Answer:
The southern lighthouse is 3.4 miles closer than the northern lighthouse
Step-by-step explanation:
From the figure we see that we need to find the distances AK and BK.
The measure of the third angle K is = 180- 25-35= 120 degrees
Using the sine ratios we can find the two distances
From the figure
The northern distance is given by
20/ sin 120 = kA/ sine 35
KA= 20 sine 35/ sine 120
KA= 13.25 miles
The southern distance is given by
20 /sine 120= KB / sine 25
20 sine 25/ sine 120 = KB
KB= 9.759=9.76 miles
Difference between the two miles =
13.25 miles - 9.76 miles = 3.49 miles
The southern lighthouse is 3.4 miles closer than the northern lighthouse
Option C is correct
One third of the box will be 3 inches long, so is equivalent to a 3-inch cube. It has a volume of
... (3 in)³ = 27 in³
The appropriate choice is ...
... D. 27 cu. in.
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Volume is found by multiplying length by width by height. When all are the same (3 in), the product is (3 in)·(3 in)·(3 in) = (3 in)³.
Answer: x = "-1 " ; <u>and</u>: "(1 ± √3) / 2" .
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Explanation:
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Given: 3x³ − 2x + 1 = 0 ; Find "x" ;
Factor: "3x³ − 2x + 1" ;
3x³ − 2x + 1 = (3x² <span>− 3x + 1)(x + 1) ;
Now, set the equation equal to "0" (zero);
</span> (3x² − 3x + 1)(x + 1) = 0 ;
x = 0 ; when:
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(x + 1) = 0 ; and/or: when:
(3x² − 3x + 1) = 0 ;
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Start with "x + 1 = 0" ;
Subtract "1" from each side of the equation ; to isolate "x" on one side of the <span>equation ; and</span> to solve for "x" ;
x + 1 − 1 = 0 − 1 ;
x = -1 ;
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Now, try:
3x² − 3x + 1 = 0 ;
Since: "3x² − 3x + 1 " cannot be factored; and since:
"3x² − 3x + 1 = 0" ; is written in the "quadratic equation format"; that is:
"ax² + bx + c = 0 ; a ≠ 0; We can use the "quadratic equation formula" to solve for "x" ;
in which "a = 3" ;
"b = -3" ;
"c = 1" ;
The quadratic equation formula is:
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x = [-b ± √(b²−4ac] / 2a ;
= ? (Let us plug in our known values for "a, b, & c"l
x = { [-(-3] ± [√[(-3²) − (4*3*1)] } / {2* 3} ;
x = [3 ± √(9 − 12)] / 6
x = [3 ± √(-3 )] / 6 ;
x = (1 ± √3) / 2 .
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So, the answers are: x = " -1 " ; and: "</span>(1 ± √3) / 2 " .
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