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Norma-Jean [14]
3 years ago
8

12 points! The interior angles formed by the sides of a hexagon have measures that some to 720°. What is the measure of angle F?

Mathematics
1 answer:
statuscvo [17]3 years ago
8 0
Sum would be equal to 720.
so, x-60 + x-40 + 130 + 120 + 110 + x-20 = 720
3x + 240 = 720
3x = 720 - 240
x = 480/3
x = 160 

Angle F = x-20 = 160 - 20 = 140

In short, Your Answer would be 140

Hope this helps!

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What is the exact solution to the equation 2^2x=5^x−1 ?
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2^2x=5^x−1

Take the log pf both sides:

ln(2^2x) = ln(5^x-1)

Expand the logs by pulling the exponents out:

2xln(2) = (x-1)ln(5)

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Write an<br> explicit formula for An, the nth term of the sequence 7, -42, 252, ....
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Answer:

A_n = 7(-6)^{n-1}

Step-by-step explanation:

<u>Key skills needed: Explicit formula, Geometric sequence</u>

1) This is a geometric sequence, meaning a constant (like 6 or 3.5) is being multiplied to every term. First we need to find the constant.

This can be done by doing -42 ÷ 7   or   252 ÷ -42

-42 ÷ 7 equals -6.

252 ÷ -42 also equals -6.

2) This means that constant is -6.

3) The general form for an explicit formula of a geometric sequence is:

a_n = a_1(r)^{n-1}

--> r means the constant (or common ratio) that is being multiplied.

--> a_1 means the first term

--> a_n means the "nth" numbered term (so a_3 is the 3rd term, a_{10} is the 10th term and so on).

--> n-1 is just the "n" in a_n minus 1.

4) We can use this formula to create an explicit formula for the geometric sequence in the problem.

--> r = -6 (Since we got -6 as the constant/common ratio).

--> a_1  = 7 (Since 7 is the 1st term)

This means that our formula would be --> A_n = 7(-6)^{n-1}

<em>Hope you understood and have a nice day!! :D</em>

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