Questions in mathematics

Questions in mathematics

📝 Answered - Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Slope $=-\frac{1}{3}$, passing through $(4,-6)$ Write an equation for the line in point-slope form. $\square$ (Simplify your answer. Use integers or fractions for any numbers in the equation.)

📝 Answered - Correcta perteneciente a cada literal. Observa la palabra que se forma. a) $\left[(2)^2\right]^{-1}$ P. 16 b) $\left\{\left[\left(\frac{122}{15}\right)^5\right]^0\right\}^{-3}=$ T. 2 c) $(0,9)^{15} \div(0,9)^{12}$ E. $\frac{1}{16^3}$ d) $[4]^2$ e) $\left[\frac{\left(4^2\right)^{-1}}{16^{-2}}\right]^{-3}$ s. $\left(\frac{9}{10}\right)^3$ 0. $\frac{5}{2}$

📝 Answered - What is $\frac{\sqrt{25 x^2 y^2}}{\sqrt{x y}}$ in simplest form? Assume $x \geq 0$ and $y \geq 0$. A. $5 \sqrt{x y}$ B. $25 \sqrt{x y}$ C. $\sqrt{5 x y}$ D. $5 x y \sqrt{x y}$

📝 Answered - A line is drawn through $(-4,3)$ and $(4,3)$. Which describes whether or not the line represents a direct variation? A. The line represents a direct variation because $-\frac{4}{3}=\frac{4}{3}$. B. The line represents a direct variation because it is horizontal. C. The line does not represent a direct variation because it does not go through the origin. D. The line does not represent a direct variation because $-4(3) \neq 4(3)$.

📝 Answered - Arrange the masses of fish 2.1 kg, 1.9 kg, 2.3 kg, and 1.7 kg in ascending order.

📝 Answered - 14. Find the remainder when [tex]x^3 - Px^2 + 6x - P[/tex] is divided by [tex]x - p[/tex]. 15. One of the zeros of the polynomial [tex]2x^2 + 7x - 4[/tex] is: (a) ... (b) ... (c) -[tex]\frac{1}{2}[/tex] (d) -2 16. Rationalize the denominator of [tex]\frac{1}{\sqrt{3} - \sqrt{2} - 1}[/tex]. 17. Find the square root of [tex]7 + 4\sqrt{3}[/tex]. 18. Factorize [tex](x^2 + 3x)^2 - 5(x^2 + 3x) - y(x^2 + 3x) + 5y[/tex]. 19. If [tex]x = \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}[/tex] and [tex]y = \frac{9}{\sqrt{3} - \sqrt{2}}[/tex], find [tex]x^2 + y^2 + xy[/tex]. 20. Find the value of [tex]x^3 + y^3 - 12xy + 64[/tex] when [tex]x + y = -4[/tex]. 21. If the polynomials [tex]az^2 + 4z^2 + 3z - 4[/tex] and [tex]z^3 - 4z[/tex] leave the same remainder when divided by [tex]z - 3[/tex], find the value of [tex]a[/tex]. 22. Without actual division, prove that [tex]2x^4 - 5x^3 + 2x^2 - x + 2[/tex] is divisible by [tex]x^2 - 3x + 2[/tex].

📝 Answered - Simplify using the order of operations. $\frac{6-(-2)(17)}{-4-2^2}=$

📝 Answered - Consider the DE \[\frac{d y}{d x}-\frac{2}{x} y=x^3 y^2, \quad x>0\] (a) Identify the type of DE and solve it. (b) Briefly state the domain of validity of your solution.

📝 Answered - Given that [tex]$\sin \theta=\frac{21}{29}$[/tex], what is the value of [tex]$\cos \theta$[/tex], for [tex]$0^{\circ}\ \textless \ \theta\ \textless \ 90^{\circ}$[/tex] ? A. [tex]$-\sqrt{\frac{20}{29}}$[/tex] B. [tex]$-\frac{20}{29}$[/tex] C. [tex]$\frac{20}{29}$[/tex] D. [tex]$\sqrt{\frac{20}{29}}$[/tex]

📝 Answered - Select all the correct answers. If the measure of angle [tex]$\theta$[/tex] is [tex]$\frac{11 \pi}{6}$[/tex], which statements are true? [tex]$\sin (\theta)=\frac{1}{2}$[/tex] [tex]$\tan (\theta)=1$[/tex] The measure of the reference angle is [tex]$60^{\circ}$[/tex] [tex]$\cos (\theta)=\frac{\sqrt{3}}{2}$[/tex] The measure of the reference angle is [tex]$30^{\circ}$[/tex] The measure of the reference angle is [tex]$45^{\circ}$[/tex]