Questions in mathematics

Questions in mathematics

📝 Answered - Determine whether the relation is a function. Give the domain and range for the relation. {(6, 8), (6, 9), (6, 10)} The domain of the relation is (Use a comma to separate answers as needed.)

📝 Answered - Korey is planning to open a comic book store. His store will cost $12,500 to open and will come with an $8,000 total annual operational cost. If his store makes $12,000 in profit during the first year, and profits increase by 6% each year from then, how long will it take for Korey to see an overall profit in his business (where total profits exceed total expenses)? [tex]A=P(1+r)^t[/tex] A. Korey will see an overall profit in his first year of business. B. Korey will see an overall profit in his second year of business. C. Korey will see an overall profit in his third year of business. D. Korey will see an overall profit in his fourth year of business.

📝 Answered - 2. a. (FUE) = {1.42, 3.15, -3.5, -2.57, -2.04, -0.693} b. (EUD) = {-3.5, -2.57, -2.04, 0.693} c. (FUD) = {1.42, 3.15, -2.4, -1.7, 3.5, 8.093} Answers: a. (FUE) = {-3.5, -2.57, -2.04, -0.69, 1.42, 3.153} b. (EUD) = {-3.5, -2.57, -2.04, -0.693} c. (FUD) = {-2.4, -1.7, 1.42, 3.15, 8.093} 3. a. (GUH) = {2/7, 1/2, 3/5, 4/3, 0.2, 0.45, 1.73, 2.83} b. (HUI) = {0.2, 0.45, 1.73, 2.8} c. (IUG) = {0, 1, 2, 2/7, 1/2, 3/5, 4/3}

📝 Answered - 2. A cellphone with original price of ₱3,000 is now sold at ₱1,800. Solve for percent of change and specify if increase or decrease. 3. Jean works in a supermarket for ₱50 per hour. If her pay is increased to ₱55, how much is the percent of increase in her pay? 4. A pair of pants that cost ₱600 last month is now at ₱550 during the sale. What is the percent of decrease? 5. Joy weighed 80 kilograms last month. She is on diet these days and now she is 76 kilograms. What is the percent of change in Joy's weight?

📝 Answered - On simplification, \( \frac{1}{1+z^{a-b}+z^{a-c}} + \frac{1}{1+z^{b-c}+z^{b-a}} + \frac{1}{1+z^{c-a}+z^{c-b}} \) would reduce to?

📝 Answered - Given that f(x) = |x| and g(x) = 4x - 7, calculate: (a) f ∘ g(x) = (b) g ∘ f(x) = (c) f ∘ f(x) = (d) g ∘ g(x) =

📝 Answered - Tickets for a school concert are sold at R6 for children and R10 for adults. The total number of children and adults that will attend the concert is 150. A total of 150 people attended the concert, and the total entrance fees collected amounted to R1,100. Determine how many children attended the concert. Two students, Sam and Thabo, attempt to solve the problem. Sam's Algebraic Attempt: Let c = number of children Let a = number of adults Eq 1: c + a = 1100 Eq 2: 6c + 10a = 150 (Sam gets stuck and cannot proceed.) Thabo's "Trial and Improvement" Attempt: "I know 150 people attended. I'll guess 100 children and 50 adults." Calculation 1: (100 x R6) + (50 x R10) = R600 + R500 = R1,100. "Oh, I got it on the first try! So, 100 children." As a student teacher, analyse their work: 3.1.1 Identify the conceptual error in Sam's setup of the algebraic equations. Explain what this error reveals about his understanding. 3.1.2 Thabo found the correct answer using a method of trial and error. Briefly explain why this is a valid, though not always efficient, problem-solving strategy.

📝 Answered - Which line is parallel to the line [tex]$8 x+2 y=12$[/tex]?

📝 Answered - [tex]$7=r^{\frac{1}{2}}$[/tex]

📝 Answered - Factor the following expression: [tex]$2 x^2-11 x+9$[/tex]