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saw5 [17]
3 years ago
10

Write the equation of the line that passes through the points (8,−7) and (−9,7). Put your answer in fully reduced point-slope fo

rm, unless it is a vertical or horizontal line.
Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
6 0

Answer:

y + 7 = (-14/17)(x - 8)

Step-by-step explanation:

We want the equation of this line in the point-slope form y - k = m(x - h).

We are given two points (8, -7) and (-9, 7), and may arbitrarily choose one of them to serve as the point (h, k) in the point-slope form shown above.  Then the other point is represented by (x, y) in the point slope form shown above:

Let (h, k) be 8, -7) and let (x, y) be (-9, 7).  Then,  y - k = m(x - h) becomes:

7 - (-7) = m(-9 - 8), so that 14 = m(-17), and the slope is thus m = -14/17

The desired equation is then y + 7 = (-14/17)(x - 8) (which is in point-slope form).  

Another way to get this result would be to find m in the usual way:

          rise           14

m = ------------- = --------- = -14/17 (same as before).

           run           -17

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The angle of depression from the top of a lighthouse to a boat is 27*. if the direct distance from the top of lighthouse to the
alisha [4.7K]

Answer:

Correct answer:  Db = 411 .18 ft

Step-by-step explanation:

Given:

α = 27°  angle of depression

Dt = 462 ft  distance from the top of lighthouse to the boat

Db = ?   distance from the base of the lighthouse to the boat

Here we have a right triangle with hypotenuse Dt and one leg Db.

By definition

cos α = Db / Dt  ⇒ Db = Dt · cos α

Db = 462 · cos 27° = 462 · 0.89 = 411 .18 ft

Db = 411 .18 ft

God is with you!!!

5 0
3 years ago
Please help me thanks!​
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5 x 16 x 4 = 320 m^3
3 0
3 years ago
3/4 x = 2/5<br><br> please answer this
Vlada [557]

Answer:

= 8 /1 5

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
A conical vessels with base radius 5 cm and height 24cm is full of water this water is emptied into a cylindrical vessel of base
Aliun [14]

Answer:

2\ cm

Step-by-step explanation:

We\ are\ given\ that,\\Radius\ of\ the\ conical\ vessel=5\ cm\\Height\ of\ the\ conical\ vessel=24\ cm\\Hence,\\As\ we\ know\ that,\\Volume\ of\ a\ cone=\frac{1}{3}\pi r^2h\\Hence,\\The\ volume\ of\ the\ conical\ vessel=\frac{1}{3}\pi (5)^224=  \frac{1}{3}\pi 25*24=200\pi \\Hence,\\The\ volume\ of\ the\ conical\ vessel=The\ amount\ of\ water\ filled\ in\ it\\Hence,\\The\ amount\ of\ water\ filled\ in\ the\ conical\ vessel=200\pi\\Lets\ consider\ the\ cylindrical\ vessel:\\Volume\ of\ a\ cylinder=\pi r^2h

As\ we\ are\ not\ said\ that\ the\ cylindrical\ vessel\ was\ empty,\ let\ its\ initial\\ height\ be\ h_1\\Radius\ of\ the\ Cylindrical\ vessel=10\ cm\\Initial\ height\ of\ the\ cylindrical\ vessel=h_1\\Initial\ volume\ of\ the\ cylindrical\ vessel=\pi *10^2*h_1=100h_1\pi \\Initial\ amount\ of\ water\ in\ the\ cylindrical\ vessel=100h_1\pi \\Hence,\\Final\ amount\ of\ water\ in\ the\ cylindrical\ vessel=Final\ amount\ of\ water\\ in\ the\ cylindrical\ vessel +Amount\ of\ water\ in\ conical\ vessel

Hence,\\Final\ amount\ of\ water\ in\ the\ cylindrical\ vessel=100h_1\pi +200\pi \\Now,\\Let\ the\ final\ height\ be\ h_2\\Hence,\\Final\ amount\ of\ water\ in\ the\ cylindrical\ vessel=\pi *10^2*h_2=100h_2\pi \\Hence,\\100h_2\pi =100h_1\pi +200\pi \\Hence,\\100h_2=100h_1+200\\100h_2-100h_1=200\\100(h_2-h_1)=200\\h_2-h_1=2\\Hence,\\As\ the\ rise\ in\ level\ is\ the\ difference\ between\ the\ initial\ and\ final\\ heights:\\The\ rise\ in\ level\ of\ water=2\ cm

8 0
3 years ago
1 + 2 + (-5) + 4 <br><br> A . -6<br> B . -5 <br> C . 0<br> D . 2<br> E . 4<br> F . 12
Dovator [93]

Answer:

Option D. 2

Step-by-step explanation:

1+2+(-5)+4

= 1+2-5+4

= 1+2+4-5

= 7-5

= 2

5 0
3 years ago
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