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Questions in mathematics

[Done] Consider the quadratic function: [tex]f(x)=x^2-a x-0[/tex] Vertex: [tex]\left(\frac{-b}{2 a}, f\left(\frac{-b}{2 a}\right)\right)[/tex] What is the vertex of the function?

[Done] Solve for $y$. $ \begin{array}{l} y+4=3(x+5) \\ y=[?] x+\square \end{array} $

[Done] What is the lowest common denominator of $\frac{x-5}{x^2-1}-1=-\frac{2 x}{x-1}$? A. $x^2+1$ B. $x^3+1$ C. $x^3-x^2-x+1$ D. $x^2-1$

[Done] Which statement describes how the graph of the given polynomial would change if the term [tex]$2 x^5$[/tex] is added? [tex]$y=8 x^4-2 x^3+5$[/tex] A. Both ends of the graph will approach negative infinity. B. The ends of the graph will extend in opposite directions. C. Both ends of the graph will approach positive infinity. D. The ends of the graph will approach zero.

[Done] The equation $h=7 \sin \left(\frac{\pi}{21} t\right)+28$ can be used to model the height, $h$, in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, $t$, in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at $t=0$, and that the windmill turns counterclockwise at a constant rate. A. 7 feet B. 14 feet C. 21 feet D. 28 feet

[Done] Use long division to find the quotient below. $\left(4 x^2-7 x-2\right)-(x-2)$ A. $4 x+1$ B. $3 x+1$ C. $4 x-1$ D. $3 x-1$

[Done] Which of the following is the graph of [tex]y=-2 \cdot 3^{5-x}[/tex]? A. (Image of graph) B. (Image of graph) C. (Image of graph)

[Done] Which equation has the solutions [tex]x=\frac{-3 \pm \sqrt{3} i}{2}[/tex]? A. [tex]x^2+3 x+3=0[/tex] B. [tex]2 x^2+6 x+9=0[/tex] C. [tex]2 x^2+6 x+3=0[/tex] D. [tex]x^2+3 x+12=0[/tex]

[Done] Survey of 9th and 10th Graders with Siblings | | Has a Sibling | Does Not Have a Sibling | Total | | :-------------------- | :------------ | :---------------------- | :---- | | 9th Graders | 64 | 17 | 81 | | 10th Graders | 52 | 23 | 75 | | Total | 116 | 40 | 156 | Which statements are correct about the two-way frequency table? Check all that apply. A. The survey represents quantitative data. B. There is a greater percentage of 10th graders who do not have a sibling than 9th graders who do not have a sibling. C. The total number of students in the poll who have a sibling is 116. D. Fifty-two 10th graders were polled. E. More 9th graders were polled than 10th graders.

[Done] Solve the equation using square roots. Select the solution(s). [tex](x+3)^2=0[/tex]