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lisabon 2012 [21]
3 years ago
13

What is an equation of the tangent line at x = 4, assuming that f(4) = 3 and f '(4) = 2? (enter your answer as an equation using

the variables y and x.)?
Mathematics
1 answer:
Margaret [11]3 years ago
3 0
The general equation for a line in the case where the slope and one point on the line are known is y-b = m(x-a), where m is the slope and (a,b) is the point.

Here f(4) = 3 corresponds to the point (4,3), and f '(4) = 2 corresponds to the slope of the tangent line at that point.

Thus the equation of the tangent line here is

         y - 3 = 2(x - 4).

An alternative form of this equation would be y = 3 + 2x - 8, or
  
          y = 2x - 5
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mash [69]

Answer:

D(-2, 5).

Step-by-step explanation:

We are given that M is the midpoint of CD and that C = (10, -5) and M = (4, 0).

And we want to determine the coordinates of D.

Recall that the midpoint is given by:

\displaystyle M = \left(\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2}\right)

Let C(10, -5) be (<em>x</em>₁<em>, y</em>₁) and Point D be (<em>x</em>₂<em>, y</em>₂). The midpoint M is (4, 0). Hence:

\displaystyle (4, 0) = \left(\frac{10+x_2}{2} , \frac{-5+y_2}{2}\right)

This yields two equations:

\displaystyle \frac{x_2 + 10}{2} = 4\text{ and } \frac{y_2 - 5}{2} = 0

Solve for each:

\displaystyle \begin{aligned}x_2 + 10 &= 8 \\ x_2 &= -2 \end{aligned}

And:

\displaystyle \begin{aligned} y_2 -5 &= 0 \\ y_2 &= 5\end{aligned}

In conclusion, Point<em> </em>D = (-2, 5).

5 0
3 years ago
6x2 + 4x -8 + 2X2 - 7x + 3
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Step-by-step explanation:

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2 years ago
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goldfiish [28.3K]

Answer:

x=4

Step-by-step explanation:

Pentagon's sum of interior angle is 540°

let's add all the given degrees

100+20x+16x+16+140+160-5x=540

Collect like terms

100+16+140+160+20x+16x-5x=540

416+31x=540

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kifflom [539]

Step-by-step explanation:

(X1,Y1) = (-2,2)

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