Questions in mathematics

Questions in mathematics

📝 Answered - Rationalize the denominator and simplify: [tex]$\frac{x}{x+\sqrt{3}}$[/tex]

📝 Answered - An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, $s$? A. $2 B. $6 C. $s<2$ or $s>18$ D. $s<6$ or $s>12.8$

📝 Answered - Which of the following is an odd function? $g(x)=x^2$ $g(x)=5 x-1$ $g(x)=3$ $g(x)=4 x$

📝 Answered - Jeremiah lives in New York City and takes a taxi almost everywhere he goes. In order to calculate the price of his taxi ride, Jeremiah came up with the equation [tex]$P=1.80\lceil x\rceil+2.50$[/tex], where [tex]$x$[/tex] is the number of miles or partial miles traveled in the taxi. Explain the meaning of the constant 2.50 as it relates to the situation. A. $2.50 is the base amount that Jeremiah must pay in order for the taxi to pick him up before he has been driven anywhere. B. $2.50 is the amount Jeremiah must pay as long as the taxi has not driven a complete mile. C. For every mile or partial mile the taxi drives, Jeremiah must pay an additional [tex]2.50[/tex]. D. Jeremiah must pay [tex]2.50[/tex] plus [tex]1.80[/tex], or [tex]4.30[/tex], per mile for each taxi ride.

📝 Answered - Evaluate the following limit using L'Hopital's rule. [tex]\lim _{x \rightarrow 0} \frac{\sqrt{x+1}-\left(\frac{x}{2}+1\right)}{x^2}=-\frac{[?]}{[]}[/tex]

📝 Answered - The volume of a rectangular prism is $(x^3-3 x^2+5 x-3)$, and the area of its base is $(x^2-2)$. If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism? A. $x-3+\frac{7 x-9}{x^2-2}$ B. $x-3+\frac{7 x-9}{x^3-3 x^2+5 x-3}$ C. $x-3+\frac{7 x+3}{x^2-2}$ D. $x-3+\frac{7 x+3}{x^3-3 x^2+5 x-3}$

📝 Answered - Simplify the complex fraction. $\frac{\frac{16 c^4 d^3}{7 c}}{\frac{4 c d^4}{d^2}}$

📝 Answered - The table below shows the average value of houses in Wilshire Woods over a period of 5 years. The equation [tex]f(x)=20,000 \cdot 3^x[/tex] describes the curve of best fit for the average value of houses [tex]f(x)[/tex]. Let [tex]x[/tex] represent the number of years since 2000, so [tex]x=0[/tex] in 2000. | Year | Average Home Value | | --- | --- | | 2000 | $19,000 | | 2001 | $60,000 | | 2002 | $182,000 | | 2003 | $540,000 | | 2004 | $1,621,000 | Using the equation for the curve of best fit, what will be the average home value in Wilshire Woods in 2005? A. $36,450,000 B. $12,154,000 C. $4,860,000 D. $750,000

📝 Answered - Find the quotient. $14 \overline{)154}$

📝 Answered - Find the $y$-intercept and $x$-intercept of the line. $-3 x+7 y=8$ $y$-intercept: $\square$ $x$-intercept: $\square$