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Questions in mathematics

📝 Answered - If you use a 5/8 inch drill bit instead of a 17/32 inch drill bit, how big is the difference?

📝 Answered - Study the steps shown to solve the given equation. [tex]\begin{array}{c} \sqrt{30-2 x}=x-3 \\ 30-2 x=x^2-6 x+9 \\ 0=x^2-4 x-21 \\ 0=(x+3)(x-7) \end{array}[/tex] Based on the above work, possible solutions of the equation are [$\square$].

📝 Answered - Match the column: Column-I | Column-II ---|--- (a) Unit digit of (36)^2 | (p) 1 (b) Number of zeroes in square of 300 | (q) 7 (c) A number that ends in ___ is never a perfect square. | (r) 6 (d) Unit digit in square of 89 | (s) 4 (1) a-s, b-p, c-q, d-r (2) a-r, b-p, c-q, d-s (3) a-s, b-p, c-q, d-p (4) a-r, b-s, c-q, d-p

📝 Answered - (a) [tex]\frac{4}{3} + \frac{3}{4}[/tex] (b) [tex]\frac{7}{4} + \frac{1}{7}[/tex] (c) [tex]\frac{1}{6} + \frac{11}{12}[/tex] (d) [tex]3\frac{2}{3} + 1\frac{3}{8}[/tex]

📝 Answered - Let f(x) = cos(α₁ + x) + (1/3)cos(α₂ + x) + (1/3²)cos(α₃ + x) + ... + (1/3^{n-1})cos(αₙ + x), where α₁, α₂, ..., αₙ ∈ ℝ. If f(x₁) = f(x₂) = 0, then |x₁ - x₂| can be: A. π B. 5π/2 C. 3π/2 D. 4π

📝 Answered - Solve: $\begin{array}{l} (x+1)\left(x^2-5 x+6\right) \leq 0 \\{[?] \leq x \leq \quad \text { or } x \leq\end{array}$

📝 Answered - Select the correct answer. Which function has a range of $[-6, \infty)$ ? A. $f(x)=\sqrt{x-4}+6$ B. $f(x)=\sqrt{x+4}-6$ C. $f(x)=\sqrt{x+6}-4$ D. $f(x)=\sqrt{x-6}+4$

📝 Answered - The function $f(x)=-0.3(x-5)^2+5$ is graphed. What are some of its key features? Check all that apply. The axis of symmetry is $x=5$. The domain is ${x \mid x$ is a real number $}$. The function is increasing over ( $-\infty, 5$ ). The minimum is $(5,5)$. The range is ${y \mid y \geq 5}$.

📝 Answered - The range of which function includes -4? [tex]y=\sqrt{x}-5[/tex] [tex]y=\sqrt{x}+5[/tex] [tex]y=\sqrt{x+5}[/tex] [tex]y=\sqrt{x-5}[/tex]

📝 Answered - How can you rewrite $(z \leq-1.75)$ in order to find the answer? A. $P (z \leq 1.75)$ B. $P (z \geq-1.75)$ C. $1-P(z \leq-1.75)$ D. $1-P(z \leq 1.75)$