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Home Question Bank Math Archive 2024 December 14

Math Questions from Dec 14,2024

Browse the Math Q&A Archive for Dec 14,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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a. \( 1=\frac{1}{2}+\square \) c. \( 1=\frac{1}{16}+\square \) A 19-f ladder is leaning against a wall and the wall is perpendicular to the ground. The base of the ladder is 8 ft from the wall. How high above the ground is the top of the ladder? The ladder reaches (Simplify your answer. Type an exact answer, using radicals as needed.) Soit \( f \) la fonction définie par : \( f(x)=\frac{\sqrt{1+x}-1}{x} \) 1) Déterminer \( D_{f} \) 2) Vérifier que \( \forall x \in D_{f} \quad f(x)=\frac{1}{1+\sqrt{x+1}} \) 3) 4ontrer que \( f \) est décroissante sur \( D_{f} \) 5) Montrer que \( \forall x \in D_{f} \quad 0<f(x) \leq 1 \) maximale de la fonction \( f(-1) \) est déduire que 1 est une valeur 15. Solve the equation. There will be more than one correct answer. \( t^{2}-24=0 \) \( t= \) Complete parts a and b. a. If triangle \( A B C \) is similar to triangle \( D E F \) and \( \frac{A B}{D E}=\frac{1}{3} \), what is the ratio of the heights of the triangles? b. What is the ratio of the areas of the two triangles? a. The ratio of the height of triangle \( A B C \) to the height of triangle \( D E F \) is \( \frac{1}{8} \). (Type an integer or a simplified fraction.) b. The ratio of the area of traingle \( A B C \) to the area of triangle \( D E F \) is \( \frac{1}{64} \). (Type an integer or a simplified fraction.) 14. Solve the equation. There will be more than one correct answer. \( x^{2}-12=0 \) \( x= \) Exercice 5 Soit \( f \) la fonction définie par : \( f(x)=\frac{\sqrt{1+x}-1}{x} \) 1) Déterminer \( D_{f} \) 2) Vérifier que \( \forall x \in D_{f} \quad f(x)=\frac{1}{1+\sqrt{x+1}} \) 3) 4) 4) Montrer que \( f \) est décroissante sur \( D_{f} \) 5) \( \forall x \in D_{f} \quad 0<f(x) \leq 1 \) maximale de la fonction \( f \) sur \( D_{f} \) \( Y \) is between \( X \) and \( Z . X Y=7 X+1, Y Z=2 X+7 \) and \( X Z=98 \). Find the value of ' \( X \) '. 2. \( m=12 \) Find the measure of each exterior angle of a 15 -gon, Set up this equation and solve: \( (2 x+2)+(3 x-7)+35=180 \) \( x= \)
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