)

Plugging in the values:

P(F or B) = 0.43 + 0.56 - 0.04

          = 0.99

Therefore, the probability that the randomly chosen athlete is either a football player or a basketball player is 99%.

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Answer:

1/6

Step-by-step explanation:

7/9 ÷ 14/3

7/9 x 3/14

7 and 14 cross off leaving 2 in the denominator

3 and cross off leaving 3 in the denominator

so you will get 1/6

Hope this helps

Pls mark brainliest

Answer:

1/6

Step-by-step explanation:

To solve this problem, we need to multiply by the reciprocal

Our problem first off is 7/9 divided by 14/3

But we can’t do that so we multiply by the reciprocal and our problem is:

7/9 x 3/14

This gets us to 21/126 but we can simplify this so we now have 1/6

One way you can remember this method is “keep, change flip”

In other words, keep the first fraction, change the sign from division to multiplication, and flip the other fraction.

Hope this helps and have a good day!!

Answer:rtyuiop

Step-by-step explanation:

Answer:

6.

Step-by-step explanation:

Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

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Answer:

Step-by-step explanation:

 8     6     9      5    10     4     11

 1st = 3rd - 1

  3rd = 5th - 1 and so on

2nd = 4th + 1

4th = 6th + 1

6th = 8th + 1

 8th = 6th - 1

         =  4 - 1

         = 3

Answer:

m is the slope (lesson on slope ) mnemonic : 'm' means 'move' b is the y -intercept ( lesson on the y-intercept ) mnemonic : 'b' means where the line begins.

Step-by-step explanation:

The simplified expression 3 x 25 - 32 x 4 - 42(6 - 2) is equal to -221. To simplify the expression 3 x 25 - 32 x 4 - 42(6 - 2), we can follow the order of operations (PEMDAS/BODMAS) which states that we should perform operations within parentheses first, then any exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

Let's simplify step by step:

Start by evaluating the expression inside the parentheses:

6 - 2 = 4

Replace the expression in the parentheses with the simplified value:

3 x 25 - 32 x 4 - 42(4)

Perform the multiplication operations within parentheses:

42(4) = 168

Replace the expression with the simplified value:

3 x 25 - 32 x 4 - 168

Multiply within each multiplication operation:

3 x 25 = 75

32 x 4 = 128

Replace the expressions with the simplified values:

75 - 128 - 168

Perform the subtraction operations from left to right:

75 - 128 = -53

-53 - 168 = -221

Therefore, the simplified expression 3 x 25 - 32 x 4 - 42(6 - 2) is equal to -221.

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Given lines CD and EF are parallel. Therefore answer is (a)

How to find slope of  two lines and check whether they are parallel or perpendicular

Given are two points P (x₁, y₁) and Q ( x₂, y₂)

Then slope of the line  PQ is given by  (y₂-y₁)/(x₂-x₁)

If two lines have slopes m₁ and m₂ respectively

Then the lines are parallel when their slopes are equal i.e. m₁=m₂

and  the lines are perpendicular when m₁*m₂= -1

Given C(5,2), D(8,3),E(3,8) F(-6,5)

Then,

Slope of CD = (3-2)/(8-5)= 1/3

Slope of EF = (5-8) / (-6-3)  = 1/3

Slope of CD=Slope of EF

Therefore CD and EF are parallel

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What we have been given here are two points.

f(3) = -4 is the same as (3, -4)

f(2) = 6 is the same as (2, 6)

We can then use these two points to find the equation of a line.

Step 1: Find the slope

Slope Formula: (y2 - y1) / (x2 - x1)

Slope = (6 - - 4) / (2 - 3) = (10) / (-1) = -10

Step 2: Find the y-intercept

To find the y-intercept, we'll take our slope and one of our points and plug them into slope-intercept form, then solve for b.

Slope-Intercept Form: y = mx + b

Point = (2, 6)

6 = 2(-10) + b

6 = -20 + b

b = 26

Step 3: Create the equation of the line

Now that we have the slope and y-intercept, all that's left to do is plug both of those values into slope-intercept form.

y = -10x + 26

Answer: y = -10x + 26

Hope this helps!

Answer:

x=4

Step-by-step explanation:

no because x=4 and you can't have multiple answerd

Using the method of cylindrical shells, the volume v generated by rotating the region bounded by the given curves about the y-axis. y = 5/x,y = 0, x₁ = 2, x₂ = 7 is 25π.

To find the volume using the method of cylindrical shells, we integrate the circumference of each shell multiplied by its height. The region bounded by the curves y = 5/x, y = 0, x = 2, and x = 7 is a region in the first quadrant of the xy-plane. When this region is revolved about the y-axis, it forms a solid with cylindrical shells.

For each shell at a given y-value, the radius is given by x, and the height is given by 5/x (the difference between the y-values on the curve and the x-axis). To find the volume, we integrate the circumferences of the shells multiplied by their heights over the interval of y from 0 to 5/2.

