Express 80 as a product of prime factors using index notation

Mathematics

1 answer:

hammer [34]3 years ago

4 0

80 = 2 x 2 x 2 x 2 x 5
80 = 2 ^4 x 5

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Lucy has two star systems left to visit on her voyage, but her ship is running low on fuel. The first system, KA-77, is 12001200

-Dominant- [34]

Answer:

1348 light years.

Step-by-step explanation:

Please find the attachment.

Let x represent the distance between KA-7 and KA-11.

We have been given that the first system, KA-7, is 1200 light years away while the second system, KA-11, is 1700 light years away. Lucy sees an angle of 52 degrees between KA-7 and KA-11.

We can see from our attachment that Lucy, KA-7 and KA-11 forms a triangle and we will use law of cosines to solve for x.

$(AB)^2=(AC)^2+(BC)^2-2(AC)(BC)*cos (C)$

Upon substituting our given values in above formula we will get,

$x^2=1200^2+1700^2-2*1200*1700*cos (52^o)$

$x^2=1440000+2890000-4080000*0.615661475$

$x^2=4330000-2511898.81933008$

$x^2=1818101.18066992$

Let us take square root of both sides of our equation.

$x=\sqrt{1818101.18066992}$

$x=1348.3698234\approx 1348$

Therefore, KA-7 and KA-11 are approximately 1348 light years apart.

6 0

2 years ago

What does the left side of the equal<br> sign simplify to?

polet [3.4K]

Answer:

Step-by-step explanation:

An expression is a mathematical statement that does not contain an equal sign. It cannot be solved for unless the value of the variable is given. An equation is a mathematical statement or sentence comprised of two equalities or expressions joined with an equal sign.

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3 years ago

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1. What is the last step in constructing an angle?<br> Help please<br> For 30 points!!!

zaharov [31]

Answer:

The second choice. Connect the endpoint and the mark at the angle measure.

Step-by-step explanation:

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