Questions in mathematics

Questions in mathematics

[Free] The equation $\frac{d}{f}=g$ represents gallons of gasoline used, $g$, in terms of distance traveled and fuel efficiency. Which of the following uses 3 gallons of gasoline? A. 57 miles and 19 miles per gallon B. 7 miles and 21 miles per gallon C. 23 miles and 20 miles per gallon D. 32 miles and 35 miles per gallon

[Free] Select the correct answer. The given equation has been solved in the table. | Step | Statement | |---|---| | 1 | [tex]$\frac{x}{2}-7=-7$[/tex] | | 2 | [tex]$\frac{x}{2}-7+7=-7+7$[/tex] | | 3 | [tex]$\frac{x}{2}=0$[/tex] | | 4 | [tex]$2 \cdot \frac{x}{2}=2 \cdot 0$[/tex] | | 5 | [tex]$x=0$[/tex] | In which step was the subtraction property of equality applied? A. step 2 B. step 3 C. step 4 D. The subtraction property of equality was not applied to solve this equation.

[Free] 10. If AC and BD are the diagonals of a parallelogram ABCD show that: a. [tex]AC ^2+ BD ^2=2\left( AB ^2+ AD ^2\right)[/tex]. b. [tex]AC ^2- BD ^2=4 \overrightarrow{ AB } \cdot \overrightarrow{ AD }[/tex]. 11. In any triangle ABC , prove by vector method: a. [tex]b=c \cos A+a \cos C[/tex] b. [tex]a=c \cos B+b \cos C[/tex] c. [tex]a^2=b^2+c^2-2 b c \cos A[/tex] d. [tex]b^2=c^2+a^2-2 c a \cos B[/tex].

[Free] Translate the following phrase into an algebraic expression. Please use the variable x. 7 less than four times a number.

[Free] The loudness, [tex]$L$[/tex], measured in decibels (Db), of a sound intensity, [tex]$I$[/tex], measured in watts is given by [tex]$L=10 \log \frac{l}{l_0}$[/tex], where [tex]$l_0=10^{-12}$[/tex] and is the least intense sound a human ear can hear. Brandon is trying to take a nap, and he can barely hear his neighbor mowing the lawn. The sound intensity level that Brandon can hear is [tex]$10^{-10}$[/tex]. Ahmad, Brandon's neighbor that lives across the street, is mowing the lawn, and the sound intensity level of the mower is [tex]$10^{-4}$[/tex]. How does Brandon's sound intensity level compare to Ahmad's mower? A. Brandon's sound intensity is [tex]$\frac{1}{4}$[/tex] the level of Ahmad's mower. B. Brandon's sound intensity is [tex]$\frac{1}{6}$[/tex] the level of Ahmad's mower. C. Brandon's sound intensity is 20 times the level of Ahmad's mower. D. Brandon's sound intensity is 80 times the level of Ahmad's mower.

[Free] What are the $x$- and $y$-coordinates of point P on the directed line segment from $A$ to $B$ such that $P$ is $\frac{1}{3}$ the length of the line segment from $A$ to $B$? $x=\left(\frac{m}{m+n}\right)\left(x_2-x_1\right)+x_1$ $y=\left(\frac{m}{m+n}\right)\left(y_2-y_1\right)+y_1$ (1,5) (0,3) (-4,-5) (-5,-7)

[Free] Annual expenses for an individual are shown in the table. To prorate the annual costs into a monthly budget, how much money per month should be budgeted for home insurance? | | Annual Expenses | | --- | --- | | Car Registration | $84.00 | | Car Insurance | $565.00 | | Home Insurance | $1,070.00 | $[?] Round to the nearest cent.

[Free] Which graph represents the piecewise-defined function [tex]f(x)=\left\{\begin{array}{ll}-x+4, & 0 \leq x < 3 \\ 6, & x \geq 3\end{array} ?\right.[/tex]

[Free] Solve the system of equations: [tex] \begin{array}{l} y=-3 x+4 \\ -4 x+y=-10 \end{array} [/tex] A. (-6,22) B. (1,1) C. (2,-2) D. No solution

[Free] If the function [tex]f(x)=m x+b[/tex] has an inverse function, which statement must be true? A. [tex]m \neq 0[/tex] B. [tex]m=0[/tex] C. [tex]b \neq 0[/tex] D. [tex]b=0[/tex]