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Alex787 [66]
2 years ago
10

Write the equation using function notation f(x). then find f(0) 2x^2 - 3y = 6

Mathematics
1 answer:
Grace [21]2 years ago
8 0

\quad \huge \quad \quad \boxed{ \tt \:Answer }

\qquad \tt \rightarrow \: f(0) = -2

____________________________________

\large \tt Solution  \: :

\qquad \tt \rightarrow \: 2 {x}^{2}  - 3y = 6

\qquad \tt \rightarrow \: 3y + 6 = 2 {x}^{2}

\qquad \tt \rightarrow \: 3y = 2 {x}^{2}  - 6

\qquad \tt \rightarrow \: y =  \cfrac{2 {x}^{2} - 6 }{3}

\qquad \tt \rightarrow \: y =  \cfrac{2 {}^{} }{3}  {x}^{2}  - 2

[ here, y can be replaced with f(x) because y is a function of x ]

\qquad \tt \rightarrow \: f(x) =  \cfrac{2 {}^{} }{3}  {x}^{2}  - 2

\large\textsf{Find f(0):}

\qquad \tt \rightarrow \: f(0) =  \cfrac{2 {}^{} }{3}  {(0)}^{2}  - 2

\qquad \tt \rightarrow \: f(0) =  0  - 2

\qquad \tt \rightarrow \: f(0) =   - 2

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

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The complete question in the attached figure

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<span>then
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the answer is the option C) (6, -8.75)

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3 years ago
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The following set of coordinates represents which figure? (7, 10), (4, 7), (6, 5), (9, 8) Parallelogram Rectangle Rhombus Square
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Answer:

The figure is a rectangle

Step-by-step explanation:

* Lets explain how to solve the problem

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  lets find the distance between each two points and the slopes of

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 d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}

- The rule of the slope is m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

- <em>Remember:</em>

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* The product of the slopes of the perpendicular lines is -1

# points (7 , 10) and (4 , 7)

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∵ m1=\frac{7-10}{4-7}=\frac{-3}{-3}=1

# points (4 , 7) and (6 , 5)

∵ d2=\sqrt{(6-4)^{2}+(5-7)^{2}}=\sqrt{8}

∵ m2=\frac{5-7}{6-4}=\frac{-2}{2}=-1

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∵ d4=\sqrt{(7-9)^{2}+(10-8)^{2}}=\sqrt{8}

∵ m4=\frac{10-8}{7-9}=\frac{2}{-2}=-1

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∵ m1 = m3 = 1 and m2 = m4 = -1

∴ Each two opposite sides are parallel

∵ m1 × m2 = 1 × -1 = -1

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1. Each two opposite sides are equal

2. Each two opposite sides are parallel

3. Each two adjacent sides are perpendicular

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