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Home Question Bank Math Algebra Archive 2024 December 17

Algebra Questions from Dec 17,2024

Browse the Algebra Q&A Archive for Dec 17,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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3. Сколько корней имеет уравнение \[ \frac{4}{x}=2 x+3 \] Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. \( x^{2}+7 \mathrm{x}+\ldots \) The perfect square trinomial is \( x^{2}+7 x+\square \) (Type an integer or a simplified fraction.) 12. Consider the expression. Which of the following is equivalent to the expression for all positive values of \( n \) ? A. \( n^{3} \) B. \( n^{6} \) C. \( n^{7} \) (D.) \( n^{12} \) Determine the constant that should be added to the following binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. \( x^{2}-20 x \) The perfect square trinomial is \( x^{2}-20 x+\square \) (Type an integer or a simplified fraction.) \( 1 \leqslant \begin{array}{l}\text { Determine the constant that should be added to the following binomial } \\ \text { so that it becomes a perfect square trinomial. Then write and factor the } \\ \text { trinomial. } \\ \qquad x^{2}+14 x \\ \text { The perfect square trinomial is } x^{2}+14 x+49 \\ \text { (Type an integer or a simplified fraction.) } \\ \text { The factored perfect square trinomial is } \\ \text { (Use integers or fractions for any numbers in the expression.) }\end{array} \). What is the equation of the line that passes through the point \( (3,-4) \) and has a slope of \( -\frac{5}{3} \) Determine the constant that should be added to the following binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. \( x^{2}+14 x \) The perfect square trinomial is \( x^{2}+14 x+\square \). (Type an integer or a simplified fraction.) Solve the quadratic equation by first factoring the perfect square trinomial on the left side. Then apply the square root property. \( x^{2}-8 x+16=81 \) The solution set is \( \} \). (Simplify your answers. Type exact answers, using radicals as needed. Type your answer in the form a + bi. Use a comma to separate answers as needed.) Solve the quadratic equation by first factoring the perfect square trinomial on the left side. Then apply the square root property. \( x^{2}-10 x+25=81 \) The solution set is \( \{ \). (Simplify your answers. Type exact answers, using radicals as needed. Type your answer in the form a + bi. Use a comma to separate answers as needed.) Use the rational zeros theorem to list all possible rational zeros of the following. \[ h(x)=10 x^{3}-7 x+5 \] Be sure that no value in your list appears more than once.
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