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Questions in mathematics

[Answered] Add. $7 \frac{1}{4}+5 \frac{8}{9}$

[Answered] Solve for $x$. $2(x+4)+2 x-1=19$

[Answered] $\begin{aligned} 6 x-2(x-5) & =-2 \\ 6 x-2 x-10 & =-2 \\ 4 x-10 & =-2 \\ 4 x-10+10 & =-2+10 \\ \frac{4 x}{4} & =\frac{8}{4} \\ x & =2\end{aligned}$

[Answered] Subtract: $\left(y^3+2 v\right)-\left(-6 y^3\right)$ Your answer should be in simplest terms.

[Answered] \begin{tabular}{|l|l|} \hline Steps & Justification \\ \hline $2,600=150 x+50$ & given \\ \hline $2,600-50=150 x+50-50$ & subtraction property of equality \\ \hline $2,550=150 x$ & simplification \\ \hline $\frac{2,550}{150}=\frac{150 x}{150}$ & division property of equality \\ \hline $17=x$ & simplification \\ \hline \end{tabular}

[Answered] Fill in the missing steps for the derivation of the quadratic formula using the choices below. A: [tex]x+\frac{b}{2 a}=\frac{ \pm \sqrt{b^2-4 a c}}{2 a}[/tex] B: [tex]x^2+\frac{b}{a} x=\frac{-c}{a}[/tex] C: [tex]x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}[/tex] D: [tex]\left(x+\frac{b}{2 a}\right)^2=\frac{-4 a c+b^2}{4 a^2}[/tex] Step 1: [tex]a x^2+b x+c=0[/tex] Step 2: [tex]a x^2+b x=-c[/tex] Step 3: [ ] Step 4: [tex]x^2+\frac{b}{a} x+\frac{b^2}{4 a^2}=\frac{-c}{a}+\frac{b^2}{4 a^2}[/tex] Step 5: [ ] Step 6: [ ] Step 7: [tex]x=-\frac{b}{2 a} \pm \frac{\sqrt{b^2-4 a c}}{2 a}[/tex] Step 8: [ ]

[Answered] The following data pairs represent the average temperature [tex]$x$[/tex] (in degrees Fahrenheit) and electricity costs [tex]$y$[/tex] (in dollars) for different homes: [tex]$\begin{array}{l} (65,147),(59,141),(71,176),(78,189),(82,183),(85,211) \\ (88,231),(91,227),(84,198),(79,188),(63,152),(59,126) \end{array}$[/tex] Which of the following values is most likely the closest to the correlation coefficient of the data? A. [tex]$r=-1$[/tex] B. [tex]$r=-0.5$[/tex] C. [tex]$r=0$[/tex] D. [tex]$r=0.5$[/tex] E. [tex]$r=1$[/tex]

[Answered] If [tex]f(x)=4-x^2[/tex] and [tex]g(x)=6x[/tex], which expression is equivalent to [tex](g-f)(3)[/tex]? A. [tex]6-3-(4+3)^2[/tex] B. [tex]6-3-(4-3^2)[/tex] C. [tex]6(3)-4+3^2[/tex] D. [tex]6(3)-4-3^2[/tex]

[Answered] 18. Higher Order Thinking a. Simplify the expression $(-13.2)+8.1$. b. How are $(-13.2)+8.1$ and $13.2+(-8.1)$ related? Explain without computing. c. Using a property of operations, what can you say about the sum of the two expressions?

[Answered] Raj's bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, [tex]y[/tex], is a function of the time in minutes, [tex]x[/tex], that it has been draining. | [tex]x[/tex] | [tex]y[/tex] | |---|---| | 0 | 40 | | 0.5 | 39.25 | | 1 | 38.5 | What is the range of this function? A. all real numbers such that [tex]37.75 \leq y \leq 40[/tex] B. all real numbers such that [tex]0 \leq y \leq 40[/tex] C. all real numbers such that [tex]y \geq 0[/tex] D. all real numbers such that [tex]y \leq 40[/tex]