Questions in mathematics

Questions in mathematics

📝 Answered - Which line is perpendicular to a line that has a slope of $-\frac{1}{3}$? line MN line $AB$ line EF line JK

📝 Answered - The sum of two positive integers, [tex]$x$[/tex] and [tex]$y$[/tex], is not more than 40. The difference of the two integers is at least 20. Haneece chooses [tex]$x$[/tex] as the larger number and uses the inequalities [tex]$y \leq 40-x$[/tex] and [tex]$y \leq x-20$[/tex] to determine the possible solutions. She determines that [tex]$x$[/tex] must be between 0 and 10 and [tex]$y$[/tex] must be between 20 and 40. Determine if Haneece found the correct solution. If not, state the correct solution. A. Yes, Chaneece found the correct solution. B. No, Chaneece mixed up the variables. The correct solution is that [tex]$x$[/tex] must be between 20 and 40 and [tex]$y$[/tex] must be between 0 and 10. C. No, Chaneece should not have restricted the solution to quadrant I. The correct solution is that [tex]$x$[/tex] can be all real numbers and [tex]$y$[/tex] must be less than 10. D. No, Chancece looked at the wrong area of the shaded graph. The correct solution is that [tex]$x$[/tex] must be between 0 and 30 and [tex]$y$[/tex] must be between 0 and 40.

📝 Answered - Solve the equation $x^2-16 x+54=0$ by completing the square. Fill in the values of $a$ and $b$ to complete the solutions.

📝 Answered - What are the $x$- and $y$-coordinates of point P on the directed line segment from $A$ to $B$ such that $P$ is $\frac{2}{3}$ the length of the line segment from $A$ to $B$? $x=\left(\frac{m}{m+n}\right)\left(x_2-x_1\right)+x_1$ $y=\left(\frac{m}{m+n}\right)\left(y_2-y_1\right)+y_1$ (2,-1) (4,-3) (-1,2) (3,-2)

📝 Answered - The equation $8(3 x-2)-4=8 x+4(4 x-3)$ has what type of solution set? A. Two-solution B. No solution C. One-solution D. Infinite

📝 Answered - Which of the following pairs are equivalent statements? A. [tex]$\log _b N=p$[/tex] and [tex]$b^p=N$[/tex] B. [tex]$N^{1 / b}=p$[/tex] and [tex]$b^p=N$[/tex] C. [tex]$\log _p N=b$[/tex] and [tex]$b^p=N$[/tex] D. [tex]$\log _N b=p$[/tex] and [tex]$b^p=N$[/tex]

📝 Answered - Rewrite the equation $3x - 5y = 30$ in slope-intercept form. A. $y=-\frac{3}{5}x+30$ B. $y=-\frac{5}{3}x-6$ C. $x=\frac{3}{3}y-6$ D. $=-\frac{3}{5}<-6$

📝 Answered - If [tex]u(x)=-2 x^2+3[/tex] and [tex]v(x)=\frac{1}{x}[/tex], what is the range of [tex](u \circ v)(x)[/tex] ? A. [tex](\frac{1}{3}, 0)[/tex] B. [tex](3, \infty)[/tex] C. [tex](-\infty, 3)[/tex] D. [tex](-\infty,+\infty)[/tex]

📝 Answered - If [tex]$f(x)$[/tex] and [tex]$f^{-1}(x)$[/tex] are inverse functions of each other and [tex]$f(x)=2 x+5$[/tex], what is [tex]$f^{-1}(8)$[/tex]?

📝 Answered - Factor the trinomial completely. $10 m^6 n+9 m^5 n^2+2 m^4 n^3$