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3 years ago

Tyler runs 8 2/3 miles in 4/3 of an hour. How long does it take each of them to run 10 miles?

Mathematics

1 answer:

adelina 88 [10]3 years ago

7 0

Answer:

It takes Tyler 65 minutes to run 10 miles.

Step-by-step explanation:

First you have to figure out what Tyler's mph is, so you divide 8 2/3 by 4/3=6.5. Then you multiply by 10 get how long it takes him to run 10 miles.

(hope this helps!)

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There are 331 boxes of melons.

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If the fifth term in a geometric sequence is 1∕27 and the common ratio is 1∕3, find the explicit formula of the sequence.

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B) The price of an electric fan is fixed 20% above its cost price. When it is sold allowing

kenny6666 [7]

Answer:

$\boxed{ \boxed{ \sf {Marked \: price \: = Rs \: 1500}}}$

$\boxed{ \bold{ \boxed{ \sf{Selling \: price = \: Rs \: 1230}}}}$

Step-by-step explanation:

Let Cost price ( C.P ) be x

Finding the Marked price and selling price 

Marked price = $\sf{x + 20\% \: of \: x}$

⇒ $\sf{x + \frac{20}{100} \times x}$

⇒ $\sf{ \frac{x \times 100 + 20x}{100} }$

⇒ $\sf{ \frac{120x}{100} }$ ⇒ ( i )

Selling price = $\sf{marked \: price \: - 18\% \: of \: marked \: price}$

⇒ $\sf{ \frac{120x}{100} - \frac{18}{100} \times \frac{120x}{100} }$

⇒ $\sf{ \frac{120x}{100} - \frac{54x}{250} }$

⇒ $\sf{ \frac{120x \times 5 - 54x \times 2}{500} }$

⇒ $\sf{ \frac{600x - 108x}{500} }$

⇒ $\sf{ \frac{492x}{500} }$ ⇒ ( ii )

Finding the value of x ( Cost price )

$\sf{loss = cost \: price - selling \: price}$

⇒ $\sf{20 = x - \frac{492x}{500} }$

⇒ $\sf{20 = \frac{x \times 500 - 492x}{500} }$

⇒ $\sf{20 = \frac{8x}{500} }$

⇒ $\sf{8x = 10000}$

⇒ $\sf{x = \frac{10000}{8} }$

⇒ $\sf{x = \: Rs \: 1250}$

Value of x ( cost price ) = Rs 1250

Now, Replacing the value of x in ( i ) in order to find the value of marked price

$\sf{marked \: price = \frac{120x}{100} }$

⇒ $\sf{ \frac{120 \times 1250}{100} }$

⇒ $\sf{ \: Rs \: 1500}$

Replacing value of x in ( ii ) in order to find the value of selling price

$\sf{selling \: price = \frac{492 \: x}{500} }$

⇒ $\sf{ \frac{615000}{500} }$

⇒ $\sf{ \: Rs \: 1230}$

Thus , Marked price of the fan = Rs 1500

Selling price of the fan = Rs 1230

Hope I helped!

Best regards!!

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3 years ago

Fill in the missing statement and reason in the proof of the Alternate Exterior Angles Theorem.

ludmilkaskok [199]

Answer:

∠EGB and ∠AGF are congruent;

Transitive Property of Equality

Step-by-step explanation:

The vertical angles theorem is about the angles that are opposite to each other. These angles are formed when two lines cross each other

Vertical angles are congruent i.e their measures are equal

Look at the attached graph

Given:

AB // CD

E , G , H , F are col-linear

The line which contains points E , G , H , F is a transversal for the parallel lines AB and CD

∵ AB and EF intersected at point G

∴ m∠EGB = m∠AGF ⇒ by the vertical angles theorem

When lines AB and EF intersected at G they formed opposite angles like angles EGB and AGF, then angles EGB and AGF are congruent ( vertical angle theorem)

∵ AB // CD and EF is a transversal

∴ m∠AGF = m∠CHF (corresponding angles theorem)

Transitive Property of Equality: if one angle is equal to two other angles, then the two other angles are equal

Therefore, If a = b and b = c, then a = c

∵ m∠EGB = m∠AGF

∵ m∠AGF = m∠CHF

∴ m∠EGB = m∠CHF (transitive property theorem)

∠EGB and ∠AGF are congruent; Transitive Property of Equality

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