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algol [13]
3 years ago
10

Niki wants to buy a dog bed the cost $87. She earns $6 per week for doing chores. How many weeks will Niki have to do her chores

in order to earn enough money to pay for the dog bed.
Mathematics
1 answer:
Viktor [21]3 years ago
7 0

Answer:

The answer to your question is 14.5 weeks

Step-by-step explanation:

Data

Total cost = C = $87

money earned = m = $6

Number of weeks to have the money = w = ?

Process

1.- Write an equation that represents the situation

            Weeks = Total cost / Money earned

             w = C/m

2.- Substitute the values

             w = 87 / 6

3.- Result

             w = 14.5

4.- Conclusion

Niki will last 14.5 weeks to have enough money to buy a dog bed.

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Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fo
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Answer:

y  = -6(x - \frac{1}{2})^2 -\frac{7}{2}

Step-by-step explanation:

Given:

y = -6x^2 + 3x + 2

Required

Rewrite in vertex form

The vertex form of an equation is in form of: y = a(x - h)^2+ k

Solving: y = -6x^2 + 3x + 2

Subtract 2 from both sides

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Factorize expression on the right hand side by dividing through by the coefficient of x²

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y - 2 = -6(x^2 - \frac{3x}{6})

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Get a perfect square of coefficient of x; then add to both sides

------------------------------------------------------------------------------------

<em>Rough work</em>

The coefficient of x is \frac{-1}{2}

It's square is (\frac{-1}{2})^2 = \frac{1}{4}

Adding inside the bracket of -6(x^2 - \frac{x}{2}) to give: -6(x^2 - \frac{x}{2} + \frac{1}{4})

To balance the equation, the same expression must be added to the other side of the equation;

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------------------------------------------------------------------------------------

The expression becomes

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y - 2 -\frac{6}{4}= -6(x^2 - \frac{x}{2} + \frac{1}{4})

y - 2 -\frac{3}{2}= -6(x^2 - \frac{x}{2} + \frac{1}{4})

Factorize the expression on the right hand side

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y - (2 +\frac{3}{2})= -6(x - \frac{1}{2})^2

y - (\frac{4+3}{2})= -6(x - \frac{1}{2})^2

y - (\frac{7}{2})= -6(x - \frac{1}{2})^2

y  +\frac{7}{2} = -6(x - \frac{1}{2})^2

Make y the subject of formula

y  = -6(x - \frac{1}{2})^2 -\frac{7}{2}

<em>Solved</em>

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