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KonstantinChe [14]
3 years ago
13

Reflect the following points over the x-axis. (-5, -3) (-2,-6) (-4,-8)

Mathematics
1 answer:
viktelen [127]3 years ago
8 0

Reflect over x-axis rule: (x,y) -> (x,-y)

(-5,3) --> (-5,-3)

(-2,-6) --> (-2,6)

(-4,-8) --> (-4,8)

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The ratio of Monarch butterflies to Queen butterflies at a butterfly farm was 8:5. If there are no additional butterflies at the
alisha [4.7K]
The ratio would be 5:13
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3 years ago
At 1 P.M., ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast i
Evgen [1.6K]
<span>The distance between the ships is changing at a rate of 21.393 km/h

</span><span>Step 1: First, you must draw an image to help better understand the problem 
</span>

The reason that ship A is moving -35km/h is because ship B acts as an "origin" and as things move closer to the "origin" they become negative and as things move away from the "origin" they become positive.

We know that the rate of Ship A is expressed as <span><span><span>dA</span><span>dt</span></span>=−35</span> and the rate of Ship B is expressed as <span><span><span>dB</span><span>dt</span></span>=25</span>

Step 2: We want to figure out how many km Ship A and Ship B traveled in 4 hours

<span>ShipA:−35<span><span>km</span>h</span>⋅4hr=−140km</span>

Now if we take this <span>−140km</span> and add it to the <span>150km</span> we can see that Ship A is now only <span>10km</span> away from where Ship B began

<span>ShipB:25<span><span>km</span>h</span>⋅4hr=100km</span>

This means that Ship B is now <span>100km</span> from where it originally started

We can now redraw our information

Step 3: We must use the Pythagorean Theorem to find the third side of the triangle

<span><span>x2</span>+<span>y2</span>=<span>z2</span>→<span>102</span>+<span>1002</span>=<span>z2</span></span>

<span>z=<span>√<span><span>102</span>+<span>1002</span></span></span></span>

Step 4: Now that we know z, we must differentiate the original equation in order to find the rate at which z in changing

<span><span>x2</span>+<span>y2</span>=<span>z2</span>→2x<span><span>dx</span><span>dt</span></span>+2y<span><span>dy</span><span>dt</span></span>=2z<span><span>dz</span><span>dt</span></span></span>

We can simplify by canceling out the 2's

<span>x<span><span>dx</span><span>dt</span></span>+y<span><span>dy</span><span>dt</span></span>=z<span><span>dz</span><span>dt</span></span></span>

Step 5: Write down all the information and then plug into equation

<span>x=10and<span><span>dx</span><span>dt</span></span>=−35</span>
<span>y=100and<span><span>dy</span><span>dt</span></span>=25</span>
<span>z=<span>√<span><span>102</span>+<span>1002</span></span></span>and<span><span>dz</span><span>dt</span></span>=?</span>

Now plug in the information

<span>x<span><span>dx</span><span>dt</span></span>+y<span><span>dy</span><span>dt</span></span>=z<span><span>dz</span><span>dt</span></span></span>

<span>10<span>(−35)</span>+100<span>(25)</span>=<span>√<span><span>102</span>+<span>1002</span></span></span><span><span>dz</span><span>dt</span></span></span>

<span>−350+2500=<span>√<span><span>102</span>+<span>1002</span></span></span><span><span>dz</span><span>dt</span></span></span>

<span>2150=<span>√<span><span>102</span>+<span>1002</span></span></span><span><span>dz</span><span>dt</span></span></span>

<span>21.393=<span><span>dz</span><span>dt</span></span></span>

The distance between the ships are increasing at a rate of 21.393 km/h

8 0
3 years ago
Why might a researcher use a sample rather than an entire population for their study?
cestrela7 [59]

Answer:

c

Step-by-step explanation:

its easier to take a group of 100 or something random people than a whole population.

6 0
3 years ago
A ship is anchored off a long straight shoreline that runs north and south. From two observation points 16 miles apart on shore,
ELEN [110]
D - the shortest distance from the ship to the shore.
d / ( 17 - x ) = tan 32° = 0.62487
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d = 0.62487 ( 17 - x )
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0.62487 ( 17 - x ) = 1.32704 x
10.62279 - 0.62487 x = 1.32704 x
x = 10.62279 : 1.95191
x = 5.44226 miles
d = 5.44226 · 1.32704
Answer:
d = 7.222  miles
6 0
3 years ago
How to find The point midway
Vadim26 [7]

Step-by-step explanation:

The Midpoint Formula works exactly the same way. If you need to find the point that is exactly halfway between two given points, just average the x-values and the y-values.

4 0
3 years ago
Read 2 more answers
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