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3 years ago

6

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1 answer:

gavmur [86]3 years ago

6 0

Answer:

no clue sorry.

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Y = 2x + 3<br> 2y = 4x + 6<br><br> The system of equations has _____ solution(s).

Len [333]

Dividing the 2nd equation by 2 gives y=2x + 3 which is the same as the too
p line. any answer to one of them is obviously an answer to the other so there are infinitely many solutions

6 0

3 years ago

Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)

vfiekz [6]

Answer:

Step-by-step explanation:

given a point $(x_0,y_0)$ the equation of a line with slope m that passes through the given point is

$y-y_0 = m(x-x_0)$ or equivalently

$y = mx+(y_0-mx_0)$ .

Recall that a line of the form $y=mx+b$ , the y intercept is b and the x intercept is $\frac{-b}{m}$ .

So, in our case, the y intercept is $(y_0-mx_0)$ and the x intercept is $\frac{mx_0-y_0}{m}$ .

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph $(x_0,\frac{1}{x_0})$ . Which means that $y_0=\frac{1}{x_0}$

The slope of the tangent line is given by the derivative of the function evaluated at $x_0$ . Using the properties of derivatives, we get

$y' = \frac{-1}{x^2}$ . So evaluated at $x_0$ we get $m = \frac{-1}{x_0^2}$

Replacing the values in our previous findings we get that the y intercept is

$(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}$

The x intercept is

$\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0$

The triangle in consideration has height $\frac{2}{x_0}$ and base $2x_0$ . So the area is

$\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2$

So regardless of the point we take on the graph, the area of the triangle is always 2.

6 0

3 years ago

If the points on a graph of a linear function are (-2,10 (0,4) (2,-2) and (4,8) what is the y-intercept

MatroZZZ [7]

Answer:

i think 5

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Shira has 20 books on her bookshelf. Of those 15 are about horses, the rest are nature books. What fraction of Shiras books are

givi [52]

Answer:

1/4

Step-by-step explanation:

15 out of the 20 books are horses. 5 of those are nature. 5/20 is the fraction, but can be simplified to 1/4

6 0

3 years ago

Compare your estimate to the exact quotient. Does your quotient seem reasonable? Explain your answer. 9 1/3 ÷ 2 3/4

dezoksy [38]

Answer:

(9(3)+1)/3÷(2(4)+3)/4

28/3÷11/4

28/3×4/11

112/33

3.393

3 0

3 years ago