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3 years ago

GIVE CORRECT ANS FOR BRAINLIEST

Mathematics

2 answers:

gizmo_the_mogwai [7]3 years ago

7 0

<h3>Solution:</h3>

$2 \frac{5}{6} - 2 \frac{1}{2} \\ = \frac{17}{6} - \frac{5}{2} \\ = \frac{17 - 15}{6} \\ = \frac{2}{6} \\ = \frac{1}{2}$

<h3>Answer:</h3>

$\frac{1}{2}$

Hope it helps.

Do comment if you have any query.

Mumz [18]3 years ago

4 0

2^5/6 - 2^1/2
=2^5/6 - 2^3/6
=5/6-3/6
=2/6

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Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

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Substitute point (0, -4) into the equation:

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$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

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Nuetrik [128]

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Step-by-step explanation:

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