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3 years ago

Put the following equation of a line into slope-intercept form, simplifying all

Mathematics

1 answer:

seraphim [82]3 years ago

8 0

6x -15y = 135

-15y = 135 -6x

y = (135-6x)/-15

y = 2/5x + 9

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Identify the common external tangent

laiz [17]

A line that is tangent to each of the two coplanar circles

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3 years ago

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Determine whether the integral is convergent or divergent. ∫[infinity] 2 e^−1/x / x^2 dx : O Convergent O divergent If it is con

monitta

Let $f(x)=e^{-1/x}$ . Then $f'(x)=\frac1{x^2}e^{-1/x}>0$ for all $x\ge2$ , so $f$ is strictly increasing. As $x\to\infty$ , $e^{-1/x}\to e^0=1$ , so $f$ is bounded above by 1. This is to say,

$e^{-1/x}$

and the integral of $\frac1{x^2}$ converges over the same domain, so this integral must also converge by comparison.

We have, by setting $y=-\frac1x$ ,

$\displaystyle\int_2^\infty\frac{e^{-1/x}}{x^2}\,\mathrm dx=\int_{-1/2}^0e^y\,\mathrm dy=e^0-e^{-1/2}=1-\frac1{\sqrt e}$

8 0

2 years ago

The line l with equation x - 2y + 2 = 0 crosses the y-axis at the point P. The line

Sauron [17]

Answer:

Area of ΔPQR is 28 units²

Step-by-step explanation:

-P is the point with coordinates ( 0, y-intercept for line x-2y+2 =0)

-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point P( 0, b)

x-2y+2 = 0, subtract x and 2 from both sides

-2y = -x-2, divide by -2 both sides

y= (1/2)x +1 so b=1 and P (0, 1)

-Q is the point with coordinates ( 0, y-intercept for line 3x+y -15 =0)

-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point Q( 0, b)

3x +y -15 =0, subtract 3x and add 15 to both sides

y= -3x +15 so b=15 and Q(0,15)

-R is the intersection of the two lines so is the solution of the system of equations y= (1/2)x +1 and y= -3x +15

(1/2)x +1 = -3x +15, add 3x and subtract1

(1/2) x+3x = 15-1, combine like terms

(7/2)x = 14 , multiply both sides by 2

7x = 28, divide both sides by 7

x= 4

y= (1/2)x +1 = (4/2) +1 =3 so R(4,3)

- the area of ΔPQR is (base *height)/2

base= 15-1= 14

height = 4

A= (14*4)/2 = 14*2 = 28

6 0

2 years ago

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x2 + 5x – 1.

Murljashka [212]

Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (−5/8,−41/16)
Focus: (−5/8,−5/2)
Axis of Symmetry: x=−5/8
Directrix: y=−21/8 x. y
−3. 20
−2. 5
−5/8. −41/16
 0. −1
1. 8

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2 years ago

3X-4 over 14 equals 9 over 10 solve for x

Maru [420]

Answer:

3x-4/14=9/10

You change the subtraction to addition

3x+4/14=9/10

Then you change the fractions to decimals

Step-by-step explanation:

8 0

2 years ago