Questions in mathematics

Questions in mathematics

📝 Answered - Susan's science class is performing an experiment that involves dropping objects from various heights, starting close to the ground and working upward to 8 feet. The function [tex]$t(x)=\frac{1}{4} \sqrt{x}$[/tex], where [tex]$x$[/tex] represents the distance from the ground, represents the time it takes for the object Susan drops to hit the ground. The graph represents the function [tex]$t(x)=\frac{1}{4} \sqrt{x}$[/tex]. Identify some of the key features of the graph. That is, determine if the function is monotonically increasing or decreasing, state the end behavior, find the [tex]$x$[/tex]- and [tex]$y$[/tex]-intercepts, find the maximum or minimum, and state the domain and the range of the graph (without considering the context).

📝 Answered - What is the inverse of the function [tex]f(x)=x+3[/tex]?

📝 Answered - How many boxes will fit along the height of the shipping crate? | | Storage Crate Size | Box Dimensions | | :----- | :----------------- | :------------- | | Width | 10 feet | 8 inches | | Height | 10 feet | 8 inches | | Length | 15 feet | 10 inches |

📝 Answered - What is the domain of [tex]f(x)=5^x-7[/tex]? A. [tex] \{x \mid x\ \textgreater \ -7\} [/tex] B. [tex] \{x \mid x\ \textless \ -7\} [/tex] C. [tex] \{x \mid x\ \textgreater \ 0\} [/tex] D. [tex] \{x \mid x \text{ is a real number }\} [/tex]

📝 Answered - What is $64-9 x^2$ in factored form?

📝 Answered - The function $f(x)=1200(0.8)^x$ represents the possible elk population of a national park $x$ years from now. What is the current population of elk at the park? A. 960 B. 768 C. 1500 D. 1200

📝 Answered - The first step for deriving the quadratic formula from the quadratic equation, $0=a x^2+b x+c$, is shown. Step 1: $-c=a x^2+b x$ Which best explains or justifies Step 1? A. subtraction property of equality B. completing the square C. factoring out the constant D. zero property of multiplication

📝 Answered - Match each quadratic equation with its solution set. [tex]2 x^2-10 x-3=0[/tex] [tex]2 x^2-9 x+6=0[/tex] [tex]2 x^2-8 x+5=0[/tex] [tex]2 x^2-9 x-1=0[/tex] [tex]2 x^2-8 x-3=0[/tex] [tex]\frac{9 \pm \sqrt{33}}{4}[/tex] [tex]\frac{4 \pm \sqrt{6}}{2}[/tex] [tex]\frac{9 \pm \sqrt{89}}{4}[/tex] [tex]\frac{4 \pm \sqrt{22}}{2}[/tex]

📝 Answered - Solve the system of equations: [tex] \begin{array}{l} y=6 x-27 \\ y=4 x-17 \end{array} [/tex] a. $(-5,3)$ b. $(-3,-5)$ c. $(5,3)$ d. No solution

📝 Answered - The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model [tex]$h$[/tex], the height in feet of the end of one blade, as a function of time, [tex]$t$[/tex], in seconds? Assume that the blade is pointing to the right, parallel to the ground at [tex]$t=0$[/tex] seconds, and that the windmill turns counterclockwise at a constant rate. A. [tex]$h=-10 \sin \left(\frac{\pi}{15} t\right)+35$[/tex] B. [tex]$h=-10 \sin (\pi t)+35$[/tex] C. [tex]$h=10 \sin \left(\frac{\pi}{15} t\right)+35$[/tex] D. [tex]$h=10 \sin (\pi t)+35$[/tex]