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Questions in mathematics

📝 Answered - Which of the following are always true in a logical system? Check all that apply. A. Theorems B. Corollaries C. Postulates D. Conditional statements

📝 Answered - Simplify the expression $(8+6 i)(8-6 i)$.

📝 Answered - Maki uses 20 gallons of a solution with an unknown ethanol concentration and 60 gallons of a [tex]$12 \%$[/tex] ethanol solution to make 80 gallons of a [tex]$10 \%$[/tex] solution. The table shows the amount of each solution. Ethanol Mixture | | Gallons | Ethanol Concentration | Total | | :------ | :------ | :-------------------- | :---- | | x% Ethanol | 20 | x | | | 12% Ethanol | 60 | 0.12 | 72 | | Mixture | 80 | 0.10 | | What is the value of [tex]$x$[/tex], the concentration of the unknown ethanol solution? A. 0.02 B. 0.04

📝 Answered - 7. Find the x and y intercepts if [tex]y =\frac{6 x+2}{2 x-4}[/tex] A. [tex](-1,0)[/tex] and [tex](0,4)[/tex] B. [tex](-\frac{1}{3}, 0)[/tex] and [tex](0,-\frac{1}{2})[/tex] C. [tex](-\frac{1}{3}, 3)[/tex] and [tex](0,7)[/tex] D. [tex](\frac{1}{3}, 0)[/tex] and [tex](0, \frac{1}{2})[/tex]

📝 Answered - Solve this equation: $-9 h-6+12 h+40=22$. A) $h=-4 / 7$ B) $h=-4$ C) $h=24$ D) $h=4$

📝 Answered - Perform the following operation and express the answer in proper scientific notation. $\frac{5.5 \times 10^7}{3.25 \times 10^{-3}}=[?] \times 10^{[?]}$ Enter the coefficient in the green box and the exponent in the yellow one. Coefficient (green)

📝 Answered - Use synthetic division to find the quotient and remainder. [tex]\frac{4 x^3-39}{x-2}[/tex] quotient $\square$ remainder $\square$

📝 Answered - In using the technique of integration by parts, you must carefully choose which expression is $u$. For the following problem, use the guidelines in this section to choose $u$. Do not evaluate the integral. $\int x^5 \ln (4 x) d x$

📝 Answered - On which triangle can the law of cosines be applied once to find an unknown angle measure? Law of cosines: [tex]a^2=b^2+c^2-2 b c \cos (A)[/tex]

📝 Answered - What is the conjugate factor of [tex]$\sqrt{5}+\sqrt{2}$[/tex]?