Find the value for x ​
(x+20) (4x-5)

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.

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.

To learn more on derivatives, we kindly invite to check this verified question: https://brainly.com/question/21202620

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

Answer:

two negitives equals a positive so C none of the above

Hope This Helps!!!

Answer:

A and B

Step-by-step explanation:

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

Step-by-step explanation: 2 × 18 = 36. Then (as there are two numbers) take the square root: √36 = 6. this is for 36

Answer: 13

Step-by-step explanation:√(5 × 36) = 13.416407865

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:

-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:

it is d

Step-by-step explanation:

Step-by-step explanation:

the scale factor is 1 : 150

you don't know what that means ?

it means that every unit (here cm) in the diagram corresponds in reality to 150 units.

so, 1 cm in the diagram is 150 cm in reality.

therefore we only need to multiply the sizes in the diagram by 150, and we get the real sizes.

length : 5 × 150 = 750 cm (7.5 m)

breadth : 3 × 150 = 450 cm (4.5 m)

and the perimeter is as for every rectangle :

2×length + 2×breadth = 2×750 + 2×450 = 1500 + 900 =

= 2400 cm (24 m)

The coordinates of the dilated vertex V' is (-6p, 5p)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.

Dilation is the increase or decrease in the size of a figure. If a point A(x, y) is dilated by a factor k, the new point is A'(kx, ky).

The Parallelogram TUVW has vertices at T(3, 4), U(-10,-2), V(-6,5) and  W (7,11). If it is dilated by a scale factor p with the origin, the new point is at:

T'(3p, 4p), U'(-10p, -2p), V'(-6p, 5p) and W'(7p, 11p)

Find out more on dilation at:https://brainly.com/question/10253650

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

Answer:

962

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

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:

C

Step-by-step explanation:

32 / 4  = 8

56 / 7 = 8

64 / 8 = 8

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:

Factors of 42: 1, 2, 3, 6, 7, 14, 21 and 42.

Step-by-step explanation:

:)

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:

157.47448

Step-by-step explanation:

here you go i did all the math hope this helped

Answer:

128.2189

Step-by-step explanation:

thats the price of the TV including tax

Answer:

After 5 minutes, it remains 75.73 grams of mass.

Step-by-step explanation:

Each minute, the mass is decreased by a 25.5%. So, we can find the mass after each minute period.

First minute.

330gr - 0.255 (330gr)= (330 - 84.15)gr = 245.85gr

Second minute.

245.85 - 0.255 (245.85) = 245.85 - 62.69 = 183.16gr

Third minute.

183.16 - 0.255 (183.16) = 183.16- 46.70= 136.45gr

Fourth minute.

136.45- 0.255 (183.16) - 136.45 - 34.80= 101.65gr

Fifth minute.

101.65 - 0.255 (101.65)= 101.65 - 25.92= 75.73gr

Therefore, after 5 minutes, it remains 75.73 grams of mass.

Answer:0.375

Step-by-step explanation:

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

Answer:

undefined.......it's infinity

Answer:

70 likes

Step-by-step explanation:

49 likes / 7 minutes = 7 likes / minute

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

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

Answer:

nobotty nows

Step-by-step explanation:

Answer:

[tex] \frac{vw}{gf} = \frac{uv}{hg} [/tex]

[tex] \frac{72}{132} = \frac{6x + 12}{143} [/tex]

[tex] \frac{6}{11} = \frac{6x + 12}{143} [/tex]

Now we cross multiply

6×143=11(6x+12)

858=66x+132

858-132=66x

726=66x

x=11

Answer:

[tex]\frac{1}{y^{3} }[/tex]

Step-by-step explanation:

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.