Questions in mathematics

Questions in mathematics

[Done] Calculate the average increase in world grain production per person per year from 1950 to 1984, given the following information: - In 1950, the production was 247 kg per person. - In 1984, the production was 342 kg per person.

[Done] Solve for x: [tex]\log_6(4x - 8) = 3[/tex]

[Done] The ratio of the radii of two circles is 4:9. What is the ratio of their circumferences?

[Done] Suppose an investment of $1,800 doubles in value every 7 years. How much is the investment worth after 42 years?

[Done] Find an equation of the tangent line to the circle [tex]x^2 + y^2 = 24[/tex] at the point [tex]\left(-2\sqrt{5}, 2\right)[/tex].

[Done] What other information do you need to prove triangle GHK is congruent to triangle KLG by SAS (Side-Angle-Side)?

[Done] Mike constructed a closed box that measures 2.5 feet long by 3 feet wide by 1.5 feet high. What is the total area of the material Mike needs to construct the box?

[Done] If [tex]2x + z = 2y[/tex] and [tex]2x + 2y + z = 20[/tex], what is the value of [tex]y[/tex]?

[Done] A number divided by 32 is 96. What is the number?

[Done] Which of the following is [tex]x^4 + y^4[/tex] identically equal to? A. \((x^2 + y^2)(x + y)(x - y)\) B. \((x^2 + xy + y^2)(x^2 - xy + y^2)\) C. \((x^2 + \sqrt{2}xy + y^2)(x^2 - \sqrt{2}xy + y^2)\) D. \((x^2 + \sqrt{3}xy + y^2)(x^2 - \sqrt{3}xy + y^2)\) E. \((x + y)^2(x - y)^2\) Can someone explain to me how to solve it step by step?