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Home Question Bank Math Archive 2025 January 20

Math Questions from Jan 20,2025

Browse the Math Q&A Archive for Jan 20,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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75MOS 2 7.6, Practice Day 1; Worksheet A Write an expression equivalent to \( 7 x+1-(3 x-1) \) that only has two terms. 6 The solution to \( \frac{4(x-5)}{3}+2=14 \) is \( \begin{array}{ll}\text { (1) } 15 & \text { (3) } 6 \\ \text { (2) } 14 & \text { (4) } 4\end{array} \) A line segment joins the points \( C(-5,6) \) and \( \mathbf{D}(7,2) \). (d) Calculate the midpoint of the line segment \( \mathbf{C D} \). (b) Find the gradient of the line segment CD. \( \begin{array}{l}£ 1800 \text { is put into an account. It gathers simple interest at } \\ \qquad \text { a rate of } 3 \% \text { per year. } \\ \text { a) How much money is added to the account each year? } \\ \text { b) How much money will be in the account after two years? } \\ \text { Give your answers in pounds }(£) \text {. }\end{array} . . \$ \). \( \frac { ( a ^ { \frac { 2 } { 3 } } \cdot b ^ { \frac { 2 } { 2 } } ) ( a ^ { - 1 } , b ^ { 2 } ) } { a ^ { \frac { 1 } { 2 } } \cdot b ^ { \frac { 1 } { 4 } } } \) Hence, simplify the expression \( \frac{x^{2}-49}{x^{2}+2 x-35} \) Let the universal set, \( U \), be the set of students at Central High, \( A \) be the set of students taking algebra, and \( C \) be the set of students taking chemistry. If a student is selected at random, describe in words what is meant by each of the following probabilities. a. \( P(A \cup C) \) b. \( P(A \cap C) \) c. \( 1-P(C) \) \begin{tabular}{|l|l|}\hline 14. \( m \angle C=90^{\circ} \) & 14. \\ \hline 15. \( \triangle A B C \) is a right triangle & \( \begin{array}{l}\text { 15. Definition of right } \\ \text { triangles }\end{array} \) \\ What reason justifies statement \( 14 ? \) \\ \( \begin{array}{l}\text { (1 point) }\end{array} \) \\ \( \begin{array}{l}\text { O Definition of right angles } \\ \text { O Definition of right triangles } \\ \text { O Reansitive Property }\end{array} \) \\ \hline\end{tabular} Find the next number in the sequence \( 128,64,32, \ldots \) Answer: \( 3-t ;-t ; \sqrt{9-2 t} \) are the first three terms of an arithmetic sequence. 3.1 Determine the value of \( t \).
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