Questions in mathematics

Questions in mathematics

📝 Answered - Have vehicles gotten more fuel-efficient over the years? Between 1960 and 1999 the size and shape of automobiles in the United States has changed almost annually. The amount of fuel consumed by these vehicles has also changed. The following table describes the average fuel consumption per year per passenger car in gallons of gasoline. | Year, $t$ | 1960 | 1970 | 1980 | 1990 | 1995 | 1997 | 1998 | 1999 | |---|---|---|---|---|---|---|---|---| | Gallons Consumed Per Passenger Car | 668 | 760 | 576 | 520 | 530 | 538 | 544 | 552 | Determine the average rate of change, in gallons of gas per year, from 1960 and 1999 and then determine what the result means in this situation. A. -0.33 gal/year; the average fuel consumption per year of a passenger car in the U.S. decreased by a third of a gallon per year. B. 0.33 gal/year; the average fuel consumption per year of a passenger car in the U.S. increased by a third of a gallon per year. C. 2.97 gal/year; the average fuel consumption per year of a passenger car in the U.S. increased by nearly 3 gal/year. D. -2.97 gal/year; the average fuel consumption per year of a passenger car in the U.S. decreased by nearly 3 gal/year.

📝 Answered - If a trinomial has a negative coefficient for the squared term, it is usually easier to factor by first factoring out the common factor - 1. Use this method to factor the following trinomial. [tex]$-4 x^2-x+5$[/tex] Select the correct choice below and fill in any answer boxes within your choice.

📝 Answered - If [tex]f(x)=3^x+10 x[/tex] and [tex]g(x)=5 x-3[/tex], find [tex](f-g)(x)[/tex]. A. [tex]18 x-3[/tex] B. [tex]3^x-5 x+3[/tex] C. [tex]3^x+15 x-3[/tex] D. [tex]3^x+5 x+3[/tex]

📝 Answered - Find the y-intercept of the line represented by the equation below: 4x - 4y = 4

📝 Answered - Use the amortization table below to find the monthly mortgage payment for a $223,000 loan at 6.50% for 30 years. | Rate (%) | 15 Years | 20 Years | 30 Years | |---|---|---|---| | 5.00 | 7.9079 | 6.5996 | 5.3682 | | 5.25 | 8.0388 | 6.7384 | 5.5220 | | 5.50 | 8.1708 | 6.8789 | 5.6779 | | 5.75 | 8.3041 | 7.0208 | 5.8357 | | 6.00 | 8.4386 | 7.1643 | 5.9955 | | 6.25 | 8.5742 | 7.3093 | 6.1572 | | 6.50 | 8.7111 | 7.4557 | 6.3207 | | 6.75 | 8.8491 | 7.6036 | 6.4860 | | 7.00 | 8.9883 | 7.7530 | 6.6530 | | 7.25 | 9.1286 | 7.9038 | 6.8218 | State your answer in terms of dollars rounded to the nearest cent, but do not include a $ sign or the word "dollars" with your response.

📝 Answered - Arrange in columns and subtract: (i) 1,342 from 7,645 (ii) 43,231 from 67,875 (iii) 7,990 from 32,489 (iv) 783 from 59,807

📝 Answered - Solve for y: 5((132 - 3y)/4) - 2y = -42

📝 Answered - Let y be a solution to the differential equation \[ y'' - 4xy' + (4x^2 - 1)y = -3e^{x^2} \sin(2x) \], with boundary conditions \( y(0) = 0 \) and \( y(\frac{\pi}{2}) = 0 \). Then the value of \( y(2\pi) \) is: (a) \( \frac{e^{\pi^2}}{4} \) (b) 0 (c) \( e^{4\pi^2} \) (d) 1

📝 Answered - What is the solution of [tex]$\sqrt{x^2+49}=x+5$[/tex]? A. [tex]$x=\frac{12}{5}$[/tex] B. [tex]$x=-\frac{12}{5}$[/tex] C. [tex]$x=-6$[/tex] or [tex]$x=-3$[/tex] D. no solution

📝 Answered - (b) [tex]\frac{25-2 u}{3}=2[/tex]