Questions in mathematics

Questions in mathematics

📝 Answered - Find the 7th term of this geometric sequence. [tex] 5, 10, 20, 40, \ldots a_7=[?][/tex]

📝 Answered - Solve: [tex]9^6=\left(3^2\right)^{2 x-2}[/tex]

📝 Answered - If $g(x)=\frac{x+1}{x-2}$ and $h(x)=4-x$, what is the value of $(g \circ h)(-3)$?

📝 Answered - Simplify the radicals. [tex]\begin{array}{l} \sqrt{10} \cdot \sqrt{8}= \\ \sqrt{2} \cdot \sqrt{10}= \end{array}[/tex]

📝 Answered - Suppose vector $u =\langle 1, \sqrt{3}\rangle, | v |=6$, and the angle between the vectors is $120^{\circ}$. What is $u \cdot v$?

📝 Answered - Given [tex]$f^{\prime \prime}(x)=9 x-4$[/tex] and [tex]$f^{\prime}(0)=2$[/tex] and [tex]$f(0)=5$[/tex]. Find [tex]$f^{\prime}(x)=[/tex] [$\square$] and find [tex]$f(2)=[/tex] [$\square$]

📝 Answered - \frac{13 \times 5^b-25 \times 5^{b-2}}{5^{b+2}-5^{b+1}}=\frac{3}{5}

📝 Answered - Find the 24th term (a_24) of the sequence: 3, -30, -63, ... Formula: a_n = a_1 + (n - 1)d Given: - First term, a_1 = 3 - Common difference, d = -33 (since -30 - 3 = -33) - Term number, n = 24 Solution: a_24 = a_1 + (24 - 1)d = 3 + 23(-33) = 3 - 759 = -756 Answer: a_24 = -756

📝 Answered - It is given that E = {11, 13, 15, 17} and F = {12, 14, 15, 16, 17, 18, 20}. (i) Draw a Venn diagram to represent the sets E and F. (ii) From the Venn diagram, list all the elements in E ∪ F in set notation.

📝 Answered - Mike is promoted to salary level 2, receives a 3% cost-of-living increase and a 10% merit bonus. What is Mike's new salary? | Level | 1 | 2 | 3 | |-------|---------|---------|---------| | Salary| $54,000 | $60,000 | $68,000 | Round to the nearest dollar.