I am a bit confused on a derivative is in Calculus. From what I understand, I derivative is the limit of a tangent line on a curve. I was wondering if someone can explain in simple terms what a derivative is and what is the point of calculating it. Thanks!

Answer:

? = 16

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan ? = opp side / adj

tan ? = 13 / 46

Taking the inverse tan of each side

tan ^ -1 ( tan ? ) = tan ^-1 ( 13/46)

? = 15.78075

To the nearest degree

? = 16

Answer:

A. 20.81 mph

Step-by-step explanation:

x = speed of the boat in still water.

one part of the trip is 10 miles downstream, where the speed of the boat and the speed of the current add together.

and the other part of the trip is the trip back the 10 miles upstream, where the speed of the current works against the speed of the boat :

10/(x + 15) + 10/(x - 15) = 2

10 + 10×(x+15)/(x-15) = 2×(x+15)

10×(x-15) + 10×(x+15) = 2×(x+15)×(x-15)

20x = 2×(x² - 225)

10x = x² - 225

0 = x² - 10x - 225

solution of a quadratic equation

x = (-b ± sqrt(b² - 4ac)) / (2a)

a = 1

b = -10

c = - 225

(10 ± sqrt(100 - 4×1×-225)) / 2 =

= (10 ± sqrt (100 + 900)) / 2 = (10 ± sqrt(1000)) / 2 =

= (10 ± 31.62) / 2

x1 = 41.62 / 2 = 20.81 mph

x2 is negative and did not make any sense.

Answer:

1

Step-by-step explanation:

Basically you just need to find the square root of all of them

36=6    -1=1      9=3 .     -1=1

6-1-3-1=1

Step-by-step explanation:

x+3=2x-1

x-2x=-1-3

-x=-4

x=4

Answer:

The slope is 1 and the y intercept is 4

Step-by-step explanation:

Slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

Rewriting

y = x+4

The slope is 1 and the y intercept is 4

Answer:

M = 1

Step-by-step explanation:

1. Convert to standard form: x - y = - 4

2. Slope using standard form: m = 1

Answer:

D

Step-by-step explanation:

[tex]5(9 + 4) \\ 5(13) \\ 65 \\ prove \: it \: d \: answer \\ 5(9) + 20 \\ 45 + 20 \\ = 65[/tex]

Answer:

2

Step-by-step explanation:

Reflection over y axis rule

(x,y) --------> (-x,y)

Rule explained:

Simply change the sign of the x value and keep the y value as it it

Coordinates of A (-4,0)

Apply reflection over y axis rule

(-4,0) -----> (4,0)

Next we want to apply a translation with the rule ( x - 5 , y + 2 )

Explanation of rule:

Simply subtract 5 from the x value and add 2 to the y value

Current coordinates of A (4,0)

Apply translation rule

(4,0) -------> ( 4 - 5 , 0 + 2 ) --------> (-1 , 2 )

The y value of coordinate A would be 2 after all of the transformations

Answer:

Step-by-step explanation:

Used property of exponents

Now we have to find,

The answer to this problem.

Then use the property of exponents,

→ [tex] \sf a^cb^c = (ab)^c[/tex]

Let's find the solution,

→ 9b²c²

→ 3²b²c²

→ (3bc)²

Hence, (3bc)² is the answer.

Answer: 4 bags of oranges and 3 bags of apple

Step-by-step explanation:

Each bag of oranges is 5 and 5 times 4 is 20 Each bag of apples is 3 and 3 times 3 is 9 so 20 + 9 = 29

Answer:

12 centimeters

Step-by-step explanation:

The side lengths of the triangle are: 26, 28, and 30 centimeters

a = 26 cm, b = 28 cm, c = 30 cm

To find the area, we first must find the semi-perimeter with the following equation:

s = (a+b+c)/2

  = (28+26+30)/2

  = 42 centimeters

Now, to find the area, we can use Heron's formula:

A = [tex]\sqrt{s (s-a)(s-b)(s-c)}[/tex]

     [tex]\sqrt{42(42-28)(42-26)(42-30)[/tex]

     [tex]\sqrt{42(14)(16)(12)}[/tex]

     [tex]\sqrt{112896}[/tex]

     336 squared centimeters

Since the area of the parallelogram is equal to the area of our triangle:

Area of Parallelogram = Area of Triangle

base ⋅ height = 336 squared centimeters

28 ⋅ height = 336 squared centimeters

height = 336/28

height = 12 centimeters

Answer:

HY = 18

Step-by-step explanation:

The distance from the vertex to the centroid is twice the distance from the centroid to the midpoint , so

HY = 2 YL = 2 × 9 = 18

It is 6x -23y. You cannot factor using GCF any further.

