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3 years ago

Consider the line y=-5/9x+6

Mathematics

1 answer:

Arlecino [84]3 years ago

4 0

Answer:

See below in bold.

Step-by-step explanation:

Use the point-slope form of a straight line

y - y1 = m(x - x1)

Here m = -5/9 , x1 = 9 and y1 = -3:, so

y - -3 = -5/9(x - 9)

y + 3 = -5/9x + 5

y = -5/9x + 2 is the equation parallel to the given line.

The line perpendicular to the given line will have a slope of - 1 / -5/9

= 9/5 so its equation is

y + 3 = 9/5(x - 9)

y = 9/5x - 81/5 - 3

y = 9/5x - 96/5 .

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PLEASE HELP NOW 20 POINTS!

ludmilkaskok [199]

Answer:

The Answer is A. 12 1/2

Step-by-step explanation:

2 x 2 1/2 = 5

5 x 2 1/2 = 12.5

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7 0

3 years ago

What is the image point of (0,1) after the transformation D4 R90? Please and thank you

Ede4ka [16]

Answer:

Image point → (-4, 0)

Step-by-step explanation:

Coordinate of a point → (0, 1)

Rule for the transformation has been given as,

D₄ o R₉₀

First use R₉₀ → Rotation of the point by 90° counterclockwise

Rule for the rotation of a point (x, y) by 90° counterclockwise about the origin,

(x, y) → (-y, x)

(0, 1) → (-1, 0)

Further use D₄ → Dilation of the point by a scale factor of 4 about the origin

If a point (x, y) is dilated by a scale factor 'k' about the origin rule for the dilation is,

(x, y) → (kx, ky)

By applying this rule,

(-1, 0) → (-4, 0)

Therefore, image point will be → (-4, 0)

5 0

3 years ago

The height (feet) of an object moving vertically is given by s= (-16t^2)+(208t)+(156), where t is in seconds.

OverLord2011 [107]

Answer:

The object's velocity at t = 7 is -16 ft/s

The maximum height is 832 ft and it occurs when $t=\frac{13}{2}$

Step-by-step explanation:

From the information given, the equation of motion of the object is

$s(t)= -16t^2+208t+156$

For any equation of motion s(t), the instantaneous velocity at time t is given by

$v(t)=\frac{ds}{dt}$

(a) To find the object's velocity at t = 7, you must:

$v(t)=\frac{d}{dt}(-16t^2+208t+156)\\\\v(t)=-\frac{d}{dt}\left(16t^2\right)+\frac{d}{dt}\left(208t\right)+\frac{d}{dt}\left(156\right)\\\\v(t)=-32t+208+0\\\\v(t)=-32t+208$

Next, we evaluate when t = 7

$v(7)=-32(7)+208=-224+208\\\\v(7)=-16$

The object's velocity at t = 7 is -16 ft/s

(b) To find the maximum of a function we always use the derivative of the function and we set it equal zero to find the critical points.

To find the maximum height and when it occurs, we set the velocity function equal to 0 and solve for t.

$-32t+208=0\\\\-32t+208-208=0-208\\\\-32t=-208\\\\\frac{-32t}{-32}=\frac{-208}{-32}\\\\t=\frac{13}{2}$

Next, we substitute this value into the equation of motion to find the maximum height

$s(\frac{13}{2})= -16(\frac{13}{2})^2+208(\frac{13}{2})+156\\\\s(\frac{13}{2})=-676+1352+156)=832$

The maximum height is 832 ft and it occurs when $t=\frac{13}{2}$

6 0

3 years ago

What's equivalent to 4(y – 3)

kiruha [24]

Answer:

that's

Step-by-step explanation:

+4y -12 thank you

8 0

3 years ago

Read 2 more answers

In 2008, the number of tourists visiting France was 7.94 x 10^7. The number of tourists visiting Italy was 4.27 x 10^7. Find the

Marizza181 [45]

Answer:

$36700000$

Step-by-step explanation:

Difference between tourists visiting France and Italy = $(7.94 - 4.27)$ × $10^{7}$

$= 3.67$ × $10^{7}$

$= 36700000$

$\therefore$ Difference between population of tourists in France and Italy are $36700000$ people.

3 0

3 years ago