Questions in mathematics

Questions in mathematics

📝 Answered - If [tex]$A =4 i -5 j +3 k , B =2 i -10 j -7 k$[/tex] and [tex]$C =5 i +7 j -4 k$[/tex], deduce the values of: i. [tex]$( A \times B ) \cdot C$[/tex] and [tex]$A \times( B \times C )$[/tex] ii. unit vectors perpendicular to [tex]$A$[/tex] and lying in the plane of [tex]$B$[/tex] and [tex]$C$[/tex].

📝 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 - A student observed the color and type of vehicle that passed by his school for an hour. The two-way table is given below: | | Red | Blue | White | Total | | :---- | :-- | :--- | :---- | :---- | | Car | 19 | 6 | 7 | 32 | | Truck | 8 | 16 | 9 | 33 | | SUV | 3 | 10 | 22 | 35 | | Total | 30 | 32 | 38 | 100 | What is the probability that a randomly selected vehicle from this observation is a car, given that it's blue? [tex]P(\text { Car } \mid \text { Blue })=[?] %[/tex] Round your answer to the nearest whole percent.

📝 Answered - Expressed as the simplest mixed number, $33 / 8$ is equal to? A. $3 \frac{5}{4}$ B. $3 \frac{9}{8}$ C. $4 \frac{1}{8}$ D. $4^{3 / 8}$

📝 Answered - Mike wants to fence in part of his backyard. He wants the length of the fenced-in area to be at least 20 feet long, [tex]$l \geq$[/tex] 20. He has 200 feet of fencing. The inequality that models the possible perimeter of the yard is [tex]$2 l+2 w \leq$[/tex] 200. Which are possible dimensions for Mike's backyard? Check all that apply. A. [tex]$w=50 ft ; l=10 ft$[/tex] B. [tex]$w=10 ft ; l=50 ft$[/tex] C. [tex]$w=20 ft ; l=60 ft$[/tex] D. [tex]$w=90 ft ; l=30 ft$[/tex] E. [tex]$w=50 ft ; l=40 ft$[/tex]

📝 Answered - Sketch the following polynomial function using the four-step process. [tex]f(x)=-x^5+6 x^4+36 x^3-216 x^2[/tex] The left-hand behavior starts $\square$ up and the right-hand behavior ends down. Find the [tex]y[/tex]-intercept. The [tex]y[/tex]-intercept is [tex]y=[/tex] $\square$ 0. The real zeros of the polynomial are [tex]x =[/tex] $\square$. (Use a comma to separate answers as needed. Type an exact answer, using radicals as needed.)

📝 Answered - Which is the correct first step in finding the area of the base of a cylinder with a volume of [tex]$140 \pi$[/tex] cubic meters and a height of 12 meters? A. [tex]$V=B h$[/tex] [tex]$12=B(140 \pi)$[/tex] B. [tex]$V=B h$[/tex] [tex]$V=140 \pi+(12)$[/tex] C. [tex]$V=B h$[/tex] [tex]$V=140 \pi(12)$[/tex] D. [tex]$V=B h$[/tex] [tex]$140 \pi=B(12)$[/tex]

📝 Answered - For the pair of functions [tex]f(x)=\sqrt{\frac{x+4}{x+6}}[/tex] and [tex]g(x)=\sqrt{x-8}[/tex] find the following. a. Find the functions [tex]f + g , f - g , fg[/tex], and [tex]\frac{ f }{ g }[/tex]. b. Determine the domain of the functions [tex]f + g , f - g , fg[/tex], and [tex]\frac{ f }{ g }[/tex]. a. [tex](f+g)(x)=\sqrt{\frac{x+4}{x+6}}+\sqrt{x-8}[/tex] (Do not simplify. Type an exact answer, using radicals as needed. Do not rationalize the denominator.) [tex](f-g)(x)=\sqrt{\frac{x+4}{x+6}}-\sqrt{x-8}[/tex] (Do not simplify. Type an exact answer, using radicals as needed. Do not rationalize the denominator.) [tex](f g)(x)=\sqrt{\frac{(x+4)(x-8)}{x+6}}[/tex] (Simplify your answer. Type an exact answer, using radicals as needed. Do not rationalize the denominator.) [tex]\left(\frac{f}{g}\right)(x)=[/tex] [tex]\square[/tex] (Simplify your answer. Type an exact answer, using radicals as needed. Do not rationalize the denominator.)

📝 Answered - Find the product. $\frac{7}{16} \times \frac{4}{49}$ Enter your simplified answer.

📝 Answered - Select the correct answer. In which direction must the graph of [tex]f(x)=7^x[/tex] be shifted to produce the graph of [tex]g(x)=7^x+7[/tex]? A. left B. down C. up D. right