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Questions in mathematics

[Done] Factor. $15 x^2+20 x$

[Done] Graph the equation $y=x^2-14 x+48$ on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Using the graph, determine the roots of the equation $x^2-14 x+48=0$.

[Done] Fifteen percent of an employee's taxable income is collected each paycheck. Before taxes are removed from each paycheck, $350 of tax-exempt expenses is taken out. If the variable x represents the employee's pay before tax-exempt expenses and taxes are removed, which expression represents the employee's take-home pay after these deductions? A. 0.15(x-350) B. x-0.15-350 C. 0.85(x-350) D. x-0.85-350

[Done] Circle $Q$ is centered at the origin and has a radius of 9 units. Which equation could represent circle Q? A. $x^2+y^2=3$ B. $x^2+y^2=9$ C. $x^2+y^2=81$ D. $(x-9)^2+(y-9)^2=1$

[Done] Which polynomial represents the sum below? $\left(18 x^2-18\right)+\left(-13 x^2-13 x+13\right)$ A. $18 x^2-31 x-18$ B. $5 x^2-13 x-5$ C. $5 x^2-13 x-31$ D. $31 x^2-31 x-5$

[Done] Solve the system of equations and enter the solution as an ordered pair in the box below. [tex] \begin{array}{l} 3 y=2 x+1 \\ 5 y=2 x+3 \end{array} [/tex]

[Done] The table shows the number of weeks of vacation employees receive each year, based on the number of years they have been employed. What does [tex]$\forall(15)=5$[/tex] mean in terms of the problem? | Years of Service | Weeks of Vacation | |---|---| | 1 | 1 | | 2 | 2 | | 5 | 3 | | 10 | 4 | | 15 | 5 | | 20 | 6 | | 30 | 8 | A. A worker took 5 weeks of vacation in 15 years. B. A worker with 5 years of service gets 15 weeks of vacation each year. C. There are 5 workers who have 15 years of service each. D. A worker with 15 years of service gets 5 weeks of vacation each year.

[Done] 1) Simplify: [tex]$0.0216 \times 10^{-3} \times 0.024 \times 10^{-4} \times 0.018 \times 10^{-5}$[/tex] / [tex]$3600 \times 10^{-6} \times 0.96 \times 10^{-3}$[/tex] 2) The first, second, and third terms of an arithmetic progression are [tex]$a, b, \frac{3}{4}$[/tex]. Find the values of [tex]$a$[/tex] and [tex]$b$[/tex]. 3) A trader buys 200 oranges for $1420. She later realizes that 10% of the oranges are rotten and cannot be sold. She sells the remaining oranges at a rate of 3 for $f. Calculate, correct to US$, the true percentage profit or loss. 4) Solve the inequality: [tex]$\frac{x}{3} \geqslant 5-4\left(x-\frac{1}{6}\right)$[/tex]

[Done] Solve the following equation for $x$. $3 x-9=-33$

[Done] On any day when she travels to college, she uses one of three options: her bike only; a bus only; or both her bike and a bus. The probability that she uses her bike, either on its own or with the bus, is 0.7. The probability that she uses both her bike and the bus is 0.3. Calculate the probability that, on any day when she travels to college, she: a) does not use her bike; b) uses only her bike; c) uses the bus; d) uses her bike, given that she used the bus.