Questions in mathematics

Questions in mathematics

📝 Answered - Find the equation of the line that is parallel to $y=-7 x+2$ and contains the point $(-5,32)$. $y=[?] x+[]$

📝 Answered - Find the difference quotient of $f(x)=x^2-4$; that is find $\frac{f(x+h)-f(x)}{h}, h \neq 0$. Be sure to simplify. The difference quotient is $\square$

📝 Answered - Solve $4 z-5 y=w+4$ for $z$

📝 Answered - $500 are deposited in an account with $7 \%$ interest rate, compounded continuously. What is the balance after 10 years? $F=\$[?]

📝 Answered - For what values of $p$ is the following statement true? Square $A$ has a perimeter that is less than the perimeter of rectangle $B$. Inequality $\qquad$ < $2($ $\qquad$ $)+2(p+$ $\qquad$ $)$ Solution $\qquad$ < $3+2 p+$ $\qquad$ $\qquad$ < $2 p+$ $\qquad$ $\qquad$ < $\qquad$ $p<$ $\qquad$ $p$ is $\qquad$ than $\qquad$ units

📝 Answered - If a population grows by 3 percent each year, the growth of the population is A. exponential B. cubic C. logarithmic D. linear

📝 Answered - Use what you know about translations of functions to analyze the graph of the function [tex]f(x)=(0.5)^{x-5}+8[/tex]. You may wish to graph it and its parent function, [tex]y=0.5^x[/tex], on the same axes. The parent function [tex]y=0.5^x[/tex] is across its domain because its base, b, is such that . The function, [tex]f[/tex], shifts the parent function 8 units . The function, [tex]f[/tex], shifts the parent function 5 units .

📝 Answered - 1.2 Let [tex]A=\left[\begin{array}{ccc} -1 & x & -1 \\ x & -3 & 0 \\ -3 & 5 & -1 \end{array}\right][/tex] (a) Find [tex]|A|[/tex], the determinant of [tex]A[/tex], by expanding by the second row. (b) By using the answer obtained in (a) above, solve for [tex]x[/tex] if [tex]|A|=0[/tex]. 1.3 Let [tex]B=\left[\begin{array}{ccc} 1 & 2 & -1 \\ 0 & 3 & 4 \\ 1 & 7 & 2 \end{array}\right][/tex] Determine whether [tex]B^{-1}[/tex], the inverse of [tex]B[/tex], exists. Justify your answer. (Do not determine [tex]B^{-1}[/tex]).

📝 Answered - Let [tex]$a=\sqrt{2}$[/tex] and [tex]$b=\sqrt{3}$[/tex]. (a) Find a rational number and an irrational number strictly between a and b. (b) Use the average of a and b to justify the denseness property of real numbers.

📝 Answered - Given that [tex]$\log _b(8) \approx 2.079, \log _b(9) \approx 2.197$[/tex], and [tex]$\log _b(17) \approx 2.833$[/tex], find [tex]$\log _b \frac{1}{72}$[/tex]. [tex]$\log _b \frac{1}{72} \approx$[/tex] (Simplify your answer. Round to the nearest thousandth.)