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Questions in mathematics

📝 Answered - Evaluate the function for the given value. $\begin{array}{c} y=3 \cdot 3^x \text { for } x=1 \\ y=[?]\end{array}$

📝 Answered - Express $16 / 3$ as a decimal correct to 4 decimal places.

📝 Answered - 13) Indicate which of the following relationships are true and which are false: a. [tex]$Z ^{\prime} \subseteq Q$[/tex] b. [tex]$R \subseteq$[/tex] c. [tex]$Q \subseteq Z$[/tex] d. [tex]$Z \cup Z=Z$[/tex] e. [tex]$Z^{-} \cap Z^{+}=n$[/tex] f. [tex]$Q \cap R = Q$[/tex] g. [tex]$Q \cup Z=Q$[/tex] h. [tex]$Z ^{\prime} \cap R = Z ^{+}$[/tex] i. [tex]$Z \cup Q=Z$[/tex]

📝 Answered - a) [tex]$4 x^4+81$[/tex] b) [tex]$x^4+625 y^4$[/tex] c) [tex]$a^4+a^2 b^2+b^4$[/tex] d) [tex]$a^4+2 a^2+9$[/tex] e) [tex]$x^4-39 x^2+25$[/tex] f) [tex]$x^4 y^4+x^2 y^2+1$[/tex] g) [tex]$8 x^3+27$[/tex] h) [tex]$135 a^6 x+5 a^3 x^4$[/tex] i) [tex]$16 a^5 b-54 a^2 b^4$[/tex] j) [tex]$a^2-8 a-9+10 b-b^2$[/tex] k) [tex]$x^2-10 x+24+6 y-9 y^2$[/tex] l) [tex]$\left(1-x^2\right)\left(1-y^2\right)+4 x y$[/tex] m) [tex]$\left(x^2-4\right)\left(y^2-9\right)-24 x y$[/tex]

📝 Answered - Make $r$ the subject of $r+n=t$

📝 Answered - A line passes through $(1,5)$ and is parallel to $y=3 x-2$. Write its equation in slope-intercept form.

📝 Answered - Which unit of measure would be appropriate for the area of a picture that is 20 centimeters tall and 15 centimeters wide? A. Square centimeters B. Meters C. Cubic centimeters D. Centimeters

📝 Answered - Ms. Sutton recorded the word counts and scores of the top ten essays in a timed writing contest. The table shows her data. Winning Essay Length | Essay Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | | ---------- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Essay Score| 9.7 | 9.5 | 9.5 | 9.0 | 8.9 | 8.9 | 8.5 | 8.4 | 8.2 | 7.0 | | Word Count | 324 | 352 | 337 | 318 | 299 | 304 | 290 | 291 | 278 | 250 | How does the word count of an essay relate to its score in the contest? A. Word count tends to decrease as the score decreases. B. Word count tends to increase as the score decreases. C. Word count tends to remain constant as the score decreases. D. Word count has no apparent relationship to the score of the essay.

📝 Answered - Simplify by using the order of operations. $-|-5-5|-(-5-5)=$

📝 Answered - Let $a=\sqrt{2}$ and $b=\sqrt{3}$. (a) Find a rational number and an irrational number strictly between $a$ and $b$.