Erica bought 2 apples from her local farmers' market. Today, she bought 1

75 POINTS Need an immediate answer please brainliest will be given! A train left a station travelling to a city at 30 mph. The t

yaroslaw [1]

The value of distance between the station and the city in terms of miles which train and car travelled at interval of 2 hours is 129.6 miles.

<h3>What is the rate of speed?</h3>

The rate of speed is the rate at which the total distance is travelled in the time taken. Rate of speed can be given as,

r=d/t

Here, (d) is the distance travelled by the object and (t) is time taken but the object to cover that distance.

The train traveled 1/3 of the distance at 30 mph and the remaining distance at 40 mph. Let <em>t</em> is the time the train has taken to travel and x is the distance it travelled. Thus,

$t=\dfrac{\dfrac{1}{3}x}{30}+\dfrac{\dfrac{2}{3}x}{40}\\t=\dfrac{x}{90}+\dfrac{x}{60}\\t=\dfrac{2x+3x}{180}\\t=\dfrac{5x}{180}\\t=\dfrac{x}{36}$

After two hour a car left the same station traveled the first 3 hours at 35 mph and the remaining distance at 51 mph. Let <em>t</em> is the time the car has taken to travel and x is the distance it travelled. Thus,

$t+2=3+\dfrac{(x-3\times35)}{51}$

As t is same, thus put the value of t in this equation,

$\dfrac{x}{36}=3-2+\dfrac{(x-3\times35)}{51}\\\dfrac{x}{36}=3-2+\dfrac{(x-3\times35)}{51}\\\dfrac{x}{36}=1+\dfrac{(x-105)}{51}\\\dfrac{x}{36}=\dfrac{(51+x-105)}{51}\\51x=36x-54\times36\\51x-36x=1944\\x=\dfrac{1944}{15}\\x=129.6$

Thus, the value of distance between the station and the city in terms of miles which train and car travelled at interval of 2 hours is 129.6 miles.

Learn more about the rate of speed here:

brainly.com/question/359790

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6 0

2 years ago

14. Team 8A is selling snacks at the football game to raise money for a field trip. They are selling popcorn for $2.50 and pretz

Mamont248 [21]

Answer:

40 popcorns and 90 pretzels sold.

============

Let the number of popcorns is x and pretzels is y.

Set up equations:

x + y = 130
2.5x + 2y = 280

Solve by elimination, multiply the first equation by 2 and subtract from the second equation:

2.5x + 2y - 2x - 2y = 280 - 2*130
0.5x = 280 - 260
0.5x = 20
x = 20/0.5
x = 40

Find y:

40 + y = 130
y = 130 - 40
y = 90

5 0

1 year ago

Read 2 more answers

Which of the following best describes the relationship between the variables on the scatter plot below?

CaHeK987 [17]

Answer:

A. negative correlation

Step-by-step explanation:

Let two variables x and y, the correlation coefficient r measure to what degree the variables x and y are related.

--- If this coefficient is positive then the relationship will be positive. This means that even an increase in the variable x will produce an increase in the variable y. In the dispersion diagram the points will be grouped, simulating a line of positive slope.

--- If this coefficient is negative then the relation will be negative. This means that even an increase in the variable x will produce a decrease in the variable y. In the dispersion diagram the points will be grouped, simulating a negative slope line.

In the diagram shown it can be noted that as the variable x increases the variable y decreases.

Therefore it can be concluded that the correlation between x and y is negative. The correct option is option A

4 0

3 years ago

4. Find the standard from of the equation of a hyperbola whose foci are (-1,2), (5,2) and its vertices are end points of the dia

Ad libitum [116K]

The <em>standard</em> form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

<h3>How to find the standard equation of a hyperbola</h3>

In this problem we must determine the equation of the hyperbola in its <em>standard</em> form from the coordinates of the foci and a <em>general</em> equation of a circle. Based on the location of the foci, we see that the axis of symmetry of the hyperbola is parallel to the x-axis. Besides, the center of the hyperbola is the midpoint of the line segment with the foci as endpoints:

(h, k) = 0.5 · (- 1, 2) + 0.5 · (5, 2)

(h, k) = (2, 2)

To determine whether it is possible that the vertices are endpoints of the diameter of the circle, we proceed to modify the <em>general</em> equation of the circle into its <em>standard</em> form.

If the vertices of the hyperbola are endpoints of the diameter of the circle, then the center of the circle must be the midpoint of the line segment. By algebra we find that:

x² + y² - 4 · x - 4 · y + 4= 0

(x² - 4 · x + 4) + (y² - 4 · y + 4) = 4

(x - 2)² + (y - 2)² = 2²

The center of the circle is the midpoint of the line segment. Now we proceed to determine the vertices of the hyperbola:

V₁(x, y) = (0, 2), V₂(x, y) = (4, 2)

And the distance from the center to any of the vertices is 2 (<em>semi-major</em> distance, a) and the semi-minor distance is:

b = √(c² - a²)

b = √(3² - 2²)

b = √5

Therefore, the <em>standard</em> form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

To learn more on hyperbolae: brainly.com/question/27799190

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5 0

1 year ago

What is the value of x3 × y1 when x = 5 and y = 10

katovenus [111]

Answer:

150

Step-by-step explanation:

To solve the problem, put 5 instead of x, so 5*3

and put 10 instead of y, so 10*1

when combined,

(5*3) * (10*1)

= 15 * 10

= 150

Hope this helps!!

Let me know if I'm wrong...

8 0

2 years ago