Questions in mathematics

Questions in mathematics

[Answered] 5. Fill in the missing numbers using the properties of integers. a. 21 + = 0. b. + 12 = 0. c. -5 x = 1 d. (-12) + 3 = 3 + () 6. Rahil travels 56 km due north from a point P to the point Q. He then goes 45 km towards south along the same road. If the distance towards north is taken as a positive integer, then how will the point P be represented? How far is Rahil from the starting point?

[Answered] $\int 2n \cdot e^{n^2} \, dn$ Solution: $I = \int 2n \cdot e^{n^2} \, dn$ Let $y = e^{n^2}$

[Answered] \frac{5}{2 x+6}-2=\frac{1-8 x}{4 x}

[Answered] The overall cost of carpet and installation from a particular company is represented by the function, where [tex]$x$[/tex] represents the square footage of the carpet. [tex]$P(x)=\$ 2.35 x+\$ 104.00$[/tex] What is the average rate of change over the interval [tex]$[2,000,2,500]$[/tex]? A. [tex]$\$[/tex]0.43 per square foot B. [tex]$\$[/tex]4.81 per square foot C. [tex]$\$[/tex]2.35 per square foot D. [tex]$\$[/tex]1.04 per square foot

[Answered] Proof: We are given that [tex]$AB =12$[/tex] and [tex]$AC =6$[/tex]. Applying the segment addition property, we get [tex]$A C+C B=A B$[/tex]. Applying the substitution property, we get [tex]$6+C B=12$[/tex]. The subtraction property can be used to find [tex]$CB =6$[/tex]. The symmetric property shows that [tex]$6=A C$[/tex]. Since [tex]$C B$[/tex] [tex]$=6$[/tex] and [tex]$6= AC , AC = CB$[/tex] by the property. So, [tex]$\overline{ AC } \cong \overline{ CB }$[/tex] by the definition of congruent segments. Finally, C is the midpoint of [tex]$\overline{ AB }$[/tex] because it divides [tex]$\overline{ AB }$[/tex] into two congruent segments.

[Answered] Solve the rational equation by multiplying both sides by the LCD. Check your results for extraneous solutions. $\frac{3}{x^2+5 x+6}+\frac{x-1}{x+2}=\frac{7}{x+3}$ x= $\square$ is a solution. x= $\square$ is an extraneous solution.

[Answered] Write each expression with a rational exponent. Do not attempt to simplify. (a) [tex]$\sqrt[11]{11 w}=[/tex] (b) [tex]$\sqrt[8]{10 t}=\sqrt[8]{10 t}$ $\sigma^6[/tex] (c) [tex]$2 \sqrt[7]{17 a}=[/tex]

[Answered] The graph of the even function [tex]f(x)[/tex] has five [tex]x[/tex]-intercepts. If [tex](6,0)[/tex] is one of the intercepts, which set of points can be the other [tex]x[/tex]-intercepts of the graph of [tex]f(x)[/tex] ? A. [tex](-6,0),(-2,0)[/tex], and [tex](0,0)[/tex] B. [tex](-6,0),(-2,0)[/tex], and [tex](4,0)[/tex] C. [tex](-4,0),(0,0)[/tex], and [tex](2,0)[/tex] D. [tex](-4,0),(-2,0)[/tex], and [tex](0,0)[/tex]

[Answered] Which of the following statements are true? Check all of the boxes that apply. [tex]f(x)=2 \sqrt{x}[/tex] has the same domain and range as [tex]f(x)=\sqrt{x}[/tex]. [tex]f(x)=-2 \sqrt{x}[/tex] has the same domain and range as [tex]f(x)=\sqrt{x}[/tex]. [tex]f(x)=-\sqrt{x}[/tex] has the same domain as [tex]f(x)=\sqrt{x}[/tex], but a different range. [tex]f(x)=\frac{1}{2} \sqrt{x}[/tex] has the same domain as [tex]f(x)=\sqrt{x}[/tex], but a different range.

[Answered] What is the following quotient? $\frac{5}{\sqrt{11}-\sqrt{3}}$