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VMariaS [17]
3 years ago
9

Jill charges an hourly rate for babysitting one or two children. Kara charges a lower hourly

Mathematics
1 answer:
Assoli18 [71]3 years ago
5 0

<u>Options</u>

Which statement is true:

a) Jill will make less money if they each work 4 hours.

b) Jill's hourly rate is $3 more than kara's.

c) Kara charges $14 and hour for babysitting two children.

d) Kara's fee for the second child is $5.

Answer:

(D)Kara's fee for the second child is $5.

Step-by-step explanation:

\left|\begin{array}{c|c|c}$Time(hr)&$Jill: Cost for Two Children& $Kara: Cost for Two Children\\-----&------&-----\\1&11&14=9+5\\2&22&23=9(2)+5\\3&33&32=9(3)+5\end{array}\right|

From the table above,

Jill Charges an hourly rate of $11

Kara charges an hourly rate of $9 and an additional $5 charge for more than one child. Therefore, the statement that is true is Option D.

Kara's fee for the second child is $5.

All other options are incorrect.

<u>Check</u>

Option A: In four hours, Jill will make $44 while Kara will make $41

Option B: Jill's hourly rate is $2 more than Kara's, NOT $3.

Option C: Kara charges $9 an hour, NOT $14.

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The equation of the parabola  that describes the path of her jump is \mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}

The given parameters are:

\mathbf{Height = 20}

\mathbf{Length = 28}

<em>Assume she starts from the origin (0,0)</em>

The midpoint would be:

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So, the vertex of the parabola is:

\mathbf{Vertex = (Mid,Height)}

Express properly as:

\mathbf{(h,k) = (14,20)}

A point on the graph would be:

\mathbf{(x,y) = (28,0)}

The equation of a parabola is calculated using:

\mathbf{y = a(x - h)^2 + k}

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\mathbf{y = a(x - 14)^2 + 20}

Substitute \mathbf{(x,y) = (28,0)} in \mathbf{y = a(x - 14)^2 + 20}

\mathbf{0 = a(28 - 14)^2 + 20}

\mathbf{0 = a(14)^2 + 20}

Collect like terms

\mathbf{a(14)^2 =- 20}

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\mathbf{a =- \frac{20}{14^2}}

\mathbf{a =- \frac{20}{196}}

Simplify

\mathbf{a =- \frac{5}{49}}

Substitute \mathbf{a =- \frac{5}{49}} in \mathbf{y = a(x - 14)^2 + 20}

\mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}

Hence, the equation of the parabola  that describes the path of her jump is \mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}

See attachment for the graph

Read more about equations of parabola at:

brainly.com/question/4074088

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Answer:

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Step-by-step explanation:

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