Questions in mathematics

Questions in mathematics

📝 Answered - Evaluate the integral $\int x^4\left(x^5-4\right)^5 d x$ by making the substitution $u=x^5-4$. $\square$ +C NOTE: Your answer should be in terms of $x$ and not $u$.

📝 Answered - Determine whether the function [tex]$f(x)=\frac{1}{x}$[/tex], defined on [tex]$R \{0\}$[/tex], is injective, surjective, and/or bijective. Justify your answer.

📝 Answered - Calculate \[\frac{6}{7} \times \frac{5}{8}\] Give your answer in its lowest terms.

📝 Answered - Giuliana has 22 quarters and dollar coins worth a total of $10.75. Which equation can be used to find $d$, the number of dollar coins Giuliana has? A. $d-22+0.25 d=10.75$ B. $0.25 d+22-d=10.75$ C. $0.25(22-d)+d=10.75$ D. $d+0.25(d-22)=10.75

📝 Answered - Simplify the imaginary number $-\sqrt{-99}$.

📝 Answered - Barbara has a roll of material that measures $14 \frac{1}{2}$ feet long. She cuts the material into pieces, each of which measures $\frac{3}{4}$ foot. How many of these pieces of material does she have? A. 16 pieces B. 17 pieces C. 18 pieces D. 19 pieces

📝 Answered - Translate the sentence into an equation. Four more than the product of a number and 2 is equal to 9. Use the variable c for the unknown number.

📝 Answered - Identify the equation as a conditional equation, contradiction, or identity. [tex]3 p+4=3 p[/tex] A. The equation is a conditional equation. B. The equation is a contradiction. C. The equation is an identity.

📝 Answered - The flag-down fare of a taxi is $3. Given that a passenger is charged $0.50 for each kilometer the taxi travels, find the amount of money the passenger has to pay if the taxi covers a distance of (i) 3 km, (ii) 6 km, (iii) 10 km. Given that $y represents the amount of money a passenger has to pay if the taxi travels $x km, copy and complete the table. | x | 3 | 6 | 10 | |---|---|---|----| | y | | | | On a sheet of graph paper, using a scale of 1 cm to represent 1 km on the horizontal axis and 2 cm to represent $1 on the vertical axis, plot the pairs of values of (x, y).

📝 Answered - Danae is choosing between two jobs. One job pays an annual bonus of $[tex]$1,500[/tex] plus $[tex]$120[/tex] per day worked. The second job pays an annual bonus of $[tex]$2,500[/tex] plus $[tex]$110[/tex] per day worked. Which equation can be solved to determine after how many days, [tex]$d$[/tex], Danae would make the same amount of money regardless of the job she chooses? A. [tex]$120 d+110 d=1,500+2,500$[/tex] B. [tex]$120+110=1,500 d+2500 d$[/tex] C. [tex]$120 d+1,500=110 d+2,500$[/tex] D. [tex]$120 d+2,500=110 d+1,500$[/tex]