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Questions in mathematics

📝 Answered - A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two congruent right triangles with areas of 44 square inches. Which statements are true? Check all that apply. A. The area of the rectangle is 88 square inches. B. The equation [tex]$x(x-3)=44$[/tex] can be used to solve for the dimensions of the triangle. C. The equation [tex]$x^2-3 x-88=0$[/tex] can be used to solve for the length of the rectangle. D. The triangle has a base of 11 inches and a height of 8 inches. E. The rectangle has a width of 4 inches.

📝 Answered - 4.92 grams to milligrams

📝 Answered - Which solution to the equation [tex]$\frac{1}{x-1}=\frac{x-2}{2 x^2-2}$[/tex] is extraneous? A. [tex]$x=1$[/tex] and [tex]$x=-4$[/tex] B. neither [tex]$x=1$[/tex] or [tex]$x=-4$[/tex] C. [tex]$x=1$[/tex] D. [tex]$x=-4$[/tex]

📝 Answered - Solve. $\begin{array}{l} -9 x+3 y=12 \\ 9 x-5 y=-2 \end{array}$

📝 Answered - Write 2 equivalent ratios for the ratio below: 22:33

📝 Answered - The first two steps in the derivation of the quadratic formula by completing the square are: Step 1: [tex]$a x^2+b x+c=0$[/tex] Step 2: [tex]$a x^2+b x=-c$[/tex] Which answer choice shows the correct next step? A. [tex]$a x+b=\frac{-c}{x}$[/tex] B. [tex]$a x^2+b x+\frac{b^2}{4}=-c+\frac{b^2}{4}$[/tex] C. [tex]$x^2+\frac{b}{a} x=\frac{-c}{a}$[/tex] D. [tex]$x^2+\frac{b}{a} x=-c$[/tex]

📝 Answered - The four diagonals of a cube are drawn to create 6 square pyramids with the same base and height. The volume of the cube is $(b)(b)(b)$. The height of each pyramid is $h$. Therefore, the volume of one pyramid must equal one-sixth the volume of the cube, or A. $\frac{1}{6}(b)(b)(2 h)$ or $\frac{1}{3} B h$. B. $\frac{1}{6}(b)(b)(6 h)$ or $B h$. C. $\frac{1}{3}(b)(b)(6 h)$ or $\frac{1}{3} B h$. D. $\frac{1}{3}(b)(b)(2 h)$ or $\frac{2}{3} B h$.

📝 Answered - Evaluate [tex]$-a^2-2 b c-|c|$[/tex] if [tex]$a=-2, b=3$[/tex], and [tex]$c=-3$[/tex].

📝 Answered - [tex]\frac{1}{2} x-4\ \textless \ 3[/tex]

📝 Answered - Draw the number line model and find the quotient [tex]$5 \div \frac{2}{3}$[/tex]