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Delicious77 [7]
2 years ago
6

Nicole left home and traveled toward the recycling plant. Two hours later Kristin left traveling at 50 km/h in an effort to catc

h up to Nicole. After traveling for three hours Kristin finally caught up. What was Nicole's average speed?
Mathematics
1 answer:
Sedaia [141]2 years ago
4 0

Answer:

Nicole's average speed is 30\ km/h.

Step-by-step explanation:

Given,

Speed of Kristen = 50\ km/h

Time taken by Kristen to cover the distance = 3\ h

Solution,

We can find out the distance traveled by Kristen by multiplying speed with time.

Distance = Speed\times Time

Distance =50\ km/h\times 3\ h=150\ km

The distance traveled by Kristen is equal to distance traveled by Nicole.

As the question said Kristen left 2 hours later and cover the distance in 3 hours.

That means Nicole take 5 hours to cover the distance.

So, For Nicole;

Distance = 150 km

Time = 5 hrs

Here we use the formula of speed.

Speed = \frac{Distance}{time}

Now substituting the values, we get;

Speed = \frac{150\ km}{5\ h}=30\ km/h

Hence Nicole's average speed is 30\ km/h.

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PQ and QR are two sides of a regular 12-sided polygon. PR is the diagonal of the polygon.
skelet666 [1.2K]

The size of angle PRQ is 15°

Step-by-step explanation:

In any regular polygon of n-sided

  • All sides are equal in length
  • All angles are equal in measure
  • The measure of each interior angle is \frac{(n-2)*180}{n}
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∵ PQ and QR are two sides of a regular 12-sided polygon

∴ PQ = QR

∵ PR is a diagonal

∴ ∠PQR is an interior angle of the polygon

- By using the rule of the interior angle above

∵ n = 12

∴ m∠PQR = \frac{(12-2)*180}{12}

∴ m∠PQR = 150°

In Δ PQR

∵ PQ = QR ⇒ sides in a regular polygon

- Δ PQR is an isosceles Δ

∴ m∠PRQ = m∠RPQ ⇒ base angles of an isosceles Δ

The sum of the measures of the interior angles of a triangle is 180°

∵ m∠PQR + m∠PRQ + m∠RPQ = 180°

∴ 150 + m∠PRQ + m∠RPQ = 180°

- Subtract 150 from both sides

∴ m∠PRQ + m∠RPQ = 30

∵ m∠PRQ = m∠RPQ

- Divide their sum by 2 to find the measure of each one

∴ m∠PRQ = m∠RPQ = 30 ÷ 2 = 15°

∴ m∠PRQ = 15°

The size of angle PRQ is 15°

Learn more:

You can learn more about the triangles in brainly.com/question/3945600

#LearnwithBrainly

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