Which description best describes the association between variables x and y?
picture is below

a) The value of [tex]k'(0)[/tex] is [tex]\frac{3\sqrt{3}}{2}[/tex].

b) The value of [tex]m'(5)[/tex] is approximately -0.034.

c) The value of [tex]x[/tex] is approximately 0.622.

a) [tex]f(x)[/tex] is a piecewise function formed by two linear functions, whose form is defined by the following definition:

[tex]f(x) = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} \cdot x + b[/tex] (1)

Where:

Now we proceed to determine the linear functions:

Line 1: [tex]x \in [-1, 2)[/tex]

[tex](x_{1}, y_{1}) = (0, 3)[/tex], [tex](x_{2}, y_{2}) = (1, 5)[/tex], [tex]b = 3[/tex]

[tex]f(x) = \frac{5-3}{1-0}\cdot x + 3[/tex]

[tex]f(x) = 2\cdot x + 3[/tex]

Line 2: [tex]x \in [2, 8][/tex]

[tex](x_{1}, y_{1}) = (2, 7)[/tex], [tex](x_{2}, y_{2}) = (8, 3)[/tex]

First, we determine the slope of function:

[tex]m = \frac{3-7}{8-2}[/tex]

[tex]m = -\frac{2}{3}[/tex]

Now we proceed to determine the intercept of the linear function:

[tex]7 = -\frac{2}{3}\cdot 2 + b[/tex]

[tex]b = \frac{25}{3}[/tex]

[tex]f(x) = -\frac{2}{3}\cdot x +\frac{25}{3}[/tex]

The first derivative of a linear function is its slope, and the first derivative of a product of functions is defined by:

[tex]k'(x) = f'(x)\cdot g(x) + f(x)\cdot g'(x)[/tex]

If we know that [tex]f(x) = 2\cdot x + 3[/tex], [tex]f'(x) = 2[/tex], [tex]g(x) = \sqrt{x^{2}-x+3}[/tex], [tex]g'(x) = \frac{2\cdot x - 1}{2\cdot \sqrt{x^{2}-x+3}}[/tex] and [tex]x = 0[/tex], then:

[tex]k'(x) = 2\cdot \sqrt{x^{2}-x+3}+\frac{(2\cdot x +3)\cdot (2\cdot x - 1)}{2\cdot \sqrt{x^{2}-x+3}}[/tex]

[tex]k'(0) = 2\sqrt{3}-\frac{3}{2\sqrt{3}}[/tex]

[tex]k'(0) = \frac{12-3}{2\sqrt{3}}[/tex]

[tex]k'(0) = \frac{9}{2\sqrt{3}}[/tex]

[tex]k'(0) = \frac{3\sqrt{3}}{2}[/tex]

The value of [tex]k'(0)[/tex] is [tex]\frac{3\sqrt{3}}{2}[/tex].

b) The derivative is found by means of the formulas for the derivative of the product of a function and a constant and the derivative of a division between two functions:

[tex]m'(x) = \frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{2\cdot [g(x)]^{2}}[/tex] (2)

If we know that [tex]f(x) = -\frac{2}{3}\cdot x +\frac{25}{3}[/tex], [tex]f'(x) = -\frac{2}{3}[/tex], [tex]g(x) = \sqrt{x^{2}-x+3}[/tex], [tex]g'(x) = \frac{2\cdot x - 1}{2\cdot \sqrt{x^{2}-x+3}}[/tex] and [tex]x = 5[/tex], then:

[tex]f(5) = 5[/tex]

[tex]f'(5) = -\frac{2}{3}[/tex]

[tex]g(5) = \sqrt{23}[/tex]

[tex]g'(5) = \frac{9\sqrt{23}}{46}[/tex]

[tex]m'(5) = \frac{\left(-\frac{2}{3} \right)\cdot \sqrt{23}-\left(-\frac{2}{3} \right)\left(\frac{9\sqrt{23}}{46} \right)}{3\cdot 25}[/tex]

[tex]m'(5) \approx -0.034[/tex]

The value of [tex]m'(5)[/tex] is approximately -0.034.

c) In this case we must find a value of [tex]x[/tex], so that [tex]h'(x) = 2[/tex]. Hence, we have the following formula below:

[tex]5\cdot e^{x}-9\cdot \cos x = 2[/tex]

A quick approach is using a graphing tool a locate a point so that [tex]5\cdot e^{x}-9\cdot \cos x = 2[/tex]. According to this, the value of [tex]x[/tex] is approximately 0.622.

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Answer:

1) Divide the numerator by the denominator.

2) Write down the whole number result.

3) Use the remainder as the new numerator over the denominator. This is the fraction part of the mixed number.

