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Karolina [17]
3 years ago
5

Point M is the midpoint of segment AB. AM=3x+40 and MB=x^2. Find x and AB

Mathematics
1 answer:
Nina [5.8K]3 years ago
5 0

\text{Hello there! :)}

x = 8\\\\AB = 128 \text{ units}

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

\text{Since Point M is the midpoint of AB, then:}\\\\AM = MB\\\\

\text{Set the two equations equal to each other:}\\\\3x + 40 = x^{2} \\\\

\text{Move all terms over to one side to simplify more easily:}\\\\0 = x^{2} - 3x - 40

\text{Factor by finding numbers that sum up to -3 and multiply into -40:}\\\\0 = (x - 8)(x + 5)\\\\x = -5, 8

\text{The length of a segment cannot be negative, so choose the positive solution:}\\\\x = 8

\text{Substitute in this value of x into either AM or MB to solve for AB:}

AB = 2(MB)\\\\AB = 2(x^{2} )\\\\AB = 2(8^{2})\\ \\AB = 2(64)\\\\AB = 128 \text{ units}

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<h3><u>Answer:</u></h3>

Hence, the sum of a 7-term geometric series is:

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<h3><u>Step-by-step explanation:</u></h3>

We have to find the sum of a 7-term geometric series (i.e. n=7) if the first term(a) is -6, the last term is -24,576, and the common ratio(r) is 4.

We know that the sum of the 7-term geometric series is given as:

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Hence, the sum of a 7-term geometric series is:

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