Mathematics Questions & Answers

\( = \sqrt { ( \operatorname { Sen } ^ { 2 } x - \operatorname { Cos } ^ { 2 } x ) ( \operatorname { Sen } ^ { 4 } x + \operatorname { Cos } ^ { 4 } x ) + \operatorname { Cos } ^ { 8 } x } \)

Which of the following is the value of \( \log 10^{20} \) ? (1 point) \( \frac{1}{2} \) 2 200 20

A line that includes the points \( (-8, v) \) and \( (-6,-10) \) has a slope of -8 . What is the value of \( v \) ?

Which of the following logarithmic expressions is undefined? (1 point) \( 0 \log _{3} 27 \) \( \log _{3}-9 \) \( \log _{0.25} 64 \) \( 0 \log _{2.5} 6.25 \)

\( 1 \leftarrow \quad \begin{array}{l}\text { A company finds it can produce } 25 \text { heaters for } \$ 6550 \text {, while producing } 30 \text { heaters costs } \$ 7800 \text {. Express the cost, } \\ \text { as a linear function of the number of heaters, } x \text {. Determine the cost to produce } 40 \text { heaters. } \\ \text { Express the cost, } y \text {, as a linear function of the number of heaters, } x \text {. } \\ y=\square \\ \text { (Simplify your answer.) } \\ \text { The cost to produce } 40 \text { heaters is } \$ \square\end{array} \).

Solve for \( m \) \[ \begin{array}{l}-8-5 m=-3 m+6 \\ m=\square \\ \text { Submit }\end{array} \]

Triangles \( \triangle A O B \) and \( \triangle A O C \) have vertices \( A(0,7), B(-1,-2), C(2,-1) \), and \( O(0,0) \). Show that \( m \angle A O B>m \angle A O C \). Select the correct choice below and fill in the answer boxes within your choice. (Type an integer or decimal rounded to the nearest thousandth as needed.) A. Since \( A B=\square \) and \( A C=\square, \overline{A B}>\overline{A C} \), and thus \( m \angle A O B>m \angle A O C \). B. Since \( A B=\square \) and \( A C=\square, \overline{A B}=\overline{A C} \), and thus \( m \angle A O B>m \angle A O C \). C. Since \( A B=\square \) and \( A C=\square, \overline{A B}<\overline{A C} \), and thus \( m \angle A O B>m \angle A O C \).

Rewrite \( 10^{3}=1000 \) as a logarithmic equation. (1 point) \( \log _{10} 1000=3 \) \( \log _{10} 3=1000 \) \( \log _{1000} 3=10 \) \( \log _{3} 1000=10 \)

5) \( \operatorname{sen}^{2}\left(x^{2}+3\right)+\cos ^{2}\left(x^{2}+3\right) \)

It costs a \( \$ 13 \) flat fee to rent a lawn mower, plus \( \$ 2 \) a day starting with the first day. Let \( x \) represent the number of days rented, so \( y \) represents the charge to the user (in dollars). Write an equation in the form \( \mathrm{y}=\mathrm{mx}+\mathrm{b} \) that represents this situation. \( \mathrm{y}=\square \) The ordered pair associated with the x -value of 5 is \( \square \). (Type your answer as an ordered pair.)