Step-by-step explanation:

not sure of this will help... but hope it does!

Answer:

Explained below :)

I tried my best to explain, sorry if it doesn't make sense

Step-by-step explanation:

Example problem: 11/4 (Mixed number)

1: 11 divided by 4 = 2 (whole number) with a remainder of 3

( Numerator divided by denominator) (Don't turn the number into a decimal leave the remainder)

2: Take the remainder and put it over the denominator 3/4

3: Whole number beside the remainder over the denominator

Your answer would be 2 3/4

Answer:

-144 feet from the surface in 4 minutes

Step-by-step explanation:

-36 x 4

With the same rate, the position of the undersea after 4 minutes will be -144.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

For example the speed 3meter/second.

As per the given,

Rate of descends = 36 feet per minute

After 4 minutes,

36 x 4 = 144

Since it is descending so it can be said to be -144.

Hence "After 4 minutes at the same rate, the position of the undersea will be -144".

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#SPJ2

Answer:

14.6

Step-by-step explanation:

the given angle 6.2 is cleared to be wrong

so we will erase the point of decimal and times sin62 with hypotenous 16.5 that will give us 14.6 length unit as 2 triangles are symmetric as the line cut them to 2 equal triangles

The different selections of one meat and one vegetable are possible are 18 selections.

Since the Hickory Stick has a selection of 3 meats and 6 vegetables, the number of ways we can select one meat out of 3 is ³C₁ = 3.

Also, the number of ways we can select one vegetable out of 6 is ⁶C₁ = 6.

So, the total number of selections of one meat and one vegetable is ³C₁ × ⁶C₁ = 3 × 6

= 18 selections

So, the different selections of one meat and one vegetable are possible are 18 selections.

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Answer:

The answer will be the third one.

Step-by-step explanation:

Hope it helps

Answer:

two negitives equals a positive so C none of the above

Hope This Helps!!!

Answer:

A and B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The product of 5 and 539 is 2695

Finding the product of numbers simply means multiplying 2 or more numbers.

Therefore, the product of 5 and 539 can be done as follows:

Multiplication or product sign is denoted as ×.

Therefore,

5 × 539 = 2695

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Answer: Karen has 20, Trey has 15, Dante has 40

Step-by-step explanation:

Karen=x+5    Trey=x     Dante=2x+10

            x+x+5+2x+10=75

                 4x+15=75

                   4x=60

                     x=15

The monthly payment if you could get a 60-month loan at 7.5% APR is $1,031.25

First, we need to get the amount on the cost of the Jeep at the rate of 7.5% using the formula

Amount = Principal + Interest

Given the following parameters

Get the interest

Get the amount;

Calculate the monthly payment:

Hence the monthly payment if you could get a 60-month loan at 7.5% APR is $1,031.25

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Answer:

-3

Step-by-step explanation:

Substitute the value of 11 into x within the function so it would be f(11) = 1/4(5-11)2 which is - 3.

Answer:

  -3/2 < a < 2/3

Step-by-step explanation:

In the fourth quarter of the coordinate plane, x > 0 and y < 0. This means ...

  2a +3 > 0

  3a -2 < 0

__

The first inequality has the solution ...

  2a > -3 . . . . subtract 3

  a > -3/2 . . . . divide by 2

The second inequality has the solution ...

  3a -2 < 0

  3a < 2 . . . . add 2

  a < 2/3 . . . divide by 3

The set of values of 'a' that put P in the fourth quarter is ...

  -3/2 < a < 2/3

For the 20ft from doc. Set up triangle, with dr/dt on the hypotenuse = 2. 6 on the y, 20 on the x. Use x^2+ y^2= r^2. Differentiate and solve for dx/dt. 2x(dx/dt) + 2y(dy/dt)=2r(dr/dt); Since y value does not change, your y vector is equal to 0. Giving us 2x(dx/dt)=2r(dr/dt) ; dx/dt=(2r(dr/dt))/2x

Do the same thing for 10ft

No it is not surprising because as the angle between the dock and the boat decreases, more force is being used to pull up on the boat, not pull it inwards. Thus, the boats horizontal velocity will slow down as it beats the dock.

Answer:

19 students ride a bike to school

Answer:

the answer is A

Step-by-step explanation:

9-2(10)         9-20

The given function is a linear function that decreases as the value of the

input x increases.

Reasons:

The given function is f(x) = 9 - 2·x

The output of the function is the value of f(x) for a given input x of the function.

The input value, x is substituted into the function to obtain the output value, f(x).

