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Questions in mathematics

📝 Answered - Solve the system of equations. $\begin{array}{l} y=x^2+46 x-45 \\ y=46 x+76 \end{array}$ Write the coordinates in exact form. Simplify all fractions and radicals.

📝 Answered - Select the best answer for the question. 6. Using the Pythagorean theorem, find the length of a leg of a right triangle if the other leg is 8 feet long and the hypotenuse is 10 feet long. A. 12.81 ft B. [tex]$\sqrt{41 ft }$[/tex] C. 6 ft D. 36 ft

📝 Answered - Graph the following inequality: [tex]y \geq x^2+2[/tex]

📝 Answered - Three rational numbers between 0.1 and 0.11

📝 Answered - Mr. Brown is creating examples of systems of equations. He completes the steps to find the solution of the equation below. [tex]\begin{array}{c} 5 x+2 y=8 \ -4(1.25 x+0.5 y=2) \ \hline 5 x+2 y=8 \ \frac{-5 x-2 y=-8}{0=0} \end{array}[/tex] Based on this work, what is the solution to the system? A. (-4,-4) B. (0,0) C. no solution D. infinitely many solutions

📝 Answered - Which equation describes a parabola that opens left or right and whose vertex is at the point ($h, v$)? A. $x=a(y-h)^2+v$ B. $x=a(y-v)^2+h$ C. $y=a(x-h)^2+v$ D. $y=a(x-v)^2+h$

📝 Answered - If [tex]f(n)=2 n^2+2 n[/tex] and [tex]g(n)=n+1[/tex], what is [tex](f \div g)(n)[/tex] when [tex]n =-2[/tex]?

📝 Answered - If the function [tex]f(x)=x^2+7[/tex] then evaluate: 1) [tex]f(3 a)=[/tex] 2) [tex]f(b-1)=[/tex] 3) [tex]\frac{f(x+\Delta x)-f(x)}{\Delta x} \quad[/tex] where [tex]\Delta x \neq 0[/tex]. Choose the correct answer: A) [tex]2 x+\Delta x[/tex] B) [tex]x+\Delta x[/tex] C) [tex]2 x-\Delta x[/tex]

📝 Answered - Consider a situation in which [tex]$P(A)=\frac{1}{8}, P(C)=\frac{1}{4}$[/tex], and [tex]$P(A$[/tex] and [tex]$B)=\frac{1}{12}$[/tex]. What is [tex]$P(B$[/tex] and [tex]$C)$[/tex]?

📝 Answered - Finding Probabilities of Compound Events Elliot wrote a computer program that randomly generates a number from 2 to 10. If he runs the program twice, what is the probability that the number generated both times is a prime number? A. [tex]$\frac{2}{15}$[/tex] B. [tex]$\frac{1}{6}$[/tex] C. [tex]$\frac{16}{81}$[/tex] D. [tex]$\frac{9}{20}$[/tex]