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Questions in mathematics

[Free] Complete the table of values for the function: [tex] \begin{array}{l} f(x)=\left(\frac{1}{3}\right)^x \\ a=9 \\ b=3 \\ c=1 \end{array} [/tex] When [tex]$b\ \textgreater \ 1$[/tex], as [tex]$x$[/tex] grows in the negative direction, [tex]$y \square$[/tex]. When [tex]$0\ \textless \ b\ \textless \ 1$[/tex], as [tex]$x$[/tex] grows in the negative direction, [tex]$y \square$[/tex]. | x | f(x) | | --- | ---- | | -2 | a | | -1 | b | | 0 | c | | 1 | 1/3 | | 2 | 1/9 |

[Free] Select whether the equation has a solution or not. [tex]\sqrt[3]{x-5}-2=0[/tex] A. no roots B. roots

[Free] a) $\left[(2)^2\right]^{-1}$ b) $\left\{\left[\left(\frac{122}{15}\right)^5\right]^0\right\}^{-3}=$

[Free] Determine the range values from an equation. Consider the functions [tex]f(x)=\left(\frac{4}{5}\right)^x[/tex] and [tex]g(x)=\left(\frac{4}{5}\right)^x+6[/tex]. What are the ranges of the two functions? [tex]\begin{array}{l} f(x):\{y \mid y\ \textgreater \ [/tex] [tex]g(x):\{y \mid y\ \textgreater \ [/tex]

[Free] Fill in the blanks. (i) 1,381 x 74 = ___ x 1,381 (ii) ___ x 67 = 67 x 1,287 (iii) 7,635 x ___ = 7,635 (iv) 6,081 x 28 = ___ x 6,081 Name the property. (i) 1,438 x 713 = 713 x 1,438 (ii) 2,317 x 0 = 0 (iii) 1,432 x (8 x 15) = (1,432 x 8) x 15 (iv) 4,135 x (10 + 9) = 4,135 x 10 + 4,135 x 9 Fill in the blanks. (i) 4,379 x 10 = ___ (ii) 8,376 x 100 = ___ (iii) 4,518 x 10 = ___ (iv) 98 x 1,000 = ___ (v) 94 x 1,000 = ___ (vi) 1,000 x 45 = ___

[Free] Write multiplication tables from 12 to 20 neatly on an A-4 size sheet and learn them.

[Free] What is the equation, in slope-intercept form, of the line that is perpendicular to the line [tex]y-4=-\frac{2}{3}(x-6)[/tex] and passes through the point $(-2,-2)$? A. [tex]y=-\frac{2}{3} x-\frac{10}{3}[/tex] B. [tex]y=-\frac{2}{3} x+\frac{10}{3}[/tex] C. [tex]y=\frac{3}{2} x-1[/tex] D. [tex]y=\frac{3}{2} x+1[/tex]

[Free] Peter wants to borrow $[tex]$3,000[/tex]$. He has two payment plans to choose from. Plan A charges 4% interest over 6 years. Plan B charges 5% interest over 4 years. The formula [tex]$m=\frac{P+Prt}{12t}$[/tex] can be used to calculate the monthly payment, [tex]$m$[/tex], where [tex]$P$[/tex] is the principle amount borrowed, [tex]$r$[/tex] is the interest rate expressed as a decimal, and [tex]$t$[/tex] is the time of the loan, years. Which statement best compares the plans? A. Plan A has a monthly payment of about $[tex]$23[/tex] less and a total interest charge of $[tex]$120[/tex] less than plan B. B. Plan A has a monthly payment of about $[tex]$23[/tex] less and a total interest charge of $[tex]$120[/tex] more than plan B. C. Plan A has a monthly payment of about $[tex]$23[/tex] more and a total interest charge of $[tex]$120[/tex] more than plan B. D. Plan A has a monthly payment of about $[tex]$23[/tex] more and a total interest charge of $[tex]$120[/tex] less than plan B.

[Free] The table represents an exponential function. | x | y | |---|---| | 1 | 2 | | 2 | [tex]\frac{2}{5}[/tex] | | 3 | [tex]\frac{2}{25}[/tex] | | 4 | [tex]\frac{2}{125}[/tex] | What is the multiplicative rate of change of the function?

[Free] Solve: $\frac{1}{3 a^2}-\frac{1}{a}=\frac{1}{6 a^2}$