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Vika [28.1K]
3 years ago
5

A grid shows the positions of a subway stop and your house. The subway stop is located at (-1, 9) and your house is located at (

2, -4). What is the distance, to the nearest unit, between your house and the subway stop? A.) 5 B.)6 C.)12 D.)13
Mathematics
1 answer:
sammy [17]3 years ago
4 0
The distance between the house and the subway is given by:
d=√[(x-x1)²+(y-y1)²]
Thus given the coordinates:
(-1,9) and (2,-4)
thus
d=√[(2-(-1))²+(-4-9)²]
d=√[(3)²+(-13)²]
d=√[9+169]
d=√178
d=13.34 ~13 units
Answer: D) 13
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Using the completing-the-square method, rewrite f(x) = x^2 + 10x + 7 in vertex form.
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f(x) = x^2 + 10x + 7 \\\\
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F(x)= 8x/ x - 2 g(x)= 6/x+3 determine the domain of f + g
aksik [14]
<span><span><span>Given <span>f(x) = 2x + 3</span><span> and </span><span>g(x) = –x2 + 5</span><span>, find </span></span><span>(<span> f</span> </span>o<span> f )(x</span><span>).</span></span><span>(<span> f</span> </span>o<span> <span>f </span>)(x) = f (<span> f</span> (x))</span><span> 
</span><span>    = f (2x + 3)</span><span> 
</span><span>    = 2(           ) + 3    </span>... setting up to insert the input<span> 
</span><span>    = 2(2x + 3) + 3</span><span> 
</span><span>    = 4x + 6 + 3</span><span> 
</span>    <span>= 4x + 9</span></span><span><span><span><span>Given </span><span>f(x) = 2x + 3</span><span> and </span><span>g(x) = –x2 + 5</span><span>, find </span></span><span>(g</span><span> o</span><span> g)(x</span><span>).</span></span><span>(g </span>o<span> g)(x) = g(g(x))</span><span> 
</span><span>    = –(             )2 + 5     </span>... setting up to insert the input<span> 
</span><span>    = –(–x2 + 5)2 + 5</span><span> 
</span><span>    = –(x4 – 10x2 + 25) + 5</span><span> 
</span><span>    = –x4 + 10x2 – 25 + 5</span><span> 
</span><span>    = </span><span>–x4 + 10x2 – 20</span></span>

Sometimes you have to be careful with the domain and range of the composite function.

<span><span><span>Given </span><span>f (x) = sqrt(x)</span><span> and </span><span>g(x) = x – 2</span><span>, find the domains of </span><span>(<span> f</span> </span>o<span> g)(x)</span><span> and </span><span>(g </span>o<span> f )(x)</span>.</span></span>
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3 years ago
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