What is x squared plus six x minus twenty seven =0

1 answer:

8 0

$x^2+6x-27=0\\\\x^2-3x+9x-27=0\\\\x\big(x-3\big)+9\big(x-3\big)=0\\\\\big(x+9\big)\big(x-3\big)=0\\\\\\x+9=0\qquad\vee\qquad x-3=0\\\\\boxed{x=-9\qquad\vee\qquad x=3}$

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Two lighthouses are located 60 miles from one another on a north-south line. If a boat is spotted S 21o E from the northern ligh

jasenka [17]

Answer:

(A)The northern lighthouse is 8.2 miles closer than the southern lighthouse.

Step-by-step explanation:

The triangle attached represents the given problem.

First, let us determine the distance of the Boat from each of the lighthouse.

In Triangle ABC,

∠A+∠B+∠C=180 degrees

21+∠B+16=180

∠B=180-37=143 degrees.

Using Law of Sines

$\frac{a}{Sin A}=\frac{b}{Sin B}\\\frac{a}{Sin 21^0}=\frac{60}{Sin 143^0} \\\text{Cross Multiply}\\a*sin143=60*sin21\\a=60*sin21\div sin143\\a=35.73 miles$

Similarly

$\frac{c}{Sin C}=\frac{b}{Sin B}\\\frac{c}{Sin 16^0}=\frac{60}{Sin 143^0} \\\text{Cross Multiply}\\c*sin143=60*sin16\\c=60*sin16\div sin143\\c=27.48 miles$