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Questions in mathematics

📝 Answered - A triangle's three angles always add up to [tex]$\qquad$[/tex]. Select one: a. [tex]$45^{\circ}$[/tex] b. [tex]$90^{\circ}$[/tex] c. [tex]$180^{\circ}$[/tex] d. [tex]$360^{\circ}$[/tex]

📝 Answered - The graph of $h(x)=|x-10|+6$ is shown. On which interval is this graph increasing? A. $(-\infty, 6)$ B. $(-\infty, 10)$ C. $(6, \infty)$ D. $(10, \infty)$

📝 Answered - A cyclist and a jogger start at the same time from the same point. The cyclist travels 15 km/h faster and arrives 2 hours earlier over 90 km. Find both speeds.

📝 Answered - What is the least common denominator of the rational expressions. $\frac{-15}{10 x^3}, \frac{1}{8 x^2(x-6)^3}, \frac{14}{x^5\left(x^2-36\right)}$ A. $80 \cdot x^2 \cdot(x-6) \cdot(x+6)$ B. $40 \cdot x^2 \cdot(x-6) \cdot(x+6)$ C. $80 \cdot x^5 \cdot(x-6)^3 \cdot(x+6)$ D. $40 \cdot x^5 \cdot(x-6)^3 \cdot(x+6)$

📝 Answered - Consider the following function: [tex]f(x) = 6\cos(x) + 2\cos(2x), \quad (0, 2\pi)[/tex] Find [tex]f'(x)[/tex]. [tex]f'(x) = -6\sin(x) - 4\sin(2x)[/tex] Find [tex]f''(x)[/tex]. Find the points of inflection of the graph of the function. (Round your answers to three decimal places. If a value does not exist, enter DNE.) (x, y) = ( [ ] , [ ] ) (x, y) = ( [ ] , [ ] ) (x, y) = ( [ ] , [ ] ) (x, y) = ( [ ] , [ ] ) largest x-value concave upwards [ ] concave downwards [ ]

📝 Answered - Select the correct answer. Which number has a terminating decimal expansion? A. [tex]$\frac{3}{4}$[/tex] B. [tex]$\sqrt{12}$[/tex] C. [tex]$\frac{8}{8}$[/tex] D. [tex]$\frac{2}{1}$[/tex]

📝 Answered - Which statement describes the solutions of this equation? [tex]\frac{x}{3}+\frac{x-1}{x+4}=\frac{x+3}{x+4}[/tex] A. The equation has no valid solutions and two extraneous solutions. B. The equation has one valid solution and no extraneous solutions. C. The equation has one valid solution and one extraneous solution. D. The equation has two valid solutions and no extraneous solutions.

📝 Answered - The sum of the lengths of all the edges of a cube is 6 cm. What is the volume, in cubic cm, of the cube? A. [tex]$1 / 8$[/tex] B. [tex]$1 / 4$[/tex] C. [tex]$1 / 2$[/tex] D. 1

📝 Answered - Write $\frac{3}{16}$ as a decimal figure.

📝 Answered - If $x=-5+2 \sqrt{-4}$, find the value of $x^4+9 x^3+35 x^2-x+4$