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2 years ago

Factor completely, show work. x² - 49

Mathematics

1 answer:

Elan Coil [88]2 years ago

4 0

You want to pull out the square roots of each term since they are both perfect squares.

Factor using the difference of squares formula: a2-b2=(a+b)(a-b)

This formula allows the middle term to cancel out.

=x2 - 49

=(x + 7)(x - 7)

ANSWER: (x + 7)(x - 7)

Hope this helps! :)

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3 years ago

Bill has 4 times as much money as Ted. If Ted spends $100 and Ted spends 75, Bill will have 5 times as much money as ted. How mu

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<h3><u>Question:</u></h3>

Bill has four times as much money as Ted. If Ted spends $100 and Bill spends $75, Bill will have five times as much money as Ted. How much money do Bill and Ted have before and after spending money?

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

Before spending money, Bill has $1700 and Ted has $425

After spending money, Bill has $ 1625 and Ted has $ 325

<h3><u>Solution:</u></h3>

Let the amount of money Bill has be "b"

Let the amount of money Ted has be "t"

Bill has 4 times as much money as Ted, we can say the following:

b = 4t ---------- eqn 1

If Ted spends $100 and Ted spends 75, Bill will have 5 times as much money as ted.

b - 75 = 5 ( t - 100 ) ----- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

4t - 75 = 5( t - 100 )

4t - 75 = 5t - 500

5t - 4t = 500 - 75

From eqn 1,

b = 4(425) = 1700

So, before spending money, Bill has $1700 and Ted has $425.

<u><em>After spending money:</em></u>

Bill = b - 75 = 1700 - 75 = $ 1625

Ted = t - 100 = 425 - 100 = $ 325

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