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3 years ago

Which of the following functions represents the graph on

Mathematics

1 answer:

Svetlanka [38]3 years ago

6 0

9514 1404 393

Answer:

f(x) = (x -6)(x +2)

Step-by-step explanation:

The graph shows the x-intercepts are -2 and +6. The factors will be binomials such that these values make the factors zero: (x +2) and (x -6).

f(x) = (x -6)(x +2)

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Read 2 more answers

Find the Value of Sin A rounded to the nearest hundredth, if necessary.

leonid [27]

Step-by-step explanation:

In trigonometry, the law of sines is an equation that relates the length of the sides of a triangle (any type of triangle) to the sines of its angles. This is expressed mathematically as

$\displaystyle\frac{a}{\sin \alpha} \ = \ \displaystyle\frac{b}{\sin \beta} \ = \ \displaystyle\frac{c}{\sin \gamma}$ ,

where $a$ , $b$ , and $c$ are the lengths of the sides of the triangle and $\alpha$ , $\beta$ , and $\gamma$ are the opposite angles (as shown in the figure below). Likewise, the law is sometimes written as it reciprocals,

$\displaystyle\frac{\sin \alpha}{a} \ = \ \displaystyle\frac{\sin \beta}{b} \ = \ \displaystyle\frac{\sin \gamma}{c}$ .

Therefore,

$\displaystyle\frac{\sin A}{BC} \ = \ \displaystyle\frac{\sin B}{AC} \\ \\ \\ \sin A \ = \ \displaystyle\frac{\sin B \ \times \ BC}{AC} \\ \\ \\\sin A \ = \ \displaystyle\frac{\sin \left(90^{\circ}\right) \ \times \ \sqrt{\left(10\right)^{2} \ - \ \left(\sqrt{78}\right)^{2}}}{10} \\ \\ \\ \sin A \ = \ \dsiplaystyle\frac{\sqrt{22}}{10} \\ \\ \\ \sin A \ = \ 0.47 \ \ \ \ (\text{nearest hundredth})$

Alternatively, you can solve this question using the definition of the trigonometric function sine. For the angle $\theta$ in the figure below,

$\sin \theta \ = \ \displaystyle\frac{\text{opposite}}{\text{hypothenuse}}$ .

Therefore,

$\sin A \ = \ \displaystyle\frac{BC}{AC} \\ \\ \\ \sin A \ = \ \displaystyle\frac{\sqrt{\left(10\right)^{2} \ - \ \left(\sqrt{78}\right)^{2}}}{10} \\ \\ \\ \sin A \ = \ \displaystyle\frac{\sqrt{22}}{10} \\ \\ \\ \sin A \ = \ 0.47 \ \ \ \ (\text{nearest hundredth})$

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2 years ago

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vlabodo [156]

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4 years ago