Solve r=100((g1-g^2)) - ScanMath

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Type your math problem... r=100((g1-g^2))

Question

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Find the vertex

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Find the axis of symmetry

Rewrite in vertex form

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(\frac{1}{2}, 25)

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Solve the equation

Solve for g

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Solve for r

g = \frac{5 + 25 - r}{10} g = \frac{5 - 25 - r}{10}

Evaluate

r = 100 (g \times 1 - g^{2})

Any expression multiplied by 1 remains the same

r = 100 (g - g^{2})

Swap the sides of the equation

100 (g - g^{2}) = r

Divide both sides

\frac{100 ( g - g ^{2} )}{100} = \frac{r}{100}

Divide the numbers

g - g^{2} = \frac{r}{100}

Move the expression to the left side

g - g^{2} - \frac{r}{100} = 0

Multiply both sides of the equation by LCD

(g - g^{2} - \frac{r}{100}) \times 100 = 0 \times 100

Simplify the equation

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100 g - 100 g^{2} - r = 0 \times 100

Any expression multiplied by 0 equals 0

100 g - 100 g^{2} - r = 0

Rewrite in standard form

- 100 g^{2} + 100 g - r = 0

Multiply both sides

100 g^{2} - 100 g + r = 0

Substitute a= 100,b= - 100 and c= r into the quadratic formula g = \frac{- b \pm b ^{2} - 4 a c}{2 a}

g = \frac{100 \pm ( - 100 ) ^{2} - 4 \times 100 r}{2 \times 100}

Simplify the expression

g = \frac{100 \pm ( - 100 ) ^{2} - 4 \times 100 r}{200}

Simplify the expression

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g = \frac{100 \pm 10000 - 400 r}{200}

Simplify the radical expression

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g = \frac{100 \pm 20 25 - r}{200}

Separate the equation into 2 possible cases

g = \frac{100 + 20 25 - r}{200} g = \frac{100 - 20 25 - r}{200}

Simplify the expression

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g = \frac{5 + 25 - r}{10} g = \frac{100 - 20 25 - r}{200}

Solution

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g = \frac{5 + 25 - r}{10} g = \frac{5 - 25 - r}{10}

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