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Questions in mathematics

[Done] Select the correct answer. Which expression is equivalent to the given expression? $3 x^2+5 x-7\left(x^2+4\right)$ A. $-4 x^2+5 x-4$ B. $x^2+28$ C. $x^2+4$ D. $-4 x^2+5 x-28$

[Done] Select the correct answer. Which equation is equivalent to the given equation? [tex]$x^2-6 x=8$[/tex] A. [tex]$(x-3)^2=17$[/tex] B. [tex]$(x-6)^2=20$[/tex] C. [tex]$(x-6)^2=44$[/tex] D. [tex]$(x-3)^2=14$[/tex]

[Done] Which of the following represents the factorization of the trinomial below? [tex]$-3 x^3-18 x^2-24 x$[/tex] A. [tex]$-3 x(x-2)(x-4)$[/tex] B. [tex]$-3 x(x+2)(x+4)$[/tex] C. [tex]$-3(x^2+2)(x+4)$[/tex] D. [tex]$-3(x^2-2)(x-4)$[/tex]

[Done] Select the correct answer. $\triangle A B C$ with vertices $A(-3,0), B(-2,3), C(-1,1)$ is rotated $180^{\circ}$ clockwise about the origin. It is then reflected across the line $y=-x$. What are the coordinates of the vertices of the image? A. $A^{\prime}(0,3), B^{\prime}(2,3), C(1,1)$ B. $A^{\prime}(0,-3), B^{\prime}(3,-2), C^{\prime}(1,-1)$ C. $A^{\prime}(-3,0), B^{\prime}(-3,2), C(-1,1)$ D. $\left.A^{\prime}(0,-3), B^{\prime}(-2,-3), C^{\prime}-1,-1\right)$

[Done] \begin{array}{l}-5 x+1 y=-3 \\ 3 x-8 y=24\end{array}

[Done] The average score for games played in the NFL is 21.2 and the standard deviation is 9 points. 48 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of [tex]$\bar{x} \sim N($[/tex] [tex]$\square$[/tex] , [tex]$\square$[/tex] ) b. What is the distribution of [tex]$\qquad x ? \sum x \sim N($[/tex] [tex]$\square$[/tex] , [tex]$\square$[/tex] ) c. [tex]$P (\bar{x}\ \textgreater \ 19.6515)= \square$[/tex] d. Find the 68th percentile for the mean score for this sample size. [tex]$\square$[/tex] e. [tex]$P (19.5515\ \textless \ \bar{x}\ \textless \ 22.5495)= \square$[/tex] f. Q1 for the [tex]$\bar{x}$[/tex] distribution [tex]$= \square$[/tex] g. [tex]$P \left(\sum x\ \textgreater \ 996.072\right)= \square$[/tex] h. For part c) and e), is the assumption of normal necessary? Yes No

[Done] What is the value of [tex]$x$[/tex] in the equation [tex]$2x + 3y = 36$[/tex], when [tex]$y = 6$[/tex]?

[Done] Jada solved the equation $-\frac{4}{9}=\frac{x}{108}$ for $x$ using the steps below. What was Jada's error? $\begin{aligned} -\frac{4}{9} & =\frac{x}{108} \\ -\frac{4}{9}\left(-\frac{9}{4}\right) & =\frac{x}{108}\left(-\frac{9}{4}\right) \\ x & =-\frac{1}{48} \end{aligned}$ A. Jada should have multiplied both sides of the equation by 108. B. Jada should have multiplied both sides of the equation by $-\frac{4}{9}$. C. The product of $-\frac{9}{4}$ and $\frac{1}{108}$ is not equal to $-\frac{1}{48}$.

[Done] A department store holds a year-end clearance sale that includes a 9.1% discount on cosmetics. Find the sale price of a bottle of perfume if its original price was $71.29.

[Done] 1) $A, B, C, D$ are points on a circle centered at $0$. $\angle ADB = 57$ and $\angle BCD = 10$. Consider the function defined on a set of numbers by $h(x) = -7px^2 + 9x - 2$. If $h(i) \Rightarrow$ card $\#(\frac{5}{2}x) = 10$, find: i) the value of $p$ and $q$ ii) the zeros of $h(x)$ iii) the points $p(60^{\circ}N, 35^{\circ}E)$ and $q(600NH8)$ lie on the surface of the earth. Illustrate the information.