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Questions in mathematics

📝 Answered - Complete the square and write the equation of the circle in standard form. Then find the center and radius of the circle and graph the equation. [tex]x^2+y^2+9 x-10 y-5=0[/tex] The equation in standard form is [tex]\left(x+\frac{9}{2}\right)^2+(y-5)^2=\frac{201}{4}[/tex]. (Simplify your answer.) The center is [tex]\left(-\frac{9}{2}, 5\right)[/tex]. (Type an ordered pair. Simplify your answer.) The radius is [tex]$\frac{\sqrt{201}}{2}[/tex]. (Simplify your answer.) Choose the correct graph of the circle. A. B. C. D.

📝 Answered - Which equation has the steepest graph? A. [tex]$y=\frac{3}{4} x-9$[/tex] B. [tex]$y=-14 x+1$[/tex] C. [tex]$y=2 x+8$[/tex] D. [tex]$y=10 x-5$[/tex]

📝 Answered - Which must be true of a quadratic function whose vertex is the same as its $y$-intercept? A. The axis of symmetry for the function is $x=0$. B. The axis of symmetry for the function is $y=0$. C. The function has no $x$-intercepts. D. The function has $1 x$-intercept.

📝 Answered - The volume of a cylinder is the base (B) times the length of its height ($h$). Which of the following is the formula for the volume of a cylinder? A. $V=\frac{1}{2} B h$ B. $V=-B h$ C. $V=2 B w$ D. $V=B h$

📝 Answered - Graph the set \{x \mid x<-5\} on the number line. Then, write the set using interval notation.

📝 Answered - Which factor do $9 x^2-12 x+4$ and $9 x^2-4$ have in common? A. $3 x+4$ B. $3 x+2$ C. $9 x^2$ D. $3 x-2$

📝 Answered - Factor the polynomial $2 x^2+7 x+6$.

📝 Answered - Locate the critical points of the following function. Then use the Second Derivative Test to determine whether they correspond to local maxima, local minima, or neither. [tex]f(x)=x^3-13 x^2-9 x[/tex] Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The critical point(s) [tex]x=[/tex] correspond to local minima and the critical point(s) [tex]x=[/tex] correspond to local maxima. The test may be inconclusive at some critical points. (Simplify your answers. Use a comma to separate answers as needed.) B. There are no critical points. C. The critical points are located at [tex]x=[/tex] . There are no local minima nor maxima or the test is inconclusive. (Simplify your answer. Use a comma to separate answers as needed.) D. The critical point(s) [tex]x=[/tex] correspond to local minima. There are no local maxima or the test is inconclusive. (Simplify your answer. Use a comma to separate answers as needed.) E. The critical point(s) [tex]x=[/tex] correspond to local maxima. There are no local minima or the test is inconclusive. (Simplify your answer. Use a comma to separate answers as needed.)

📝 Answered - Which of the following statements completely describes the solution set for [tex]8(x-13)=8 x-104[/tex]? A. There is no solution for x B. [tex]x=13[/tex] C. [tex]x=0[/tex] only D. All real numbers are solutions for x E. [tex]x=8[/tex] only

📝 Answered - Check the definition below. Present another real-life situation to explain the meaning of functions. - The area [tex]$A$[/tex] of a circle depends on the radius [tex]$r$[/tex] of the circle. The rule that connects [tex]$r$[/tex] and [tex]$A$[/tex] is given by the equation [tex]$A=\pi r^2$[/tex]. With each positive number [tex]$r$[/tex] there is associated one value of [tex]$A$[/tex], and we say that [tex]$A$[/tex] is a function of [tex]$r$[/tex].