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Questions in mathematics

[Jawaban] (a) Express y = -x² + 2x + 3 in the form a(x + p)² + q. (b) Hence, write down the coordinates of the turning point on the graph of y = -x² + 2x + 3.

[Jawaban] Fill in the blanks: 1. A sphere has ______ corners. 2. The dice is an example of a cube. 3. A cylinder has 2 flat faces. 4. A solid having ______ surface rolls. 5. A cuboid has 12 edges.

[Jawaban] \begin{array}{l}2 x-3 y=4 \\ 4 x-y=13\end{array}

[Jawaban] Write each of the following numbers as a power with an exponent to the base 4. [tex]$\frac{1}{256}$[/tex]

[Jawaban] Summer Plans | | Camp | No Camp | Total | | :-------------------- | :--- | :------ | :---- | | Swimming Lessons | 42 | 32 | 74 | | No Swimming Lessons | 18 | 4 | 22 | | Total | 60 | 36 | 96 | Which is the joint relative frequency for school children who plan to attend camp and have swimming lessons? Round the answer to the nearest percent. A. 4% B. 19% C. 33% D. 44%

[Jawaban] Suppose that two certain cars have the following average operating and ownership costs. | | Average Costs per Mile | | :---- | :-------------------------------------------------- | | | Operating | Ownership | Total | | Car A | $0.24 | $0.74 | $0.98 | | Car B | | | | If you drive 30,000 miles per year, by how much does the total annual expense for Car A exceed that of Car B over six years? The total annual expense for Car A exceeds that of Car B by $$\square$$ over six years. (Round to the nearest dollar as needed.)

[Jawaban] Use Kelly's steps to simplify this expression. $\left(5 w^7\right)^2$ What is the simplified power of the product? $5 w^9$ $10 w^{14}$ $25 w^9$ $25 w^{14}$

[Jawaban] Solve for $g$ in the proportion. [tex]\frac{172}{g}=\frac{2}{9}[/tex] $g=\square$

[Jawaban] Choose the correct simplification and demonstration of the closure property given: $\left(2 x^3+x^2-4 x\right)-\left(9 x^3-3 x^2\right)$. A. $-7 x^3+4 x^2-4 x$; may or may not be a polynomial B. $-7 x^3+4 x^2-4 x$; is a polynomial C. $11 x^3-2 x^2-4 x$; may or may not be a polynomial D. $11 x^3-2 x^2-4 x ;$ is a polynomial

[Jawaban] If [tex]f(x)=x^4-x^3+x^2[/tex] and [tex]g(x)=-x^2[/tex], where [tex]x \neq 0[/tex], what is [tex](f / g)(x)[/tex]? A. [tex]x^2-x+1[/tex] B. [tex]x^2+x+1[/tex] C. [tex]-x^2+x-1[/tex] D. [tex]-x^2-x-1[/tex]