Answer:

4,324,386 students

Step-by-step explanation:

Student population in 2015 = 3,845,721

Percentage of students population in 2015 = 100%

Percentage increase of students each year = 1.18%

What will the student population of Algebra City be in the year 2025?

2025 population = 3,845,721(100% + 1.18%)^t

Where

t = number of years

= 2025 - 2015

= 10 years

2025 population = 3,845,721(100% + 1.18%)^t

= 3,845,721(1 + 0.118)^10

= 3,845,721(1.0118)^10

= 3,845,721(1.1244670934955)

= 4,324,386.7152646077555

Approximately,

= 4,324,386 students

9514 1404 393

Answer:

  (3x-7)/(x^2-5x+6)

Step-by-step explanation:

Not particularly hard, just tedious. You need to factor all the quadratics, cancel common factors, and combine terms using a common denominator.

  [tex]\dfrac{x-1}{x^2-3x+2}+\dfrac{x-2}{x^2-5x+6}+\dfrac{x-5}{x^2-8x+15}\\\\=\dfrac{x-1}{(x-1)(x-2)}+\dfrac{x-2}{(x-2)(x-3)}+\dfrac{x-5}{(x-3)(x-5)}=\dfrac{1}{x-2}+\dfrac{1}{x-3}+\dfrac{1}{x-3}\\\\=\dfrac{1}{x-2}+\dfrac{2}{x-3}=\dfrac{(x-3)+2(x-2)}{(x-2)(x-3)}=\dfrac{x-3+2x-4}{x^2-5x+6}\\\\\boxed{\dfrac{3x-7}{x^2-5x+6}}[/tex]

Answer:

[tex]\rm \displaystyle \frac{3x - 7}{ {x}^{2} - 5x + 6 } [/tex]

Step-by-step explanation:

we would like to simplify the following:

[tex] \rm\displaystyle \frac{x - 1}{ {x}^{2} - 3x + 2 } + \frac{x - 2}{ {x}^{2} - 5x + 6} + \frac{x - 5}{ {x}^{2} - 8x + 15}[/tex]

to simplify algebraic expression the first step is to figure out the LCM of the denominator in order to do so we can factor the denominators therefore factor the denominators and work out the LCM

[tex]\rm\displaystyle \frac{x - 1}{ (x - 1)(x - 2)} + \frac{x - 2}{ (x - 2)(x - 3)} + \frac{x - 5}{(x - 5)(x - 3)}[/tex]

reduce fraction:

[tex]\rm\displaystyle \frac{1}{ x - 2} + \frac{1}{ x - 3} + \frac{1}{x - 3}[/tex]

figure out the LCM and divide it by the denominator and multiply the result with the numerator which yields:

[tex]\rm\displaystyle \frac{1}{ x - 2} + \frac{1}{ x - 3} + \frac{1}{x - 3} \\ \\ \displaystyle \frac{x - 3 + x - 2 + x - 2}{(x - 2)(x - 3)} [/tex]

simplify addition:

[tex]\rm \displaystyle \frac{3x - 7}{(x - 2)(x - 3)} [/tex]

further expansion if necessary:

[tex]\rm \displaystyle \frac{3x - 7}{ {x}^{2} - 5x + 6 } [/tex]

Given:

The inequality is:

[tex]x>111[/tex]

To find:

The x-values that are the solutions to the given inequality.

Solution:

We have,

[tex]x>111[/tex]

It means all the real numbers greater than 111 are the solutions to the given inequality.

[tex]97<111[/tex], so 97 is not a solution.

[tex]101<111[/tex], so 101 is not a solution.

[tex]119>111[/tex], so 119 is a solution.

Therefore, the correct option is C.

Given:

The inequality is:

To find:

The x-values that are the solutions to the given inequality.

Solution:

We have,

It means all the real numbers greater than 111 are the solutions to the given inequality.

, so 97 is not a solution.

, so 101 is not a solution.

, so 119 is a solution.

Therefore, the correct option is C.

Answer:

the slope is 1

Step-by-step explanation:

Answer:

slope = 1

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, 9)

m = [tex]\frac{9-4}{4-(-1)}[/tex] = [tex]\frac{5}{4+1}[/tex] = [tex]\frac{5}{5}[/tex] = 1

Answer:

y= $(1-0.08)y

Step-by-step explanation:

9514 1404 393

Answer:

  35 cm²

Step-by-step explanation:

You can count the squares, or ...

