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Questions in mathematics

[Jawaban] What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point $(4,1)$? A. $y-1=-2(x-4)$ B. $y-1=-\frac{1}{2}(x-1)$ C. $y-1=\frac{1}{2}(x-4)$ D. $y-1=2(x-4)$

[Jawaban] If $y$ varies directly as $x$, and $y$ is 18 when $x$ is 5, which expression can be used to find the value of $y$ when $x$ is 11? A. $y=\frac{5}{18}(11)$ B. $y=\frac{18}{5}(11)$ C. $y=\frac{(18)(5)}{11}$ D. $y=\frac{11}{(18)(5)}$

[Jawaban] Given: A. [tex]$\sin (x)$[/tex] B. [tex]$\cos (x)$[/tex] C. [tex]$\cos (y)$[/tex] D. [tex]$\sin (y)$[/tex] Use the drop-down menus in the derivation of the cosine sum identity: [tex]$\begin{array}{l} sin (x+y) \ =\cos \left(\frac{\pi}{2}-(x+y)\right) \ =\cos \left(\left(\frac{\pi}{2}-x\right)-y\right) \ =\cos \left(\frac{\pi}{2}-x\right) \quad \hat{0}+\sin \left(\frac{\pi}{2}-x\right) \ =\sin (x) \cos (y)+\cos (x) \sin (y) \end{array}$[/tex]

[Jawaban] Which of the following points lies on the line [tex]$3 x-y=-1$[/tex]? (-1,3) (1,2) (1,4) (2,5)

[Jawaban] Evaluate the limit [tex]$\lim _{x \rightarrow \infty} \frac{9 x^3-2 x^2-3 x}{8-11 x-3 x^3}$[/tex]

[Jawaban] 1) Find the midpoint of the line with endpoints A(-3, -2) and B(4, 3). 2) Copy and complete the table for $f(x) = 7 + 4x - 3x^2$ for the interval $-3 \leq x \leq 3$. | x | -3 | -2 | -1 | 0 | 0.5 | 1.5 | 2.5 | 3 | |---|---|---|---|---|---|---|---|---| | f(x) | -32 | | | 7 | 7.5 | | 1 | 8 | 3) Using 1 cm as 1 unit on the x-axis and 2 units on the y-axis, draw the graph of $y = f(x)$ for the given interval.

[Jawaban] In the form of a guide, write numbers 1 to 100. a. Identify all prime numbers by applying the division rule. b. Find the common multiple of 4, 5, 6.

[Jawaban] The equation below models the height in feet, $h$, of a softball $t$ seconds after it is hit by a batter. $h=-16 t^2+105 t+3$ Why is the height of the ball a function of time? A. Each value of time is associated with exactly one height. B. Each height of the ball is associated with exactly one moment in time. C. There is exactly one time at which the maximum height is attained. D. There is a maximum and minimum height that the ball can reach.

[Jawaban] The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

[Jawaban] Choose the correct simplification of [tex]$9 x^2\left(4 x+2 x^2-1\right)$[/tex]. A. [tex]$18 x^4+36 x^3-9 x^2$[/tex] B. [tex]$18 x^4-36 x^3+9 x^2$[/tex] C. [tex]$36 x^4+18 x^3-9 x^2$[/tex] D. [tex]$36 x^4-13 x^3+9 x^2$[/tex]