Caroline's car used 16 gallons to travel 544 miles. How far can she travel on 9 gallons?

Mathematics

1 answer:

kicyunya [14]2 years ago

8 0

Answer:

306 gallons

Step-by-step explanation:

Caroline traveled 544 miles on 16 gallons. We do some simple math and divide 544/16 and receive 34 miles/gallon. All we do now is multiply 34 * 9 and we receive 306 gallons.

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Angie and Kenny play online video games. Angie buys 1 software package and 3 months of game play. Kenny buys 2 software packages

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Answer:

$10

Step-by-step explanation:

cost of one month of game play = x

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1 year ago

A system for tracking ships indicated that a ship lies on a hyperbolic path described by 5x2 - y2 = 20. the process is repeated

zysi [14]

Answer:
The ship is located at (3,5)

Explanation:
In the first test, the equation of the position was:
5x² - y² = 20 ...........> equation I
In the second test, the equation of the position was:
y² - 2x² = 7 ..............> equation II
This equation can be rewritten as:
y² = 2x² + 7 ............> equation III

Since the ship did not move in the duration between the two tests, therefore, the position of the ship is the same in the two tests which means that:
equation I = equation II

To get the position of the ship, we will simply need to solve equation I and equation II simultaneously and get their solution.

Substitute with equation III in equation I to solve for x as follows:
5x²-y² = 20
5x² - (2x²+7) = 20
5x² - 2y² - 7 = 20
3x² = 27
x² = 9
x = <span>± </span>√9

We are given that the ship lies in the first quadrant. This means that both its x and y coordinates are positive. This means that:
x = √9 = 3

Substitute with x in equation III to get y as follows:
y² = 2x² + 7
y² = 2(3)² + 7
y = 18 + 7
y = 25
y = +√25
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Based on the above, the position of the ship is (3,5).

Hope this helps :)

8 0

2 years ago

Paul and Charlene are 420 miles apart. They start toward each other with Paul driving 16 mph faster than Charlene. They meet in

Thepotemich [5.8K]

Answer:

34 mph.

Step-by-step explanation:

Let x be speed of Charlene, then speed of Paul will be x+16 as we are given that Paul is driving 16 mph faster than Charlene.

Let y be distance covered by Charlene, then distance covered by Paul will be 420-y.

Now we will use formula $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$ . Upon using our given information we will get two equation and two unknowns as: