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Algebra Warmups

From cracking cryptograms to calculating the top speed of a rocket, algebra gives you tools to apply mathematical reasoning to a wide range of problems. Dive in and see what you already know!

Algebra Warmups: Level 2 Challenges

         

Evaluate the following expression:

\[123456789^{2} - (123456788 \times 123456790).\]

If you use a calculator whose precision is not strong enough to answer this question, then you will answer this problem incorrectly.

\[ \large\color{green} 6^{\color{blue} 6} + \color{green} 6^{\color{blue} 6} + \color{green} 6^{\color{blue} 6} + \color{green} 6^{\color{blue} 6} + \color{green} 6^{\color{blue} 6} + \color{green} 6^{\color{blue} 6} = \color{green}6^ {\color{brown}a} \]

If \(\color{brown} a\) satisfies the equation above, what is the value of \(\color{brown} a\)?

What is the value of

\[ \large \sqrt{1\text{%}}\, ? \]

\[ \large \frac { 1 }{ { 2 }^{ 3 } } +\frac { 1 }{ { 2 }^{ 6 } } +\frac { 1 }{ { 2 }^{ 9 } } + \cdots = \ ? \]

If 7 cows need 7 days to eat 7 grass fields, how many days would it take for 5 cows to eat 5 grass fields?

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