Questions in mathematics

Questions in mathematics

📝 Answered - Solve for x. $\frac{x}{5}+5=15$

📝 Answered - Suppose a diver dives from a platform 4 feet above the water and stops at -8 feet to pick up some scallops. Which expression models this situation and tells how far below the platform the diver is? A) $|4|+|8|$ B) $-4+|-8|$ C) $4-|-8|$ D) $4+|-8|$

📝 Answered - Brendan's original plan was to visit Stuttgart, Dresden, Weisbaden, and Berlin. However, he would like to keep his costs under €860. Which change to Brendan's travel plans would result in his staying under, but closest, to his original budget? a. Replace Dresden with Potsdam. b. Replace Stuttgart with Kiel. c. Replace Berlin with Munich. d. Replace Weisbaden with Hanover.

📝 Answered - What is the probability of rolling a number greater than or equal to 5 on a standard six-sided die? Express your answer as a fraction or a decimal number rounded to three decimal places, if necessary.

📝 Answered - If f(x) = x^2 - 7x and g(x) = x + 3, then what is the minimum value of f(g(x)) - 3x? (1) -15 (2) -20 (3) -16 (4) -12

📝 Answered - Complete the following patterns by writing the next two numbers: Natural numbers: Start from 1; examples: 1, 2, , Even numbers: Divisible by 2; examples: 2, 4, ,

📝 Answered - Simplify the expression \(\frac{\tan\theta + \sec\theta - 1}{\tan\theta - \sec\theta + 1}\) and determine which of the following it equals: A. \(\frac{1 + \sin\theta}{\cos\theta}\) B. \(\frac{1 - \sin\theta}{\cos\theta}\) C. \(1 + \tan\theta\) D. \(\sec\theta + \csc\theta\) E. None of these

📝 Answered - Tina bought a packet of cookies. There were 72 cookies inside the packet. She decided to give 2/3 of the cookies to her brother and 1/3 to her sister. How many cookies did her brother and sister get?

📝 Answered - 2. Solve the following exponential equations. (a) \(\sqrt{3^{x-2}} = 27\) (b) \((\sqrt[4]{2})^{3x-1} = \frac{1}{16}\) (c) \(5^{\sqrt{x+3}} = 5^{\sqrt{x+2}}\) (d) \((\sqrt[3]{2})^{2x-3} = 2 \cdot (\sqrt[4]{4})^{1+x}\) (e) \((\sqrt{16})^{x+2} = (\sqrt{8})^{x+4}\) (f) \((\frac{x\sqrt{3}}{2})^{-6} = \frac{4}{9}\) (g) \((0.125)^{-x-1} = (0.5)^{2x}\) 3. Solve the following exponential equations. (a) \(2^{x+2} + 2^x = 20\) (b) \(3^{x+1} + 3^x = 12\) (c) \(2^{x+4} - 2^{x+2} = 48\) (d) \(2^x + 2^{x+1} + 2^{x+2} = 56\) (e) \(3^x + 3^{x+1} + 3^{x+2} = 39\) (f) \(3^{x+3} + 3^{x+1} = 1\frac{1}{9}\) (g) \(5^x + 5^{x+1} + 5^{x+2} = 775\) (h) \(\frac{2^{x+2} + 2^{x+3}}{2} = 1\) (i) \(3^{x+1} + 6 \cdot 3^{x-1} = 5\) (j) \(5^{x-1} + 10 \cdot 5^{x-2} = 75\) (k) \(2^x + 2^{x-2} = \frac{5}{8}\) (l) \(3^{x+1} = 3^{x-1} + \frac{8}{27}\) (m) \(3^{2x+3} - 2 \cdot 9^{x+1} = \frac{1}{3}\) (n) \(5 \cdot 2^{3x-1} - 2 \cdot 8^x = 4\) 4. Solve the following exponential equations. (a) \(2^{x+1} \cdot 3^{x-1} = 24\) (b) \(2^{x+2} \cdot 5^{x-1} = 8\) (c) \(5^{2x-1} \cdot 3^{2x+3} = 81\) (d) \(2^{x-3} \cdot 3^x \cdot 2^{x+1} = \frac{16}{16}\) (e) \(2 \cdot 9^{3x-1} = 8^x\) (f) \(2^{1-x} = a^{x-1}\) (g) \(9^{2x+1} = 27^{x+2}\) (h) \(25^{4x-3} = 125^{2x-4}\) (i) \(10^{x+1} = \frac{1}{0.01}\) (j) \(125^x = \frac{1}{0.04}\) (k) \(16^{x+1} = 0.25\) (l) \((\frac{2}{7})^{x-5} = \frac{49}{4}\) (m) \(5 \cdot 25^{x+1} = (125)^{2x-1}\) (n) \(64 \cdot 16^x = \frac{1}{32^{x-3}}\) (o) \(3^{x-4} = 81^{x-1}\)

📝 Answered - 1. Tim covers 1.345 km in 1 hour and 2.378 km in the next 2 hours. What distance does he cover in 3 hours? 2. 1746.25 ml of milk and 899.75 ml of strawberry pulp are used to make a batch of milkshake. The entire quantity is divided equally into 21 bottles. How much milkshake does each bottle hold? Write your answer in L and mL. 3. Aria had $354.40. She spent one-eighth of the amount on a box of cupcakes and 3/10 of the remaining amount on a book. How much money was she left with?