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Bad White [126]
3 years ago
10

A business rents bicycles and in-line skates. Bike rentals cost $25 a day and skates cost $20 a day. The business had 20 rentals

that day and sold $455 worth of bikes and skates. Write a system of linear equations to represent this situation.
Mathematics
1 answer:
Lena [83]3 years ago
6 0
25x+20y=455
x+y=20


20x+20y=400
-25x-20y=-455
-5x=-55
x=11
11+y=20
y=9

Solved it as well, sorry if I wasn't supposed to

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To conserve water, many communities have developed water restrictions. The water utility charges a fee of $38, plus an additiona
earnstyle [38]

Using a linear function, the correct option regarding the situation is given by:

C) 57 ≤ 1.28x + 38 ≤ 87; To stay within the range, the usage should be between 14.8 and 38.3 HCF.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The bill is modeled by a linear function, with an <u>intercept of $38 and a slope of $1.28</u>, hence it is given by:

C(x) = 1.28x + 38

The bill should be between $57 and $87 dollars per month, hence:

57 <= C(x) <= 87.

The values of x are:

C(x) >= 57

1.28x + 38 >= 57

x >= 19/1.28

x >= 14.8.

C(x) >= 87

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x >= 49/1.28

x >= 38.3.

Hence option C is correct.

More can be learned about linear functions at brainly.com/question/24808124

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The arch beneath a bridge is​ semi-elliptical, a​ one-way roadway passes under the arch. The width of the roadway is 38 feet and
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Answer:

Only truck 1 can pass under the bridge.

Step-by-step explanation:

So, first of all, we must do a drawing of what the situation looks like (see attached picture).

Next, we can take the general equation of an ellipse that is centered at the origin, which is the following:

\frac{x^2}{a^2}+\frac{y^2}{b^2}

where:

a= wider side of the ellipse

b= shorter side of the ellipse

in this case:

a=\frac{38}{2}=19ft

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so we can go ahead and plug this data into the ellipse formula:

\frac{x^2}{(19)^2}+\frac{y^2}{(12)^2}

and we can simplify the equation, so we get:

\frac{x^2}{361}+\frac{y^2}{144}

So, we need to know if either truk will pass under the bridge, so we will match the center of the bridge with the center of each truck and see if the height of the bridge is enough for either to pass.

in order to do this let's solve the equation for y:

\frac{y^{2}}{144}=1-\frac{x^{2}}{361}

y^{2}=144(1-\frac{x^{2}}{361})

we can add everything inside parenthesis so we get:

y^{2}=144(\frac{361-x^{2}}{361})

and take the square root on both sides, so we get:

y=\sqrt{144(\frac{361-x^{2}}{361})}

and we can simplify this so we get:

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and now we can evaluate this equation for x=4 (half the width of the trucks) so:

y=\frac{12}{19}\sqrt{361-(8)^{2}}

y=11.73ft

this means that for the trucks to pass under the bridge they must have a maximum height of 11.73ft, therefore only truck 1 is able to pass under the bridge since truck 2 is too high.

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Step-by-step explanation:

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