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Questions in mathematics

[Answered] Subtract: $-10 b^3-\left(-11 b^3+n\right)$ Your answer should be in simplest terms.

[Answered] Solve the problem. The formula [tex]$A=P+P r t$[/tex] represents the value, [tex]$A$[/tex], of an investment of [tex]$P$[/tex] dollars at a yearly simple interest rate, [tex]$r$[/tex], for [tex]$t$[/tex] years. The equation to model the value, [tex]$A$[/tex], of an investment of [tex]$$54$[/tex] at 9.26% for [tex]$t$[/tex] years is given by [tex]$A=54+5 t$[/tex] The equation to model the value, [tex]$A$[/tex], of an investment of [tex]$$84$[/tex] at 2.38% for [tex]$t$[/tex] years is given by [tex]$A=84+2 t .$[/tex] Assuming [tex]$A$[/tex] has the same value, the given equations form a system of two linear equations. Solve this system using an algebraic approach and interpret your answer. a. [tex]$t =5$[/tex] The two investments will reach the same value in 5 years. b. [tex]$t=20$[/tex] The two investments will reach the same value in 20 years. c. [tex]$t =1000$[/tex] The two investments will reach the same value in 1000 years. d. [tex]$t=10$[/tex] The two investments will reach the same value in 10 years.

[Answered] What is [tex]$\left(\frac{1}{7}\right)^3$[/tex] equal to? A. [tex]$\frac{1}{10}$[/tex] B. [tex]$\frac{3}{21}$[/tex] C. [tex]$\frac{1}{343}$[/tex] D. [tex]$\frac{3}{2401}$[/tex]

[Answered] Select the correct answer. Patty is a customer service representative for a company. She earns $18 an hour, plus an additional $2.50 each time one of her customers completes a company survey. This week, Patty plans to work 38 hours. If Patty wants to earn at least $750 this week, which inequality could she solve to find the number of surveys, $s$, she needs her customers to complete this week? A. $\quad 18(2.5 s+38) \geq 750$ B. $18(s+2.5)>750$ C. $18(38)+2.5 s \geq 750$ D. $20.5 s>750$

[Answered] Simplify the following expression. $x^4 \cdot x^4$ A. $x^{\frac{2}{11}}$ B. $x^{\frac{1}{1}}$ C. $x^{15}$ D. $x^4$

[Answered] The hypotenuse of a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle measures $7 \sqrt{2}$ units. What is the length of one leg of the triangle? A. 7 units B. $7 \sqrt{2}$ units C. 14 units D. $14 \sqrt{2}$ units

[Answered] (3) [tex]\frac{2^9}{2^5}[/tex]

[Answered] Which number can each term of the equation be multiplied by to eliminate the fractions before solving? [tex]6-\frac{3}{4} x+\frac{1}{3}=\frac{1}{2} x+5[/tex]

[Answered] Convert the point-slope form below to slope-intercept form and identify the key features. [tex]y+10=-5(3 x+5)[/tex] Answers must be written as proper fractions, improper fractions, or integers. Slope: [ ] y-intercept: [ ]

[Answered] Write the domain in interval notation of each function: a. [tex]$y=x^2+7$[/tex] b. [tex]$g(x)=\frac{3 x-2}{(x+6)(x-4)}$[/tex] c. [tex]$f(x)=\sqrt{x-2}$[/tex] d. [tex]$y=\frac{1}{\sqrt{5-x}}$[/tex] e. [tex]$h(x)=\frac{x}{x^2-2 x}$[/tex] f. [tex]$f(x)=\frac{5}{x+4}-\frac{2}{x}$[/tex] g. [tex]$y=\frac{1}{x^2+6}$[/tex] h. [tex]$g(x)=\frac{\sqrt{8-x}}{(x+4)\left(x^2+1\right)}$[/tex]