Questions in mathematics

Questions in mathematics

📝 Answered - Rewrite without rational exponents, and simplify, if possible. [tex]$\left(a^2 b^2\right)^{\frac{1}{9}}=\square$[/tex] (Simplify your answer. Type in radical form)

📝 Answered - 1. Find the solution set of the linear inequality [tex]x+4 \leq 3x-16x[/tex]. The domain is [tex] \{1,2,3,4,5,7,8,9,10\} [/tex]. 2. If [tex]x[/tex] is defined as natural numbers, find the solution set for the inequality [tex]21-5x\ \textless \ 1[/tex]. 3. The variable [tex]k[/tex] has a domain [tex] \{1,2,3,4,5,6,7,8,9, 10\} [/tex]

📝 Answered - If $y=2 x+1$ were changed to $y=\frac{1}{2} x+1$, how would the graph of the new function compare with the first one? A. It would be shifted left. B. It would be less steep. C. It would be shifted down. D. It would be steeper.

📝 Answered - Which expression is equivalent to [tex]$\log _w \frac{\left(x^2-6\right)^4}{\sqrt[3]{x^2+8}} ?[/tex] A. [tex]$4 \log _w \frac{x^2}{1296}-\frac{1}{3} \log _w(2 x+8)$[/tex] B. [tex]$4 \log _w\left(x^2-6\right)-3 \log _w\left(x^2+8\right)$[/tex] C. [tex]$4 \log _w\left(x^2-6\right)-\frac{1}{3} \log _w\left(x^2+8\right)$[/tex] D. [tex]$4\left(\log _w x^2-\frac{1}{3} \log _w\left(x^2+8\right)-6\right)$[/tex]

📝 Answered - Find all relative extrema of the function. Use the second derivative test where applicable. (If an answer does not exist, enter DNE.) [tex]f(x)=x^2+5 x-5[/tex] relative maximum (x, y) = ( relative minimum (x, y) = (

📝 Answered - A GP has a first term of a, a common ratio of [tex]$r$[/tex] and its 6th term is 768. Another GP has a first term of a, a common ratio of [tex]$6r$[/tex] and its 3rd term is 3456. Evaluate a and [tex]$r$[/tex].

📝 Answered - Which expression is equivalent to $\left(\frac{4^{\frac{5}{4}} \cdot 4^{\frac{1}{4}}}{4^{\frac{1}{2}}}\right)^{\frac{1}{2}}$ A. $\sqrt[16]{4^5}$ B. $\sqrt{2^5}$ C. 2 D. 4

📝 Answered - A coffee shop sells regular and large coffees. A regular coffee costs $3, and a large coffee costs $5. If the shop sells 50 coffees and collects $180, what system of equations represents the situation? a. $5x+3y=50, x+y=180$ b. $3x+5y=180, x+y=50$ c. $3x+5y=50, x+y=180$ d. $5x+3y=180, x+y=50

📝 Answered - Steps for solving $6x - 18 = 54$ are shown. Explain how Step 1 helps solve the equation. $6x - 18 = 54$ Original equation $6x - 18 + 18 = 54 + 18$ Step 1 $6x = 72$ Step 2 $\frac{6x}{6} = \frac{72}{6}$ Step 3 $x = 12$ Step 4 A. Adding 18 to both sides isolates the variable. B. Subtracting 18 from both sides combines like terms. C. Adding 18 to both sides isolates the variable term. D. Subtracting 18 from both sides undoes the subtraction.

📝 Answered - What is the degree of the polynomial [tex]x^2+6 x+7[/tex]?