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Questions in mathematics

[Done] If [tex]$\cos 45^{\circ}=\frac{1}{\sqrt{2}}$[/tex], prove that [tex]$\tan 22 \frac{1}{2}^{\circ}=\sqrt{2}-1$[/tex]

[Done] Chin canned a number of quart jars and a number of pint jars of tomatoes from his garden. A pint is 16 ounces and a quart is 32 ounces. The number of pints he canned is represented by $p$, and the number of quarts he canned is represented by $q$. Which equation models the scenario if Chin canned a total of 1,280 ounces? A. $1,280+16 p=32 q$ B. $1,280+32 q=16 p$ C. $32 q-16 p=1,280$ D. $16 p+32 q=1,280

[Done] $3 < 2a + 9 \leq 7$

[Done] What is [tex]$\cos 60^{\circ} ?$[/tex] A. [tex]$\frac{\sqrt{3}}{2}$[/tex] B. [tex]$\frac{1}{\sqrt{2}}$[/tex] C. 1 D. [tex]$\frac{1}{2}$[/tex] E. [tex]$\sqrt{3}$[/tex] F. [tex]$\frac{1}{\sqrt{3}}$[/tex]

[Done] Simplify the following: $(8 x-6)\left(-2 x^2+4 x-3\right)$

[Done] Solve $u^3=28$ where $u$ is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas.) $u=$

[Done] Replace the ? with one of the following symbols ($&lt;,&gt;,=$, or $\neq$ ). $4+3+7 ? 7+0+7$ A) &lt; B) &gt; C) = D) $\neq$

[Done] 1) Evaluating a function a. Means finding the value of f(x) or y that corresponds to a given value b. Means finding the value of f(x) or x that corresponds to a given value c. Both a and b. d. None of the above. 2) How do you evaluate a function? a. To evaluate function is to change its variable with a given number or expression. b. To evaluate function is to replace its variable with a given number or expression. c. To evaluate function is to replace its variable with a given number or functions. d. Both b and c. 3) It is represented by x and the output by f(x). a. Input b. Output c. Variable d. Function 4) If f(x) = 9 - 6x, evaluate f(-1). a. 15 b. 16 c. 17 d. 18 5) Find g(2-x) if g(x) = x² - 4x a. x² - 5x + 4 b. x² - 3x - 4 c. x² + 5x - 4 d. x² + 3x + 4

[Done] Use the vertex formula to determine the vertex of the graph of the function. f(x) = -x² + 8x + 1 (x, y) = ( ) Write the function in standard form. f(x) =

[Done] 1. Which of the following is the Kaprekar's constant? A) 6382 B) 8632 C) 6174 D) 6714 2. How many rounds does the number 6382 take to reach the Kaprekar's constant? A) 2 B) 4 C) 6 D) 3 3. The German mathematician Lothar Collatz conjectured that the sequence will always reach A) 1 B) 2 C) 0 D) 5 4. Which of the following number is supercell for the sequence 43, 79, 75, 63, 10? A) 43 B) 79 C) 75 D) 10 5. What is the smallest number whose digit sum is 14? A) 59 B) 95 C) 149 D) 68 6. Which of the following is the largest 5-digit number whose digit sum is 14? A) 10049 B) 94001 C) 93002 D) 94100 7. Which of the following is palindrome number? A) 1212 B) 123456 C) 12321 D) 625 8. Which of the following is the largest 3-digit palindrome number? A) 101 B) 989 C) 898 D) 999 9. Which of the following is the smallest 3-digit palindrome number? A) 101 B) 989 C) 898 D) 999