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5 7 \[ \left(x^{2} y-3 y^{2}+5 x y^{2}\right)-\left(-x^{2} y+3 x y^{2}-3 y^{2}\right) \] Which of the following is equivalent to the expression above? A) \( 4 x^{2} y^{2} \) B) \( 8 x y^{2}-6 y^{2} \) C) \( 2 x^{2} y+2 x y^{2} \) D) \( 2 x^{2} y+8 x y^{2}-6 y^{2} \) 6 \[ h=3 a+28.6 \] A pediatrician uses the model above to estimate the height \( h \) of a boy, in inches, in terms of the boy's age \( a \), in years, between the ages of 2 and 5 . Based on the model, what is the estimated increase, in inches, of a boy's height each year? A) 3 B) 5.7 C) 9.5 D) 14.3 \[ m=\frac{\left(\frac{r}{1,200}\right)\left(1+\frac{r}{1,200}\right)^{N}}{\left(1+\frac{r}{1,200}\right)^{N}-1} P \] The formula above gives the monthly payment \( m \) needed to pay off a loan of \( P \) dollars at \( r \) percent annual interest over \( N \) months. Which of the following gives \( P \) in terms of \( m, r \), and \( N \) ? A) \( P=\frac{\left(\frac{r}{1,200}\right)\left(1+\frac{r}{1,200}\right)^{N}}{\left(1+\frac{r}{1,200}\right)^{N}-1} m \) B) \( P=\frac{\left(1+\frac{r}{1,200}\right)^{N}-1}{\left(\frac{r}{1,200}\right)\left(1+\frac{r}{1,200}\right)^{N}} m \) C) \( P=\left(\frac{r}{1,200}\right) m \) D) \( P=\left(\frac{1,200}{r}\right) m \)

Ask by Brooks Williams. in the United Arab Emirates
Mar 11,2025

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1. The simplified expression is \(2x^{2}y + 2xy^{2}\). 2. The estimated increase in height each year is 3 inches. 3. The formula for \(P\) in terms of \(m\), \(r\), and \(N\) is: \[ P=\frac{\left(1+\frac{r}{1,200}\right)^{N}-1}{\left(\frac{r}{1,200}\right)\left(1+\frac{r}{1,200}\right)^{N}}\,m. \]

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Beyond the Answer

To solve the expression \(\left(x^{2} y-3 y^{2}+5 x y^{2}\right)-\left(-x^{2} y+3 x y^{2}-3 y^{2}\right)\), start by distributing the negative sign and combining like terms. You’ll find that the terms simplify beautifully, revealing a match to one of the options listed. Remember, factoring and combining can often unveil hidden relationships in polynomial expressions! When analyzing the height estimation formula \(h=3 a+28.6\), it's clear that the coefficient of \(a\) reveals the rate of height increase. Since the coefficient is 3, this means the boy is projected to grow an estimated 3 inches each year from ages 2 to 5. Understanding linear relationships often simplifies growth predictions in real-life scenarios!

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