Mathematics, 19.01.2020 01:31 Jessicawilliams3569

Aschool, hospital, and a supermarket are located at the vertices of a right triangle formed by three highways. the school and hospital are 14.7 miles apart. the distance between the school and the supermarket is 8.82 miles, and the distance between the hospital and the supermarket is 11.76 miles.

a service road will be constructed from the main entrance of the supermarket to the highway that connects the school and hospital. what is the shortest possible length for the service road? round to the nearest tenth.

Answers: 1

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Answers

Answer from: fara26

7.1 miles

Step-by-step explanation:

Consider right triangle HospitalSchoolSupermarket. In this triangle:

HospitalSchool = 14.7 mi;HospitalSupermaket = 11.76 mi;School Supermarket = 8.82 mi.

The shortest road from the main entrance of the supermarket to the highway that connects the school and hospital will be the height drawn from the point Supermarket to the hypotenuse HospitalSchool.

Let the length of this road be x mi and the distance from School to point A be y mi. Use twice the Pythagorean theorem for right triangles Supermarket SchoolA and SupermarketHospitalA:

$\left\{\begin{array}{l}x^2+y^2=8.82^2\\ \\x^2+(14.7-y)^2=11.76^2\end{array}\right.$

Subtract from the second equation the first one:

$x^2+(14.7-y)^2-x^2-y^2=11.76^2-8.82^2\\ \\14.7^2-2\cdot 14.7y+y^2-y^2=11.76^2-8.82^2\\ \\-29.4y=11.76^2-8.82^2-14.7^2\\ \\29.4y=155.5848\\ \\y\approx5.24\ mi$

Thus,

$x^2=8.82^2-5.24^2=50.3348\\ \\x\approx 7.1\ mi.$

Aschool, hospital, and a supermarket are located at the vertices of a right triangle formed by three

Answer from: Quest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

−−−−−

←

add

94.09

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