Matemáticas preguntas y respuestas

Suppose we know that the last two digits of a number are 50. Use appropriate divisibility tests to select all the statements that we know *must* be true. divisible by 4 divisible by 9 divisible by 5 divisible by 3 divisible by 10 divisible by 2 \( > \) Next Question

6. Al resolver el sistema \( \left\{\begin{array}{l}5 x+6 y=20 \\ 4 x-3 y=-23\end{array}\right. \) \( \begin{array}{rlrl}5 x . x=2 & \text { b. } x=-2 & \text { c. } x=5 & \text { d. } x=-5 \\ y=5 & y=5 & y=-2 & y=2\end{array} \)

e. \( a+b \) es divisor de \( a^{4}+b^{4} \). ( ) f. \( a-b \) es divisor de \( a^{5}+b^{5} \). ( ) g. \( \quad \) El grado del polinomio cociente entre \( x^{5}+y^{5} y \) \( x+y \) es 4. ( ) h. La cantidad de términos del polinomio co- ciente entre \( x^{7}-y^{7} y x-y \) es 7 . ( )

Suppose we know that the *sum* of the digits of a number is 42. Use appropriate divisibility tests to select all the statements that we know *must* be true. divisible by 5 divisible by 3 divisible by 9 divisible by 2 divisible by 10 divisible by 4 \( > \) Next Question

\( f(x)=3 x^{2}+6 x-45 \) A. The parabola opens downward and has a maximum value of -48 . B. The parabola opens upward and has a minimum value of (c) What is the range of \( f(x) \) ? The range of \( f(x) \) is \( [-48, \infty) \). (Type your answer in interval notation. Use integers or fractions for any nungibers in the expression.) (d) On what interval is the function increasing? The function is increasing on \( (-1, \infty) \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) On what interval is the function decreasing? The function is decreasing on \( \square \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

- \( \frac{b}{h^{2}} \div \frac{b^{2}}{h^{3}} \)

\( \begin{array}{ll}\text { (e) }-2 x y^{2} z \times 14 x^{2} y^{4} \times 5 z & \text { (f) }(-6 l m n) \times\left(\frac{-7}{4} l^{2} m^{2} n\right)\end{array} \) (g) \( \frac{4}{5} a^{2} x y \times \frac{20}{16} x^{2} y a \)

3. Calcula el sen \( x, \cos x y \operatorname{tg} x ; \) en función de \( \operatorname{tg} x / 2 \).

box is made from a piece of cardboard that measures 15 by 9 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular hat size square should be cut from each comer to obtain maximum volume? with a side of length \( \square \) inches should be cut away from each corner to obtain the maximum volume. to the nearest hundredth as needed.)

Your answer should be a polynomial in standard form. \[ (-8 k+1)(-8 k+1)=\square \]