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natima [27]
3 years ago
9

Sophie earns $12.80 per hour babysitting. She has to repay a loan to her parents in the

Mathematics
1 answer:
Lyrx [107]3 years ago
6 0

Answer:

Sophie has to work 18 hours to buy the sneakers.

Step-by-step explanation:

Since Sophie earns $ 12.80 per hour babysitting, and she has to repay a loan to her parents in the amount of $ 100, and after repaying the loan, she wants to have at least enough money to buy herself a pair of sneakers costing $ 130.40, for write an inequality modeling the number of hours, X, Sophie needs to work to have enough money to buy the sneakers, the following mathematical reasoning must be carried out:

12.80X = 100 + 130.40

12.80X = 230.4

X = 230.4 / 12.8

X = 18

So Sophie has to work 18 hours to buy the sneakers.

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\bf \stackrel{\textit{ball's height}~\hfill }{\stackrel{\downarrow }{h}=1+15t-5t^2}\implies \stackrel{\textit{ball's height}~\hfill }{\stackrel{\downarrow }{6}=1+15t-5t^2}\implies 0=-5+15t-5t^2 \\\\\\ ~~~~~~~~~~~~\textit{using the quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{5}t^2\stackrel{\stackrel{b}{\downarrow }}{-15}t\stackrel{\stackrel{c}{\downarrow }}{+5}=0 \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}

\bf t=\cfrac{-(-15)\pm\sqrt{(-15)^2-4(5)(5)}}{2(5)}\implies t=\cfrac{15\pm\sqrt{225-100}}{10} \\\\\\ t=\cfrac{15\pm\sqrt{125}}{10}\implies t=\cfrac{15\pm\sqrt{5^2 \cdot 5}}{10}\implies t=\cfrac{\stackrel{3}{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\pm ~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\sqrt{5}}{\underset{2}{~~\begin{matrix} 10 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}

\bf t=\cfrac{3\pm \sqrt{5}}{2}\implies t= \begin{cases} \frac{3+ \sqrt{5}}{2} \approx 2.618\\\\ \frac{3- \sqrt{5}}{2}\approx 0.382 \end{cases}

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3 years ago
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Answer:

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Step-by-step explanation:

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3 years ago
Un número real no puede pertenecer a los racionales y a los irracionales a la vez?​
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6 0
3 years ago
Part A: Write an algebraic expression for 6 more than 7 times a number. (5 points)
m_a_m_a [10]

The algebraic expression of the part A is 6+7x. And the verbal expression for 3*(n+8) is "the triple of the sum between the numbers n and 8".

<h3>Linear Expression</h3>

A linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=2x+7.

  • Part A

First, you should choose a variable for unknow number. Here, the variable will be x. Then, 7 times a number can be represented for 7x.

The word <em>more </em>will be represented for the add symbol (+). Thus,

the algebraic expression is 6+7x.

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The expression 3*(n+8) can be represented for the sentence:

The triple of the sum between the numbers n and 8.

Learn more about the algebraic expression here:

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2 years ago
Consider circle C with radius 5 cm and a central angle measure of 60°. What fraction of the whole circle is arc RS?
skelet666 [1.2K]

Answer:

There are a total of 360° in any given circle, so an arc swept out by 60° of that 360° would make up 60/360 = 1/6 of the circle's circumference.

The formal for the circumference of a circle comes out of the definition of one of the most famous constants in mathematics: π. π is defined as the ratio between a circle's circumference and its diameter, or:

From this definition, we can multiply both sides of the equation by d to obtain

or, circumference is π times the diameter. To find the diameter, we just need to double the radius, giving us 5 * 2 = 10cm. Usually you'll see π approximated as 3.14, which is likely what they want you to use here. Using that approximation, we find the circumference to be 3.14 * 10 = 31.4 cm.

Finally, to get the length of that arc, we just need to take 1/6 of the circumference (since the arc sweeps out 1/6 of the circle), giving us 31.4 * 1/6 ≈ 5.2 cm.

Step-by-step explanation:

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