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nikdorinn [45]
3 years ago
11

The graph shows the relationship between x, the amount of time in hours and y, the distance traveled in miles, by a probe before

it reaches Mars. Does the graph represent a proportional relationship? Justify your answer. Determine the number of miles the probe travels in 5.5 hours.

Mathematics
1 answer:
LenKa [72]3 years ago
4 0

1) Yes

2) 66,000 miles

Step-by-step explanation:

1)

The graph is missing, so you can find it in attachment.

Two variables y,x are said to be in a proportional relationship with each other when there exist a relationship in the form:

y=kx

where

k is called "constant of proportionality"

In other words, two variables are in a proportional relationship if, when one of the two variable increases, the other one increases by the same proportion.

In this problem, the two variables represented are distance (y-axis) and time (x-axis); from the graph, we see that their relationship is represented by a straight line, which is in the form y=kx; therefore, the two variables are in a proportional relationship.

2)

We can find the constant of proportionality by re-arranging the equation:

k=\frac{y}{x}

And by taking the values of y and x at a certain point along the graph.

For instance, by taking

x = 4 h

d = 48,000 mi

We find

k=\frac{48,000}{4}=12,000 mi/h

which means that the probe travels 12,000 miles per hour.

Therefore, we can now find the distance travelled by the probe when

x = 5.5 h

We find:

y=kx=(12,000)(5.5)=66,000 mi

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Step-by-step explanation:

Let us solve the question

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∵ You bought three shirts that cost x dollars each

∴ The cost of a shirt = $x

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→ Substitute the value of total money and the cost of the shirts

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Read 2 more answers
Elimination was used to solve a system of equations.
astra-53 [7]

The system of equation that could have led to the equation 9x = 27 is

7x - 2y = 15

x + y = 6

The correct option is the third option

7x - 2y = 15

x + y = 6

<h3>Solving systems of equations</h3>

From the question, we are to determine the system that could have led to 9x = 27


1.

9x + 2y = 21

-9x - 2y = 21

Subtracting, we get

9x + 2y = 21

-9x - 2y = 21

-------------------

18x + 4y = 0

2.

10x - y = 15

x + y = - 12

Subtracting, we get

10x - y = 15

x + y = - 12

---------------------

9x -2y = 27

3.

7x - 2y = 15

x + y = 6

Here, multiply the second equation by 2

2 × [x + y = 6]

2x + 2y = 12

Now, add to the first equation

7x - 2y = 15

2x + 2y = 12

------------------

9x = 27

4.

4x + 3y = 24

-5x - 3y = 3

Subtracting, we get

4x + 3y = 24

-5x - 3y = 3

---------------------

9x + 6y = 21

Hence, the system of equation that could have led to the equation 9x = 27 is

7x - 2y = 15

x + y = 6

The correct option is the third option

7x - 2y = 15

x + y = 6

Learn more on Systems of equations here: brainly.com/question/12691830

#SPJ1

5 0
2 years ago
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