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Home Question Bank Math Algebra Archive 2024 December 21

Algebra Questions from Dec 21,2024

Browse the Algebra Q&A Archive for Dec 21,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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(2) If \( 2^{x-4}=\frac{1}{16} \), then \( x=\ldots \) \( \begin{array}{llll}\text { (a) } 0 & \text { (b) } \frac{1}{4} & \text { (c) } \frac{1}{3} & \text { (d) } \frac{1}{2}\end{array} \) (2) Henry has 50 apples. He gives 4 apples each to \( f \) friends. What is the difference in the expression \( 50-4 f \) ? What does the difference represent? A unicorn daycare center requires there to be 2 supervisors for every 18 baby unicorns. Write an equation that shows the relationship between \( n \), the number of supervisors, and \( u \), the number of baby unicorns. Please note that this is a magical daycare center, so fractional supervisors are allowed. We can calculate the depth \( d \) of snow, in centimeters, that accumulates in Harper's yard during the first \( h \) hours of a snowstorm using the equation \( d=5 h \). How many hours does it take for 1 centimeter of snow to accumulate in Harper's yard? How many centimeters of snow accumulate per hour? Set 4 Interpret Algebraic Expressions in Real-World Problems Identify and interpret the parts of each expression. 1) A pen costs \( \$ 2.50 \). The expression \( 4 n+2.50 \) represents the cost of buying 4 notebooks and a pen. What is the product in the expression? What does the product represent? 2) Henry has 50 apples. He gives 4 apples each to \( f \) friends. What is the difference in the expression \( 50-4 f \) ? What does the difference represent? 3) The number of roses and daisies in 5 bouquets is \( 5(r+d) \). What is the sum in the expression? What does the sum represent? Airplane A travels 2400 km at a certain speed. Plane B travels 1800 km at a speed \( 50 \mathrm{~km} / \mathrm{h} \) faster than Plane A in 2 hours less time. Find the speed of each plane. Solve the formula \( W=2 \sqrt{\frac{1}{L C}} \) for \( C \) Solve the formula \( A=L^{2}+2 R \) for \( L \) Look at this set of ordered pairs: \[ \begin{array}{l}(15,9) \\ (12,14) \\ (5,7) \\ (-2,-13)\end{array} \] Is this relation a function? Solve the equation \( 6^{2 x-1}=2^{3 x+1} \)
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