Any way you do this, there are 35 square, so the area is 35 square centimeters.

Answer:

C. 50 degrees

Step-by-step explanation:

Angle EDG is 90 degrees

x = 10

5 multiplied by 10 is 50

4 multiplied by 10 is 40

40+50=90

Answer:

50 = EDH

Step-by-step explanation:

We know that angle EDG is a right triangle (measures 90°). We also know that angle EDH and angle HDG make up angle EDG which is 90°. So ultimately we can state that;

EDH + HDG = EDG

 5x  +   4x  =   90

      9x = 90

        x = 90/9

        x = 10

Now that we know that value of x, we can say that;

EDH = 5x

since x = 10

EDH = 5(10)

EDH = 50

Hope this helps!

Answer:

38.4

Step-by-step explanation:

tan38 = 30/x

x = 30/tan38 = 38.39834 = 38.4 (nearest tenth)

Answer:

yea your answer is 38.4

Step-by-step explanation:

I just did that question

Answer:

A conjecture that can be made is that the line that contains the diagonal from the tip to the vertex of the tail of a dart and the diagonal that joins the fin angles are perpendicular to each other

Step-by-step explanation:

Question; Make a conjecture about the line that contains the diagonal from the tip to the vertex of the tail of a dart and the diagonal that joins the fin angles

Explanation;

We note that a diagonal is a straight line that joins one corner of a polygon with another corner of the polygon from the vertex points of the connected corners

The diagonal that joins the fin angles forms an isosceles triangle at the tail of the dart, and the locus of the line that forms the diagonal from the tip to the tail is a equidistant from the vertex of the fin angles

Therefore, the diagonal from the tip bisects the diagonal that joins the fin angles bisects the base of the formed isosceles triangle while passing through the vertex of the isosceles triangle, it is therefore, perpendicular to the base of the isosceles triangle which is the diagonal that joins the fin angles

A conjecture that can be made is that the line that contains the diagonal from the tip to the vertex of the tail of a dart and the diagonal that joins the fin angles is therefore, that they are perpendicular to each other

Answer:

C. 64°

Step-by-step explanation:

[tex]{ \tt{ \cos( \theta) = \frac{adjacent}{hypotenuse} }} \\ \\ { \tt{ \cos( \theta) = \frac{7}{16} }} \\ \\ { \tt{ \theta = { \cos }^{ - 1} ( \frac{7}{16} )}} \\ \\ { \tt{ \theta = 64 \degree}}[/tex]

Answer:  Choice C) 64 degrees

Work Shown:

[tex]\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(\theta) = \frac{7}{16}\\\\\cos(\theta) = 0.4375\\\\\theta = \cos^{-1}(0.4375)\\\\\theta \approx 64.0555^{\circ} \\\\\theta \approx 64^{\circ} \\\\[/tex]

Note: some calculators will use the notation arccos in place of the [tex]\cos^{-1}[/tex]

Answer:

Wait did you mean how many points will it be after an entire SEASON?

Answer:

500

Step-by-step explanation:

( 4 x 10^7 ) ÷ ( 8 x 10^4 )

= ( 4 x 10^4 ) ( 10^3 ) ÷ ( 4 x 10^4 ) x 2

= 10^3 ÷ 2

= 1000 ÷ 2

= 500

Answer:

45

Step-by-step explanation:

(3x) + x = 180 =

4x = 180

----    -----

4        4

x = 45

The answer is 45.

Answer:

Post them individually

Step-by-step explanation:

1. B

2. 4th option ,----> Megan's at 2.5 per week

Megan's plant:

slope = 7-4.5/2-1 = 2.5= growth rate

Suzanne's plant:

slope = 7-5/2-1= 2 = growth rage

3.D

4 2nd option , $2 for each song

Rate of change = 6-4/3-2 = 2

Answer:

non of the above thanks

don't ask me again please

Answer:

where are the functions ???

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

In fact the point doesn’t lies on the graph or between the lines

Answer and Explanation:

Volume of a cylinder is given by

V= Pi*r²*h

where v= volume of the cylinder

Pi is constant = 22/7 or 3.14159

r= radius of the circle of the cylinder

h= height of the cylinder

If two cylinders are measured proportionally to the other based on radius and height of each cylinder, we look at the proportional equality of the ratio of the radius and height of one cylinder to the other. If one cylinder for example has ratio of radius and height =2/4 then it is proportional to the other cylinder with ratio 1/2

Answer: One of the cylinders is short and wide, while the other is tall and thin.