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Questions in mathematics

[Done] Simplify the expression below. $\frac{12 x^3-14 x^2-40 x}{2 x-5}$ A. $2 x^3+3 x$ B. $3 x^2-15$ C. $6 x^2+8 x$ D. $7 x^2-4 x$

[Done] A student solved the equation below by graphing. [tex]$\log _6(x-1)=\log _2(2 x+2)$[/tex] Which statement about the graph is true? A. The curves do not intersect. B. The curves intersect at one point. C. The curves intersect at two points. D. The curves appear to coincide.

[Done] Expand the following logarithmic expression. $\log _5\left(8 \frac{\sqrt{t}}{v}\right)$

[Done] Solve for x. 3x = 6x - 2

[Done] Sameer chose 12 different toppings for his frozen yogurt sundae, which was $\frac{3}{4}$ of the total number of different toppings available at the make-your-own sundae shop. To determine the number of different toppings available at the shop, Sameer set up and solved the equation as shown below. $\begin{aligned} \frac{3}{4} & =\frac{x}{12} \\ \frac{3}{4}(12) & =\frac{x}{12}(12) \\ 9 & =x \end{aligned} Which best describes the error that Sameer made? A. Sameer did not use the correct equation to model the given information. B. Sameer should have multiplied both sides of the equation by $\frac{4}{3}$ instead of by 12.

[Done] True or False: 1) The predecessor of 100 is 99.

[Done] 3. Write a 9-digit number where each digit is bigger than the previous one. How many such numbers exist? 4. Strike out 10 digits from the number 123451234512345 so that the remaining number is as large as possible. 5. The words 'zero' and 'one' share letters 'e' and 'o'. The words 'one' and 'two' share a letter 'o', and the words 'two' and 'three' also share a letter 't'. How far do you have to count to find two consecutive numbers which do not share an English letter in common?

[Done] Round each decimal number to the nearest whole number. 2.94 = 3 34.33 = 35 44.9 = 45 17.723 = 59.04 = 60 119.6 = 39.672 = 40 88.667 = 68.841 = 69 0.993 = 1.137 = 2 80.82 = 39.762 = 40 72.93 = 8.72 = 9 6.6794 = 3.898 = 4 2.93 = 3

[Done] Which of the following sequences is an arithmetic sequence and why? 1. $3,7,11,15,19$ 2. $4,16,64,256$ 3. $48,24,12,6,3, \ldots$ 4. $1,4,9,16,25,36$ 5. $1, \frac{1}{2}, 0,-\frac{1}{2}$ 6. $-2,4,-8,16, \ldots$ 7. $1,0,-1,-2,-3$ 8. $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots$ 9. $3 x, x, \frac{x}{3}, \frac{x}{9}, \ldots$ 10. $9.5, 7.5, 5.5$

[Done] Solve the equation for $X$. $X-3\left[\begin{array}{cc} 2 & -8 \\ -4 & 2 \end{array}\right]=\left[\begin{array}{cc} 4 & -6 \\ 2 & -8 \end{array}\right]$