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Home Question Bank Math Algebra Archive 2025 January 13

Algebra Questions from Jan 13,2025

Browse the Algebra Q&A Archive for Jan 13,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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For \( k(q)=\frac{q^{2}}{2 q^{2}+3 q-27} \) (a) Write the domain in set-builder notation, (b) Write the domain in interval notation, Express numbers as integers or simplified fractions, Part: \( 0 / 2 \) Part 1 of 2 (a) Write the domain in set-builder notation. OThe domain is the empty set, The domain written in set-builder notation is \( \{q \mid q \) is a real number \( \} \) \( \{q \mid q \) is a real number and \( 6^{3} y^{3} 3 y^{2} 6^{2} \) y \( 5 y^{3} \) \( f(a)=4(a+5)-4 \) \( f(4)=\square \) (Simplify your answer.) Determine the function values, if possible. Express all numbers as integers or simplified fractions. Select "Undefined" if applicable. \[ f(x)=\frac{4}{x+2} \] Homework Section 5.1 Question 2 of 16 (1 point) I Question Attempt: 1 of Unlimited \[ f(x)=\frac{4}{x+2} \] Part 1 of 4 \( f(0) \) is 2 . Unermine the function values, if possible. Express all numbers as integers or simplified fractions. Select "Undefined" if applicable. Part 2 of 4 \( f(1) \) is Determine the function values, if possible. Express all numbers as integers or simplified fractions. Select "Undefined" if applicable. \[ f(x)=\frac{4}{x+2} \] Part 1 of 4 \( f(0) \) is Need to know how to - Plot and label an ordered pair on a coordinate plane. Example \( \mathrm{A}(2,5), \mathrm{B}(-5,4), \mathrm{C}(-6,-6), \mathrm{D}(4,-2) \) - Find the midpoint, slope and length of a line segment - Find the equation of a line using \( y=m x+b \) i.e. equation of a right bisector - Find the Point of Intersection of two lines. Solving linear systems algebraically. - Classify triangles i.e. right, isosceles, equilateral etc... - Solve a right triangle using SOHCAHTOA or Pythagorean Theorem. - Solve an acute triangle using Sine law/Cosine Law i.e. AAS. SSA, SAS, SSS - Change a quadratic relation from standard to vertex form \( \quad \boldsymbol{y}=\boldsymbol{a x} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} \) to \( \boldsymbol{y}=\boldsymbol{a}(\boldsymbol{x}-\boldsymbol{h})^{2}+\boldsymbol{k} \) - Find the \( x \) and \( y- \) intercepts - Graph a line/parabola. - Simplify algebraic expressions i.e. multiplying two binomials, expanding a square \( \quad \) of a binomial, collecting like terms \( \quad \) Example: Expand \( (x-3)(x+5) \) or \( (x+4)^{2} \) - Identify a linear or quadratic relation. - Factor a trinomial using the different methods of factoring. - Find the corresponding value of \( y \) when the \( x \) value is given. \( \quad \) Example: Given \( y=x^{2}-2 x-8 \), what is \( y \) when \( x \) is 3 ? (d) The ratio \( \frac{a-b}{a-b}=\square \), whereas the ratio \( \frac{a-b}{b-a}=\square \) provided that \( a \neq b \) (a) A (Choose one) \( \mathbf{\nabla} \) function is a function that can be written as \( f(x)=\frac{p(x)}{q(x)} \), where \( p(x) \) and \( q(x) \) are polynomial functions and \( q(x) \neq 0 \). Part 2 of 4 (b) The domain of a rational function is all real numbers excluding the values of the variable that make the (Choose one) \( \mathbf{\nabla} \) equal to zero. Part 3 of 4 (c) For polynomials \( p, q \), and \( r \), where \( (q \neq 0 \) and \( r \neq 0), \frac{p r}{q r} \) simplifies to \( \square \) For the following function, \( h(x)=x^{2}+3 x-28 \) : (a) Find the values of \( x \) for which \( h(x)=0 \). (b) Find \( h(0) \). Express numbers using integers or simplified fractions. Part 1 of 2 Separate multiple answers using a comma, if necessary. \( h(x)=0 \) when \( x=4,-7 \).
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