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Questions in mathematics

📝 Answered - Let [tex]$\log \frac{P}{N}=6$[/tex] and [tex]$\log \frac{M}{N}=8$[/tex]. What is the relationship between [tex]$P$[/tex] and [tex]$M$[/tex]? A. [tex]$M=100 P$[/tex] B. [tex]$M=.001 P$[/tex] C. [tex]$P=100 M$[/tex] D. [tex]$M=2 P$[/tex]

📝 Answered - Solve the system of equations: [tex] \begin{array}{l} y=6 x-27 \\ y=4 x-17 \end{array} [/tex] A. (-5,3) B. (-3,-5) C. (5,3) D. No solution

📝 Answered - Which of the following statements is true? [tex]$10 \times \frac{7}{2}$[/tex] A. The product will be less than 10. B. The product will be greater than 10. C. The product will be equal to 10.

📝 Answered - An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

📝 Answered - What is the simplest form of $\frac{2 \sqrt{3}}{\sqrt{6}}$?

📝 Answered - Find the exact value of each of the following under the given conditions below. [tex]$\tan \alpha=-\frac{3}{4}, \frac{\pi}{2}\ \textless \ \alpha\ \textless \ \pi ; \sin \beta=\frac{1}{2}, 0\ \textless \ \beta\ \textless \ \frac{\pi}{2}[/tex] (a) [tex]$\sin (\alpha+\beta)$[/tex] (b) [tex]$\cos (\alpha+\beta)$[/tex] (c) [tex]$\sin (\alpha-\beta)$[/tex] (d) [tex]$\tan (\alpha-\beta)$[/tex]

📝 Answered - Define the piecewise function: f(x) = { x² - x + 10, if x ≤ 3 x - 5, if x ≥ 3 } Find: a. f(2) b. f(-2) c. f(10) d. f(7) e. f(3)

📝 Answered - Calculate the value of the expression: 4.2 ÷ 0.21 + 0.45 × 0.3.

📝 Answered - Present the above numbers in the place value tables. Express them in the expanded form. Use comma (,) according to the international numeral system. Write the numbers name in the international numeral system. (i) 3278002 (ii) 3234534 (v) 78792402 (vii) 30020102 (vi) 10200530 (ix) 50100357

📝 Answered - Which equations represent the line that is perpendicular to the line [tex]$5 x-2 y=-6$[/tex] and passes through the point [tex]$(5,-4)$[/tex]? Select three options. [tex]$y=\frac{2}{5} x-2$[/tex] [tex]$2 x+5 y=-10$[/tex] [tex]$2 x-5 y=-10$[/tex] [tex]$y+4=-\frac{2}{5}(x-5)$[/tex] [tex]$y-4=\frac{5}{2}(x+5)$[/tex]