Math Questions from Jan 23,2025

Browse the Math Q&A Archive for Jan 23,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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2. Read the story situation: A total of 987 aluminum cans, plastic bottles, and glass bottles were recycled last month. Four hundred nine glass bottles were recycled. One hundred fourteen fewer plastic bottles were recycled than glass bottles. How many aluminum cans were recycled? a. Draw a bar model to represent the story situation. The vertices of a figure are \( G(-2,-2), H(-2,6), J(2,6) ; k=0.25 \). Draw the tigure and its image amter a diabuon with th given scale factor. \[ \triangle \text { TOOLS } \] Solve the following equation for \( x \). \[ a x-8=19 \] A \( x=27 a \) B \( \quad x=\frac{a}{27} \) C \( x=\frac{27}{a} \) D \( x=\frac{11}{a} \) Solve. Show your work. (3) There are 1500 students in a school \( 65 \% \) of them are in Grades 9 and 10 How many Grade 9 and 10 students are there in the school? Factorise the following : (ii) \( y z(y-z)+z x(z-x)+x y(x-y) \) (ii) \( y z(y+z)+z x(z+x)+x y(x+y)+2 x y z \) Solve the following inequality for \( x \). \[ a x+14<45 \] A \( x<31 a \) B \( x<\frac{31}{a} \) C \( x<\frac{a}{31} \) D \( x>\frac{31}{a} \) 6. In Austin, Texas, the State Capitel Building has a height of 308 feet. This is 274,4 feet higher than the Alame located in San Antonio, Texas, What is the height of the Alamo? Define a variable and write an equation for this real-world problem. Variable: equation: Question 5 of 20 If \( f(x)=5^{x}+2 x \) and \( g(x)=3 x-6 \), find \( (f+g)(x) \) 2. Compute each of the following limits. \( \begin{array}{lll}\text { a) } \lim _{x \rightarrow \infty} \frac{1}{x} & \text { d) } \lim _{x \rightarrow-\infty}\left(\frac{-5}{2 x^{3}}-7+\frac{8}{x}\right) & \text { g) } \lim _{x \rightarrow \infty} \frac{-5 x^{3}-2 x+4}{x^{2}} \\ \text { b) } \lim _{x \rightarrow-\infty} \frac{1}{x} & \text { e) } \lim _{x \rightarrow \infty}\left(-2 x^{3}+1-\frac{5}{x}+\frac{12}{x^{4}}\right) & \text { h) } \lim _{x \rightarrow \infty} \frac{-5 x^{3}-2 x+4}{x^{3}} \\ \text { c) } \lim _{x \rightarrow \infty} \frac{-5}{2 x^{3}} & \text { f) } \lim _{x \rightarrow-\infty} \frac{3 x-2}{x} & \text { i) } \lim _{x \rightarrow \infty} \frac{-5 x^{3}-2 x+4}{x^{4}}\end{array} \) 1) Ben has three pizzas. He cuts each pizza into fourths. How many slices of pizza does Ben have?
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