Given that the input, x = 10

We have;

f(10) = 9 - 2×10 = -11

Therefore, the correct option for f(10) is A. -11

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Answer:

[tex]V(1,2) \to V \ ' \ (0.5,1)\\\\U(0,2) \to U \ ' \ (0,1)\\\\T(-1,0) \to T \ ' \ (-0.5, 0)\\\\W(1,-2) \to W \ ' \ (0.5,-1)\\\\[/tex]

===========================================================

Explanation:

Multiply each coordinate by 0.5, which is the same as the fraction 1/2.

This causes the preimage to shrink to a smaller image.

The rule I'm using is [tex](x,y) \to (kx,ky)[/tex] where the scale factor is k = 0.5

Answer:

962

Step-by-step explanation: 30²- 6² is 962

Answer:

[tex]3x + 14[/tex]

Step-by-step explanation:

Step 1:  Distribute

[tex]4x + 2(3x + 7) - 7x[/tex]

[tex]4x + (2 * 3x) + (2 * 7) - 7x[/tex]

[tex]4x + 6x + 14 - 7x[/tex]

Step 2:  Combine like terms

[tex]4x + 6x + 14 - 7x[/tex]

[tex](4x + 6x - 7x) + 14[/tex]

[tex]3x + 14[/tex]

Answer:  [tex]3x + 14[/tex]

Answer:

5x + 6 = 0

5x = - 6

x = - 6/5

-6/5 is the answer

Answer:0.375

Step-by-step explanation:

1/8 + 1/4 = 3/ 8=0.375

Answer:

All of them are composite

Step-by-step explanation:

In math, composite numbers can be defined as the whole numbers that have more than two factors. Whole numbers that are not prime are composite numbers, because they are divisible by more than two numbers.

Answer:

nobotty nows

Step-by-step explanation:

Answer:

47

Step-by-step explanation:

Each new term is the previous term +2.

1st term = 1

5th term = 9

10th term = 19

15th term = 29

20th term = 39

25th term = 49 - 2 = 47 = 24th term

Answer: 11/15 hours

Step-by-step explanation:

Find LCD (lowest common denominator)

1/3=5/15

2/5=6/15

6/15+5/15=11/15 hours or 44 minutes

Using the slope of the linear function, it is found that:

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

In this problem:

Two of the points are: (0,0) and (2,1).

[tex]m = \frac{1 - 0}{2 - 0} = \frac{1}{2} = 0.5[/tex]

Then, applying the interpretation:

To learn more about slopes and linear functions, you can take a look at https://brainly.com/question/16302622

Answer:

hes correct. the slope is 0.5 and it grows 0.5 inches everyday

Step-by-step explanation:

Answer:

-21=-4w

w=5.25

but you don’t want decimals

so- you round down

w=5

Step-by-step explanation:

You combine like terms, and then make sure your variable is alone, the only way to get it alone from a ”mixed number”  is to divide

you do the same thing to both sides

so divde each side by -4

-21/-4 = 5.25

or with it rounded down since it’s under a five

It’s 5 with the decimals removed

i hope this helps

Answer:

70 likes

Step-by-step explanation:

49 likes / 7 minutes = 7 likes / minute

10 minutes * 7 likes / minute = 70 likes / 10 minutes

Answer:

see explanation

Step-by-step explanation:

(1)

[tex]\frac{5}{60}[/tex] ( divide numerator/ denominator by 5 )

= [tex]\frac{1}{12}[/tex] ( in simplest form )

(2)

both quantities must have the same units

1 hour = 60 minutes , then

[tex]\frac{60}{40}[/tex] ( divide numerator/ denominator by 20 )

= [tex]\frac{3}{2}[/tex] ( in simplest form )

(3)

1 week = 7 days then 2 weeks = 2 × 7 = 14 days , so

[tex]\frac{14}{4}[/tex] ( divide numerator/ denominator by 2 )

= [tex]\frac{7}{2}[/tex] ( in simplest form )

(4)

[tex]\frac{8}{30}[/tex] ( divide numerator/ denominator by 2 )

= [tex]\frac{4}{15}[/tex] ( in simplest form )

(5)

[tex]\frac{9}{45}[/tex] ( divide numerator/ denominator by 9 )

= [tex]\frac{1}{5}[/tex] ( in simplest form )

Answer:

-2(x^2+1)

Step-by-step explanation:

1. Divide The Numbers:

-2x^2+2(-3/3)

-2x^2+2(-1)

2. Multiply The Numbers:

-2x^2+2(-1)

-2x^2-2

3. Common Factor:

a. Factor by grouping

-2x^2+2(-3/3)

-2x^2-2

b. Factor by Grouping

-2x^2-2

-2(x^2+1)

-2x^2+(2)(-3/3)

Solution: -2(x^2 + 1)