Questions in mathematics

Questions in mathematics

📝 Answered - The sum of two positive numbers is 37, and their difference is 7. If [tex]$x$[/tex] and [tex]$y$[/tex] represent the unknown numbers, which two equations belong to the system of equations that represents this situation? [tex]$x=y+37$[/tex] [tex]$x-y=37$[/tex] [tex]$x+y=37$[/tex] [tex]$x-y=7$[/tex] [tex]$x+y=7$[/tex]

📝 Answered - There is a step missing from the proof. Identify where the proof there is missing and what this step should be. (these are fill in the blank so for option one it says 1 and 2, 8 and 9, 2 and 3, and 4 and 5.) (option 2 says because the student did not state the m (option 3 says This statement is true because of the definition or perpendicular line segments, addition properly of equality, definition of commentary angles, and the final one is angle addition postulate.) PLEASE HELP !!

📝 Answered - 1. Divide $\sqrt[3]{128}$ by $\sqrt[5]{64}$. Without actually calculating, find the value of the following (i) $96 \times 104$ (ii) $995 \times 995$ Factorise (i) $x^3-2 x^2-x+2$ (ii) $x ^3+13 x ^2+32 x +20$ Locate $\sqrt{3}$ on the number line.

📝 Answered - If [tex]a^{1 / 3}+b^{1 / 3}+c^{1 / 3}=0[/tex] then: a) [tex]a+b+c=0[/tex] b) [tex](a+b+c)^3=27 a b c[/tex] c) [tex]a+b+c=3(a b c)^{1 / 3}[/tex] d) [tex]a^3+b^3+c^3=0[/tex]

📝 Answered - Suppose that two cards are randomly selected from a standard 52-card deck. (a) What is the probability that the first card is a queen and the second card is a queen if the sampling is done without replacement? (b) What is the probability that the first card is a queen and the second card is a queen if the sampling is done with replacement? (a) If the sampling is done without replacement, the probability that the first card is a queen and the second card is a queen is $\square$ (Round to three decimal places as needed.)

📝 Answered - A parabola is represented by the equation $y^2=5 x$. Which equation represents the directrix? A. $y=-20$ B. $x=-20$ C. $y=-\frac{5}{4}$ D. $x=-\frac{5}{4}$

📝 Answered - For the inverse variation equation [tex]$p=\frac{8}{1 / V}$[/tex], what is the value of [tex]$V$[/tex] when [tex]$p=\frac{1}{2}$[/tex]?

📝 Answered - Convert the following number into correct scientific notation. [tex] \begin{array}{l} 56.42 \times 10^{-6} \ {[?] \times 10^{[?]}} \end{array} [/tex] Enter the coefficient in the green box and the exponent in the yellow box. Coefficient $\square$ Exponent $\square$

📝 Answered - How does the graph of $y=3^{-x}$ compare to the graph of $y=\left(\frac{1}{3}\right)^x$? A. The graphs are the same. B. The graphs are reflected across the $x$-axis. C. The graphs are reflected across the $y$-axis.

📝 Answered - Consider this unfinished equation. [tex]$4+9=\ldots+3$[/tex] What number should go in the blank space?