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Questions in mathematics

[Done] Write the multiples of 6 that are greater than 20 but less than 50. Write all the multiples of 17 that are less than 80. Write all the multiples of 19 that are two-digit numbers. Find the LCM of: (a) 5 and 10 (b) 5, 6 and 10 (c) 6 and 8

[Done] Describe the key features of a parabola with the equation [tex]x^2=40 y[/tex]. The value of [tex]p[/tex] is $\square$. The parabola opens $\square$. The coordinates of the focus are $\square$. The equation for the directrix is $\square$.

[Done] Which fraction is equivalent to $\frac{2}{6} $? A. $\frac{3}{7}$, because $\frac{2}{6}=\frac{2+1}{6+1}=\frac{3}{7}$ B. $\frac{3}{9}$, because $\frac{2}{6}=\frac{1}{3}$ and $\frac{1}{3}=\frac{3}{9}$ C. $\frac{3}{12}$, because $\frac{2}{6}=\frac{1}{3}$ and $\frac{1}{3}=\frac{3}{12}$ D. $\frac{3}{8}$, because $\frac{2}{6}=\frac{1}{2}=\frac{2+1}{6+2}=\frac{3}{8}$

[Done] Given the following system of equations: [tex] \begin{array}{l} 2 x+6 y=12 \\ 4 x+3 y=15 \end{array} [/tex] Which action creates an equivalent system that will eliminate one variable when they are combined? A. Multiply the second equation by -2 to get [tex]$-8 x-6 y=-30$[/tex]. B. Multiply the first equation by 2 to get [tex]$4 x+12 y=24$[/tex]. C. Multiply the second equation by -4 to get [tex]$-16 x-12 y=-60$[/tex]. D. Multiply the first equation by -4 to get [tex]$-8 x-24 y=-48[/tex]

[Done] What is the greatest common factor of the polynomial below? [tex]12 x^2-9 x[/tex] A. [tex]3 x[/tex] B. [tex]4 x[/tex] C. [tex]3 x^2[/tex] D. [tex]4 x^2[/tex]

[Done] Write as a radical expression and evaluate if possible. [tex]$32^{\frac{1}{5}}$[/tex] A. [tex]$\sqrt[5]{32}=-2$[/tex] B. [tex]$\sqrt[5]{32}=3$[/tex] C. [tex]$\sqrt[5]{32}$[/tex], not possible D. [tex]$\sqrt[5]{32}=2$[/tex]

[Done] Orchid wants to retile her bathroom floor, which has an area of 40 square feet. She is deciding between two types of custom tiles. The square tile is [tex]$\frac{1}{2}$[/tex] foot by [tex]$\frac{1}{2}$[/tex] foot and costs $0.45 per tile. The rectangular tile is 2 feet by [tex]$\frac{1}{4}$[/tex] foot and costs $0.80 per tile. Which tile should Orchid choose to minimize costs? Explain. A. She should choose the square tiles because the total cost will be $8 less. B. She should choose the rectangular tiles because the total cost will be $8 less. C. She should choose the square tiles because the total cost will be $14 less. D. She should choose the rectangular tiles because the total cost will be $14 less.

[Done] Select the correct answer. What is the complete factorization of $x^2+4 x-45 ?$ A. $(x+15)(x-3)$ B. $(x-9)(x+5)$ C. $(x+9)(x-5)$ D. $(x-15)(x+3)$

[Done] Which points lie on the graph of the function [tex]f(x)=\lceil x\rceil+2[/tex]? Check all that apply. [tex](-5.5,-4)[/tex] [tex](-3.8,-2)[/tex] [tex](-1.1, 1)[/tex] [tex](-0.9, 2)[/tex] [tex](2.2,5)[/tex] [tex](4.7,6)[/tex]

[Done] Points and their residual values are shown in the table. | x | y | Residual | |---|---|----------| | 1 | 2 | -0.4 | | 2 | 3.5 | 0.7 | | 3 | 5 | -0.2 | | 4 | 6.1 | 0.19 | | 5 | 8 | -0.6 | Which residual value is the farthest from the line of best fit? A. 0.19 B. 0.7 C. 2 D. 8