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Questions in mathematics

[Answered] 1. (3x³ + 4x² - 5x - 30) ÷ (x - 2) = 2. (-4x³ + 6x² + 4x - 6) ÷ (2x - 3) = 3. (2x³ - 3x² + 17x + 39) ÷ (2x + 3) = 4. (x³ + x² + 3x - 18) ÷ (x - 2) = 5. (x³ - 2x² + 16) ÷ (x + 2) = 6. (4x³ - 2x² + 2x - 1) ÷ (2x - 1) = 7. (5x³ - 2x² + 5x - 2) ÷ (5x - 2) = 8. (x³ - 2x² - 2x + 12) ÷ (x + 2) =

[Answered] 14. Let's evaluate. a) 4^(1/2) b) 25^(3/2) c) (4/9)^(1/2) d) (8/27)^(1/3) e) (16/81)^(1/4) f) (32/243)^(1/5) 15. Let's simplify. a) (a^5 × a^7) / a^9 b) (p^6 × p^4) / p^3 c) (x^7 × x^(-2)) / x^3 d) (y^10 × y^(-4)) / y^4 e) (4x^5 × 3x) / 6x^2 16. Let's simplify. a) (2^2)^3 b) (3^4)^3 c) (5 / 5^4)^2 d) (9^2 / 3^2)^3 e) (4^3 / 2^3)^4 f) (8^2 / 2^9)^5 g) (27^2 / 3^10) 17. Let's simplify. a) (2^3 × 4^3 × 8^4) / (2^2 × 4^5 × 16^2) b) (3^2 × 9^3 × 27^4) / (3^3 × 9^4 × 81^2) c) (2^2 × 3^4 × 12^3) / (2^5 × 6^3) d) (6^4 × 9^2 × 25^3) / (3^2 × 4^2 × 15^6) e) (4^3 / 25^2)^2 × (3^4 / 3^2)^2 × (9^2 / 27^2)^2 f) (5^3 / 25^2)^2 × (8^2 / 4^2)^3 × (5 / 2)^4 18. Let's simplify. a) x^(a-b) × x^(b-a) b) x^(a-b) × x^(b-c) × x^(c-a) c) (x^a)^(b-c) × (x^b)^(c-a) × (x^c)^(a-b) d) (x^(p-q))^r × (x^(q-r))^p × (x^(r-p))^q e) (x^(a+b) × x^(b+c) × x^(c+a)) / (x^(2a) × x^(2b) × x^(2c)) f) ((x^2)^(a+b) × (x^2)^(b+c) × (x^2)^(c+a)) / (x^a × x^b × x^c)^4 19. a) If a = 1 and b = 2, find the value of: (i) a^b (ii) b^a (iii) (a+b)^(a+b) b) If x = 5 and y = 3, find the value of: (i) x^y (ii) y^x (iii) (x-y)^(x-y)

[Answered] The graph of $h(x) = -\log_5(x+5)$. Find the coordinates of the intercepts and the equation of the asymptote of $h(x)$. Explain how to find these using the graph.

[Answered] Which equation represents a line that passes through $(5,1)$ and has a slope of $\frac{1}{2}$? A. $y-5=\frac{1}{2}(x-1)$ B. $y-\frac{1}{2}=5(x-1)$ C. $y-1=\frac{1}{2}(x-5)$ D. $\left.y-1=5^{\prime} x-\frac{1}{2} \right\rvert\,$

[Answered] Which values represent solutions to the equation? [tex]\tan \left(\frac{3 \pi}{4}-2 x\right)=-1[/tex], where [tex]$x \in[0, \pi]$[/tex] A. [tex]$\left\{0, \pi\right\}$[/tex] B. [tex]$\left\{0, \frac{\pi}{2}, \pi\right\}$[/tex] C. [tex]$\left\{0, \pi, 2 \pi\right\}$[/tex]

[Answered] Some researchers claim there is an association between owning a dog and developing a flea infestation at home. They took a random sample of people living in St. Louis, Missouri, and recorded whether they had a dog and whether they had a flea infestation in their home. The results are shown in the following two-way relative frequency table: | | Has Flea Infestation | Does Not Have Flea Infestation | Row Totals | | :-------------------- | :------------------- | :----------------------------- | :--------- | | Does not have a dog | 0.015 | 0.652 | 0.667 | | Has one dog | 0.022 | 0.261 | 0.283 | | Has more than one dog | 0.032 | 0.019 | 0.050 | | Column Totals | 0.069 | 0.931 | 1 | What is the conditional relative frequency of having more than one dog, given there is a flea infestation? Round your answer to the nearest thousandths place.

[Answered] What is the midpoint of a line segment with the endpoints (8,-3) and (-5, -9)? A. (-6, 1.5) B. (1.5, -6) C. (2.5,-7) D. (-7, 2.5)

[Answered] Let the universal set be the natural numbers from 40 to 60 inclusive. The universal set contains the following subsets: - [tex]$F=$[/tex] {multiples of 6 } - [tex]$T=$[/tex] {multiple of 2 } True or False. [tex]$F \subset T$[/tex]?

[Answered] What is the relationship between the successive terms in the sequence shown? [tex]$9,-1,-11,-21, \ldots$[/tex] A. The common difference is -10. B. The common difference is 10. C. The common ratio is -9. D. The common ratio is 9.

[Answered] On any given day, the number of users, [tex]$u$[/tex], that access a certain website can be represented by the inequality [tex]$|125-u| \leq 30$[/tex]. Which of the following represents the range of users that access the website each day? A. [tex]$u \geq 95$[/tex] or [tex]$u \leq 155$[/tex] B. [tex]$95 \geq u \geq 155$[/tex] C. [tex]$u \leq 95$[/tex] or [tex]$u \geq 155$[/tex] D. [tex]$95 \leq u \leq 155$[/tex]