The integral for the volume is given by:

v = ∫[0 to 5/2] 2πx(5/x) dy

v = 10π ∫[0 to 5/2] dy

v = 10π [y] from 0 to 5/2

v = 10π (5/2 - 0)

v = 25π

Therefore, the volume v generated by rotating the region about the y-axis is 25π.

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If the angle of depression of a point on the ground, from the top T of a building is 23.6°, the distance from p to the foot of the building is 50 cm, then the height is 56 meters.

To solve this problem, we can use trigonometry and set up a right triangle with the building, the ground point, and the point T on top of the building. The angle of depression, 23.6°, is the angle between the horizontal and the line of sight from point T to the ground point.

Therefore, the complementary angle, which is the angle between the vertical and the line of sight, is 90° - 23.6° = 66.4°.

Let's denote the height of the building as h and the distance from point T to the ground point as d. We know that the tangent of the complementary angle is equal to the ratio of the height of the building to the distance d, i.e., tan 66.4° = h/d. Rearranging this equation, we get h = d * tan 66.4°.

We are given that the distance from the ground point to the foot of the building is 50 cm. To find the distance d from point T to the ground point, we can use the fact that the angle of depression is equal to the angle of elevation from the ground point to point T.

Therefore, we can draw a vertical line from the ground point to intersect with the line of sight from point T, creating a right triangle with the distance d as the adjacent side and the height of the building as the opposite side. The tangent of the angle of depression is equal to the ratio of the opposite side to the adjacent side, i.e., tan 23.6° = h/d.

Rearranging this equation, we get d = h / tan 23.6°. We can substitute this expression for d into the equation for h, yielding h = (50 cm) * tan 66.4° / tan 23.6° ≈ 56 meters (to the nearest meter).

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The given relation can be written as:

y = $5*x + $20

Notice that we have a constant term, thus it is not a proportional relation.

A general proportional relationship can be written as:

y = k*x

Where k is a constant of proportionality.

The given case is:

" A bike rental store charges $20 as a flat fee, plus $5 per hour."

We know that there is a flat fee of $20 plus $5 per hour, so we can write the equation:

y = $5*x + $20

Notice that we have a constant term, thus, it is not a proportional relation.

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To prove the inequality 9/8 < ∑ 1/n^3 < 5/4 where n = 1, we need to find the summation of the series 1/n^3 for n = 1 and compare it to the given range.

The series in question is a p-series, where p = 3, with p > 1.

This means the series converges. The exact value of the sum is given by the Riemann zeta function ζ(3), also known as Apery's constant, which is approximately 1.2020569.

Now, let's compare this value to the given range:

9/8 = 1.125
5/4 = 1.25

Since 1.125 < 1.2020569 < 1.25, we can conclude that 9/8 < ∑ 1/n^3 < 5/4 for n = 1.

The series is proved 9/8 < ∑ 1/n^3 < 5/4, where n = 1 true for the lower and upper bounds .

9/8 < ∑ 1/n^3 < 5/4, where n = 1,

Use the fact that the sum of the reciprocals of cubes of natural numbers is a convergent series with a well-known value.

∑ 1/n^3

= ζ(3)

= 1.202056903159594285399738161511449990764986292...

where ζ(3) is the Riemann zeta function evaluated at 3.

To prove that 9/8 < ζ(3) < 5/4,

Use some known bounds on the Riemann zeta function.

One such bound is,

ζ(s) > 1 + 1/2^(s-1)  for s > 1

Applying this to s = 3, we get,

ζ(3) > 1 + 1/2^2 = 5/4

So we have the lower bound,

9/8 < ζ(3)

To get the upper bound,

Use another known bound on the Riemann zeta function,

ζ(s) < 1 + 1/(s-1) for s > 1

Applying this to s = 3, we get,

ζ(3) < 1 + 1/2 = 3/2

So we have the upper bound,

ζ(3) < 3/2

Combining these two bounds, we get,

9/8 < ζ(3) < 3/2

which implies,

9/8 < ∑ 1/n^3 < 5/4

Therefore, it is proved that 9/8 < ∑ 1/n^3 < 5/4 by evaluating the bounds of the series, where n = 1.

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Answer:

6.9

Step-by-step explanation:

I will use cross-multiplication for this problem:

\(\frac{4}{7} =\frac{x}{12} \\\\7x=48\\\\x=\frac{48}{7} \\\\x=6.857\)

Rounded to tenths:

6.9

Answer:

Regular Price = $56

Step-by-step explanation:

3/4 x = 42

42/3 * 4 = x

14 * 4 = 56

x - 56

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

...........

2(x + 2) + 2x = 20

Answer:

x(x+2) = 20

Step-by-step explanation:

Perimeter Formulas of rectangle is: Perimeter = 2 × (a + b)