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Joel can run around a 14– mi track in 81 sec, and Jason can run around the track in 69 sec. If the runners start at the same poi

Alenkasestr [34]

Answer:37.2 sec

Step-by-step explanation:

Given

Joel takes 81 sec for 14 mile long track

speed of joel $\frac{14}{1.35}$ mi/min=10.37 mi/min

Jason takes 69 sec for 14 mi track

so jason speed is $\frac{14}{1.15} mi/min=12.17 mi/min$

if both starts from same spot in opposite direction then

$\frac{x}{10.37}=\frac{14-x}{12.17}$

where x is distance covered by Joel

then x=6.44 miles

therefore time required

$t=\frac{6.44}{10.37}=0.621 min\approx 37.2 sec$

8 0

3 years ago

100 Points! What are the classifications of each system?

alexdok [17]

Answer:

Part 1) Is a inconsistent system

Part 2) Is a consistent independent system

Part 3) Is a consistent dependent system

see the attached figure

Step-by-step explanation:

we know that

If a system has at least one solution, it is said to be consistent .

If a consistent system has exactly one solution, it is independent .

If a consistent system has an infinite number of solutions, it is dependent

If a system not have solution, it is said to be inconsistent

Part 1) we have

$x+5y=-2\\x+5y=4$

This system of linear equations has two parallel lines (their slopes are equal) with different y-intercept

so

The lines don't intersect

The system has no solution

therefore

Is a inconsistent system

Part 2) we have

$y=3x+4\\-2x+y=4$

we know that

If two lines have different slopes, then the lines intersect at one point and the system of equations has one solution

In this problem, the lines have different slopes (m=3 and m=2)

so

The lines intersect at one point

The system has one solution

therefore

Is a consistent independent system

Part 3) we have

$3x+y=4$ ----> equation A

$-6x-2y=-8$ ----> equation B

Multiply equation A by -2 both sides

$-2(3x+y)=-2(4)$

$-6x-2y=-8$ ----> equation C

Compare equation B and equation C

Are identical lines

so

The system has infinity solutions

therefore

Is a consistent dependent system

4 0

3 years ago

3x+y=115x-y=21 Directions: Solve each system of equations by elimination. Clearly identify your solution.

olchik [2.2K]

To solve, we will follow the steps below:

3x+y=11 --------------------------(1)

5x-y=21 ------------------------------(2)

since y have the same coefficient, we can eliminate it directly by adding equation (1) and (2)

adding equation (1) and (2) will result;

8x =32

divide both-side of the equation by 8

x = 4

We move on to eliminate x and then solve for y

To eliminate x, we have to make sure the coefficient of the two equations are the same.

We can achieve this by multiplying through equation (1) by 5 and equation (2) by 3

The result will be;

15x + 5y = 55 ----------------------------(3)

15x - 3y =63 --------------------------------(4)

subtract equation (4) from equation(3)

8y = -8

divide both-side of the equation by 8

y = -1

8 0

1 year ago

Which of these represents categorical data?

Viktor [21]

Answer:

the answer is D) the most popular foods in the cafeteria

~batmans wife dun dun dun....

7 0

3 years ago

Mary works as a sales rep and receives $24 for every $160 she sells. What is her rate of commission?

Sophie [7]

It is 24 / 160 - 15 percent

5 0

2 years ago

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