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Questions in mathematics

📝 Answered - If \( x = 2 - 2^{\frac{1}{3}} + 2^{\frac{2}{3}} \), find the value of \( x^3 - 6x^2 + 18x + 18 \). (a) 22 (b) 33 (c) 40 (d) 45

📝 Answered - Which of the following can be the total number of the five types of animals together present in the given five reserved forests? 1. The number of Rhinos present in JNP, PWS, NNP, MNP, and KNP are in the ratio 1:2:11:17:23 in that order. This is true for any of the other four animals. 2. If we randomly select any one of these five reserve forests, the ratio of the number of Rhino, Leopard, Gibbon, Sambar, and Wild Pigs in that order is 1:2:11:17:23. Options: 65068 66068 67068 68068

📝 Answered - In a row of people, Rathna is 16th from the left end. Rathna is ninth to the left of Amrinder who is fourth to the right of Mahendran who is 24th from the right end. Then, how many people are there in the row? (a) 43 (b) 42 (c) 20 (d) 44

📝 Answered - Solve this system of equations: [tex]\begin{array}{l} y=x^2-3 x+12 \\ y=-2 x+14 \end{array}[/tex] What are the solutions of the system of equations? One solution is (-1, ). The second solution (2, ). Substitute the values of [tex]x[/tex], -1 and 2, into either original equation to solve for the values of [tex]y[/tex].

📝 Answered - Select the correct answer. Cole's age is 3 years less than his sister Tina's age, [tex]$t$[/tex]. If Cole is 18, which equation represents this situation, and how old is Tina? A. The equation that represents this situation is [tex]$t-3=18$[/tex]. Tina is 21. B. The equation that represents this situation is [tex]$t+3=18$[/tex]. Tina is 15. C. The equation that represents this situation is [tex]$3-t=18$[/tex]. Tina is 21. D. The equation that represents this situation is [tex]$-3-t=18$[/tex]. Tina is 15.

📝 Answered - $\frac{4}{x+16}-\frac{3}{x-16}=\frac{5 x}{x^2-256}$ a. Write the value or values of the variable that make a denominator zero. $x = \square$ -16,16 (Use a comma to separate answers as needed.) b. What is the solution of the equation? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\{-4\}$. (Use a comma to separate answers as needed.) $\square$ B. The solution set is $\{x \mid x$ is a real number $\}$. C. The solution set is $\varnothing$.

📝 Answered - If [tex]f(x)=16 x-30[/tex] and [tex]g(x)=14 x-6[/tex], for which value of [tex]x[/tex] does [tex](f-g)(x)=0[/tex]?

📝 Answered - Which statements about the function [tex]f[/tex] are true? Check all that apply. The domain of [tex]f(x)[/tex] is all real numbers. The range of [tex]f(x)[/tex] is all real numbers. The domain of [tex]f(x)[/tex] is [tex]{x \mid x>0}[/tex]. The range of [tex]f(x)[/tex] is [tex]{y \mid y>0}[/tex]. [tex]f(2)=4[/tex] [tex]f(2)=2(\frac{1}{2} x+3)[/tex]

📝 Answered - Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) [tex]\frac{5}{x}-\frac{15}{x-2}+4=0[/tex]

📝 Answered - What kind of display would be the best way to represent the data below? | Type of species | Critically endangered (%) | Endangered or vulnerable (%) | |-----------------|---------------------------|-----------------------------| | Plants | 13 | 70 | | Invertebrates | 0 | 35 | | Freshwater fish | 9 | 37 | | Amphibians | 7 | 30 | | Reptiles | 5 | 28 | | Birds | 0 | 12 | | Mammals | 2 | 21 | A. bar graph B. pie chart C. line graph D. scatter plot