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Questions in mathematics

📝 Answered - What is the $y$-value of the vertex of the function $f(x)=-(x-3)(x+11)$?

📝 Answered - Select all the correct answers. The slope-intercept form of a line is $y=m x+b$, where $m$ is the slope and $b$ is the $y$-intercept. If Shawn knows that the slope of the line is 4 and the line passes through the point $(1,-8)$, which equation should he use to find the $y$-Intercept and what is the $y$-intercept of the line? A. $b=y+m x$ B. $b=y-m x$ C. $b=\frac{y-m}{z}$ D. $b=-12$ E. $b=-4$ F. $b=2

📝 Answered - What is the center of a circle represented by the equation $(x+9)^2+(y-6)^2=10^2$? A. $(-9,6)$ B. $(-6,9)$ C. $(6,-9)$ D. $(9,-6)$

📝 Answered - Let $Z \sim N(0,1)$. Find $P(-1.96 < Z < 1.96)$.

📝 Answered - Read all questions carefully and understand. Question 1: Use grouping symbols to factorise the following: A. [tex]x^3-2 x^2-16 x+32[/tex]

📝 Answered - [tex]$5 x^2-2\left(x-3 x^2\right)$[/tex]

📝 Answered - If $x=3$ and $y=-1$, evaluate $2(x^2-y^3)$

📝 Answered - Which formula can be used to describe the sequence? $-\frac{2}{3},-4,-24,-144 \ldots$ A. $f(x)=6\left(-\frac{2}{3}\right)^{x-1}$ B. $f(x)=-6 \frac{2}{3}$ C. $f(x)=-\frac{2}{3}(6)^{x-1}$ D. $f(x)=\frac{2}{3} f-9,4$

📝 Answered - Mavis decided to tile the living room using marble tiles. The dimensions of the tiles are given below: | Tile type | Length | Width | | ----------- | --------- | -------- | | Rectangular | 900 mm | 0.5 m | | Square | 0.5 m | 0.5 m | Use the table above to answer the questions that follow. 4.3.1 Mavis claims that she will need a minimum of 30 rectangular tiles to tile the living room only. Verify, showing ALL calculations, whether her statement is valid. 4.3.2 It takes tilers 45 minutes to lay 15 tiles and 25 minutes to grout the whole living room. Mavis claims that the tilers will finish tiling the living room at 9:28 if they started at 8:15 in the morning. Verify, showing ALL calculations, whether her statement is valid.

📝 Answered - Find the average rate of change of the function over the given intervals. [tex]f(x)=10 x^3+10[/tex]; a) [tex][2,4][/tex], b) [tex][-5,5][/tex] a) The average rate of change of the function [tex]f(x)=10 x^3+10[/tex] over the interval [tex][2,4][/tex] is ____. (Simplify your answer.)