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liq [111]
3 years ago
9

At bike shop x it costs $2.75 per hour plus a $3.00 deposit to rent a bike. at bike shop z it costs $1.75 per hour plus a $7.00

deposit to rent a bike.
a.) write the system of equations that could be used to find c, the total cost for renting a bike for n hours at each shop.
b.) graph the system of equations.
c.) when would it cost less to rent a bike from bike shop x? explain.

Mathematics
2 answers:
dem82 [27]3 years ago
6 0

Answer:

Multiply the rate per hour by the number of hours (n) and add the deposit.

A)

Bike shop x: c = 2.75n + 3.00

Bike shop z: c = 1.75n + 7.00

B) to find when they will cost the same set the equations equal to each other and solve for n:

2.75n + 3.00 = 1.75n + 7.00

Subtract 3 from each side:

2.75n = 1.75n + 4.00

Subtract 1.75n from both sides:

1.00n = 4.00

Divide both sides by 1:

n = 4 hours

Doss [256]3 years ago
3 0
The answer to you was like a lot more people and I couldn’t live in
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Answer:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0

Step-by-step explanation:

We want to write the trignometric expression:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)

Take the secant of both sides:

\displaystyle \sec(\theta)=\frac{u}{10}

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}

By substitutition:

\displaystyle= \sin(2\theta)

Using an double-angle identity:

=2\sin(\theta)\cos(\theta)

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)

Simplify. Therefore:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0

4 0
3 years ago
Translate each verbal phrase into an algebraic expression or equation.
mario62 [17]

Answer:

13) 7 + x/2 = 10

14)  2x - 5 = 7

15) 4x - 1 = 11

16) 6x - 6 = 12

17) x/3 + 10 = 12

18) 2x + 7 = 1

19) 9 + x/7 = 11

20) 8(n - 3)

Step-by-step explanation:

The quotient of x and 2 = x ÷ 2 = x/2

The product is the result of multiplying two or more other numbers

The sum is the result of adding two or more numbers

The difference is the result of subtracting one number from another

13) 7 + x/2 = 10

14)  2x - 5 = 7

15) 4x - 1 = 11

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17) x/3 + 10 = 12

18) 2x + 7 = 1

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3 years ago
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Amiraneli [1.4K]

Answer:

<h3>The answer is 17.80 units</h3>

Step-by-step explanation:

The distance between two points can be found by using the formula

d =  \sqrt{ ({x1 - x2})^{2} +  ({y1 - y2})^{2}  } \\

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-8,19) and (3,5)

The distance between them is

d =  \sqrt{ ({ - 8 - 3})^{2}  +  ({1 9 - 5})^{2} }  \\  =  \sqrt{( { - 11})^{2}  +  {14}^{2} }  \\  =  \sqrt{121 + 196}  \\  =  \sqrt{317}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  = 17.804493...

We have the final answer as

<h3>17.80 units to the nearest hundredth</h3>

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