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Questions in mathematics

[Jawaban] The hypotenuse of a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle measures 128 cm. What is the length of one leg of the triangle? A. 64 cm B. $64 \sqrt{2} cm$ C. 128 cm D. $128 \sqrt{2} cm$

[Jawaban] Given various values of the linear functions $f(x)$ and $g(x)$ in the table, determine the $y$-intercept of $(f-g)(x)$. | x | -6 | -4 | -1 | 3 | 4 | | :---- | :---- | :---- | :---- | :---- | :---- | | f(x) | -36 | -26 | -11 | 9 | 14 | | g(x) | 15 | 11 | 5 | -3 | -5 | A. $(0,9)$ B. $(0,3)$ C. $(0,-3)$ D. $(0,-9)$

[Jawaban] 2. [tex]x^2=x+6[/tex]

[Jawaban] Which function has a vertex at the origin? [tex]f(x)=(x+4)^2[/tex] [tex]f(x)=(x-4)(x+4)[/tex] [tex]f(x)=x(x-4)[/tex] [tex]f(x)=-x^2[/tex]

[Jawaban] Solve the system of equations. Enter your answer as an ordered pair. [tex] \begin{array}{l} 2 x+4 y=-8 \\ -3 x+4 y=2 \end{array} [/tex]

[Jawaban] An Insurance agent claims that the average age of policy holders who insure through him is less than the average age of all other agents, which is 30 years. A random sample of 100 policy holders who had insured through the agent gave the adjoining age distribution. | Age | 16-20 | 21-25 | 26-30 | 31-35 | 36-40 | 41-45 | |---|---|---|---|---|---|---| | Number of persons | 12 | 16 | 18 | 20 | 10 | 10 | Test the claim that the average age is less than the figure for all the other agents at a 5% level of significance.

[Jawaban] Which shows how to solve the equation [tex]$\frac{3}{4} x=-6$[/tex] for [tex]$x$[/tex] in one step? A. [tex]$\frac{4}{3}\left(\frac{3}{4}\right) x=-6\left(\frac{4}{3}\right)$[/tex] B. [tex]$4\left(\frac{3}{4}\right) x=-6(4)$[/tex] C. [tex]$4\left(\frac{3}{4}\right) x=-6(3)$[/tex] D. [tex]$\frac{4}{3}\left(\frac{3}{4}\right) x=-6\left(\frac{3}{4}\right)$[/tex]

[Jawaban] What is one of the solutions to the following system? [tex]\begin{array}{l} y-3=x \ x^2-6 x+13=y\end{array}[/tex] A. (8,5) B. (-5,2) C. (2,5) D. (-2,1)

[Jawaban] Which equations have the same value of $x$ as $\frac{5}{6} x+\frac{2}{3}=-9$ ? Select three options. $6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9$ $6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9(6)$ $5 x+4=-54$ $5 x+4=-9$ $5 x=-13$ $5 x=-58$

[Jawaban] Graph the equation. [tex]$y=-\frac{3}{2} x^2-6 x$[/tex]