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andrezito [222]
2 years ago
9

2r + 3s = 14 2( )+ 3s = 14 +3s = 14 3s= S =

Mathematics
1 answer:
Soloha48 [4]2 years ago
5 0

Answer:

4

Step-by-step explanation:

3s=14-2

3s=12

3s/3=12/3

s=4

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Piravena must make a trip from A to B then from B to C, then from C to A. Each of these three parts of the trip is made entirely
anyanavicka [17]

Answer:

a) Cost of flying from A to B = $425

b) Total distance travelled by Piravena during the complete trip = 7,500 km

c) To minimize cost and arrive at the final cost given, she must have travelled by bus from B to C and then travelled by taking an airplane from C to A.

Step-by-step explanation:

The complete question is presented in the attached image to this question.

Full Question

a) To begin her trip she flew from A to B. Determine the cost of flying from A to B.

b) Determine the distance she travels for her complete trip.

c) Piravena chose the least expensive way to travel between cities and her total cost was $1012.50. Given that she flew from A to B, determine her method of transportation from B to C and her method of transportation from C to A.

Solution

a) The distance from A to B is given as 3250 km.

To take an airplane, it costs her a $100 booking fee, plus $0.10 per kilometer.

So, to fly 3250 km, she will pay

100 + (0.10×3250) = $425

b) For her complete journey, she is to make a trip from A to B then from B to C, then from C to A.

Her complete distance travelled = AB + BC + CA

But it is given that the three cities form a right angled triangle as given in the question with AB serving as the hypotenuse side.

Pythagoras theorem gives that the square of the hypotenuse side is equal to the sum of the respective squares of the other two sides

AB² = BC² + CA²

3250² = BC² + 3000²

BC² = 3250² - 3000² = 1,562,500

BC = √1,562,500 = 1,250 km

Total distance covered by Piravena during the entire trip = AB + BC + CA = 3250 + 1250 + 3000 = 7,500 km

c) Her total cost of travel = $1012.50

But she definitely flew from A to B at a cost of $425

This means she spent (1012.50 - 425) on the rest of the journey, that is, $587.5

Note that to travel by bus, it is $0.15 per kilometre and to travel by airplane is $100 + $0.10 per kilometre. Indicating that the airplane saves cost on long distance travels while the bus saves cost on short distance travels.

To confirm this, we calculate the two options (bus or airplane) for each route.

If she travels B to C by bus, cost = 0.15 × 1250 = $187.5

If she travels B to C by airplane, cost = 100 + (0.10×1250) = $225

Hence, the bus obviously minimizes cost here.

If she travels from C to A by bus, cost = 0.15 × 3000 = $450

If she travels from C to A by airplane, cost = 100 + (0.10×3000) = $400

Here, travelling by airplane minimizes the cost.

So, if we confirm now that she travelled from B to C by bus and then from C to A by airplane, total cost = 187.5 + 400 = $587.5

which is the remaining part of her total cost is she minimized expenses!

Hope this Helps!!!

7 0
3 years ago
Summarize the possible relationships for the y -intercepts, slopes, and number of solutions in a system of two linear equations
ale4655 [162]

A consistent system of equations has at least one solution.

A consistent system is considered to be an independent system if it has a single solution, such as the example we just explored. The two lines have different slopes and intersect at one point in the plane.

A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line. Every point on the line represents a coordinate pair that satisfies the system. Thus, there are an infinite number of solutions.

Another type of system of linear equations is an inconsistent system, which is one in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no points common to both lines; hence, there is no solution to the system.

For more information on slopes click on the link below:

brainly.com/question/3493733

#SPJ4

4 0
1 year ago
Evaluate the expression:<br><br> 2/3-1/4+(-5/6)
Aliun [14]

Answer:

\\  \frac{2}{3}  -  \frac{1}{4}  +  \frac{( - 5)}{6}

\\  =  \frac{2}{3}  -  \frac{1}{4}  -  \frac{5}{6}

\\  =  \frac{8 - 3 - 10}{12}

\\  =  \frac{8 - 13}{12}

\\  =  \frac{ - 5}{12}

3 0
3 years ago
Here is a list of numbers: 2 , 8 , 1 , 7 , 4 , 10 , 1 , 15 , 20 State the median.
mel-nik [20]

Answer:

7

Step-by-step explanation:

1, 1, 2, 4, 7, 8, 10, 15, 20

median = 7

7 0
1 year ago
Ram noticed three students used 1 2/10 dm of tape.what was the total used for three students???
OLga [1]

Answer:

18/5

Step-by-step explanation:

<em>From my understanding, this is 1 whole 2 upon 10</em>

<u>Step 1: Convert mixed fraction into fraction</u>

<em>Multiply whole number by denominator: 1 x 10 = 10</em>

<em>Add numerator: 10 + 2 = 12</em>

<em>Write the result as the numerator and use the same denominator.</em>

12/10

<u>Step 2: Find the total tape used</u>

<em>From my understanding, each student used 12/10 of the tap</em>

<em>So 3 students used: 12/10 x 3 =</em> 18/5

Therefore, the total tape used for three students was 18/5.

!!

7 0
3 years ago
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