1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
andrew-mc [135]
3 years ago
8

Find the slope and the equation of the line tangent to f (x )equals StartFraction 2 x minus 1 Over x plus 7 EndFraction at x​ =

2. The slope of the line tangent to​ f(x) at x​ = 2 is nothing. Answer the following in​ slope-intercept form. ​ (y = mx​ + b) The equation of the tangent line is y​ = nothing
Mathematics
1 answer:
kondor19780726 [428]3 years ago
6 0

Answer:

y=\frac{5}{27} x-\frac{1}{27}

Step-by-step explanation:

f(x)=\frac{2x-1}{x+7}

To find slope of f(x) at x=2, find the derivative f'(x)

apply quotient rule to find derivative

f(x)=\frac{2x-1}{x+7}\\f'(x)=\frac{2(x+7)-1(2x-1)}{(x+7)^2} \\f'(x)=\frac{15}{(x+7)^2}

f'(x) is the slope . Now find slope at x=2. plug in 2 for x

f'(x)=\frac{15}{(x+7)^2}\\f'(2)=\frac{15}{(2+7)^2}=\frac{5}{27}

find out f(x) when x=2

f(x)=\frac{2x-1}{x+7}\\f(2)=\frac{2(2)-1}{2+7}=\frac{1}{3}

Now frame the equation of the line

(2,1/3) slope = 5/27

y-y_1=m(x-x_1)\\y-\frac{1}{3}=\frac{5}{27} (x-2)\\y-\frac{1}{3}=\frac{5}{27} x-\frac{10}{27}\\\\y=\frac{5}{27} x-\frac{1}{27}\\\\

You might be interested in
What is the value of x?
kicyunya [14]

Answer:

(5(x-4))0

evaluate

1

Step-by-step explanation:

your answer is one i believe

6 0
3 years ago
Read 2 more answers
SOMEONE PLEASE HELP ASAPP I NEED HELP
fenix001 [56]
11

A diagonal connects a vertex to another vertex without being a side of the polygon. There are 14 vertices in a 14-gon. This leaves 13 vertices left to connect to (since we cannot connect the vertex to itself). However, two of these vertices will form the sides of the 14-gon. This leaves us with 11 possible diagonals we can draw.
6 0
1 year ago
Read 2 more answers
What’s the slope of (9,10) and (2,14)
denis23 [38]

Answer:

4/-7

Step-by-step explanation:

14-10/2-9=

4/-7

4 0
2 years ago
Read 2 more answers
How can you calculate the area of the circle if you know the circle's circumference?
Jobisdone [24]

<u>Answer with step-by-step explanation:</u>

We know that the formula for area of a circle is given by:

<em>Area of a circle = \pi r ^ 2</em>

So to find the area of circle, we basically need to know the radius of the circle.

If we know the circumference of the circle, we can calculate the area of the circle too.

Formula for the circumference of the circle is given by:

2\pi r

So if we know the circle's circumference, we can find the value of radius and then find the area of circle with it.

5 0
3 years ago
Read 2 more answers
Four times the quotient of 3 and 4
Lina20 [59]

Answer:

3

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Other questions:
  • Is 15/4 an irrational number?
    14·1 answer
  • 4 (2/3) is the same as 4 groups of (2/3).
    11·1 answer
  • 0.002 centigrams = _____ kilograms ?
    10·2 answers
  • Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
    9·2 answers
  • What is 3.4,3.14,3.04,4.4,4.03 from least to greatest
    13·2 answers
  • 11. Write the equation of the line in slope-intercept form that is parallel to the line y = - 4x + 2 and
    15·1 answer
  • Lines m and n are parallel what is the measure of angle 5
    7·2 answers
  • If 4 is subtracted from twice a number, the result is 10 less than the number. Find the number. *
    6·2 answers
  • Help Solve for c and round to the nearest tenth
    5·1 answer
  • Help will give brainliest !!! PLEASE ITS EASY
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!