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Yuki888 [10]
3 years ago
13

At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist headi

ng north is riding 5 km/hour faster than the bicyclist heading south. At 10:45, they are 47.25 km apart. Find the two bicyclists’ rates.
Mathematics
2 answers:
Romashka-Z-Leto [24]3 years ago
8 0

Answer:

Between 9:00 am and 10:45 am, there have been 1 hour and 45 minutes or 1.75 hours have passed. Let x be the speed of the slower cyclist and x+ 5 be the rate of the second cyclist. The given situation is best represented through the equation below,

                                x(1.75) + (x + 5)(1.75) = 47.25 km

The value of x from the equation is 11. Thus, the two bicyclists' rates are 11 km/h and 16 km/h. 

Studentka2010 [4]3 years ago
8 0

Answer:

Cyclist A travels at 11 km/hr and cyclist B travels at 16 km/r

Step by step explanation:

The cyclist B is riding 5 km/hr faster than cyclist A. From 09:00  till 10:45 is 1 hour and 45 minutes. This is 60 plus 45 minutes:

=60+45=105

In 105 minutes they are 47.25 km apart. Let x be the speed of cyclist A and y be the speed of cyclist B. We can write x in terms of y:

y=x+5

We can write an expression relating the two cyclists to the total speed of the cyclists.

We know that in 105 minutes they are 47.25 km apart.

We can substitute the 47.25 km into the following expression:

47.25=(x)\cdot(105/60)+y\cdot{105/60}

47.25=(x)\cdot(1.75)+(x+5)\cdot{1.75}

Solve for x

47.25/1.75=2x+5

22/2=x

x=11

Therefore y is:

y=11+5=16

Cyclist A travels at 11 km/hr and cyclist B travels at 16km/r

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2 years ago
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3 years ago
Read 2 more answers
A segment XD is drawn in rectangle QUAD as shown
grin007 [14]

Answer:

∠XDQ : 41°

∠UXD: 139 °

Step-by-step explanation:

Allow me to rewrite your answer for a better understanding and please have a look at the attached photo.

<em>A segment XD is drawn in rectangle QUAD as shown  below. </em>

<em>What are the measures of ∠XDQ and ∠UXD ? </em>

My answer:

As we can see in the photo, ∠ADX = 49° and ∠ADU =90°

=>  ∠XDQ = ∠ADU - ∠ADX

= 90°  - 49°  = 41°

In the triangle ADX, we can find out the angle of ∠DXA

= 180° - ∠DAX - ∠ADX

= 180° - 90° - 49°

= 41°

=> <em>∠UXD = </em>180° - ∠DXA  (Because UA is a straight line)

=180° - 41°  

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5 0
3 years ago
Point A is (-9,-3) and is translated 4 left and 2 down. Where is A' at?
mezya [45]

Answer:

A translation maps point A(3,7)A(3,7)A, left parenthesis, 3, comma, 7, right parenthesis to point A'(6,-2)A

′

(6,−2)A, prime, left parenthesis, 6, comma, minus, 2, right parenthesis. Let's determine what translation this is.

Solution

Step 1: Horizontal shift. AAA is shifted 333 units to the right because (6)-(3)=\tealD{+3}(6)−(3)=+3left parenthesis, 6, right parenthesis, minus, left parenthesis, 3, right parenthesis, equals, start color #01a995, plus, 3, end color #01a995.

Step 2: Vertical shift. AAA is shifted 999 units down because (-2)-(7)=\maroonD{-9}(−2)−(7)=−9left parenthesis, minus, 2, right parenthesis, minus, left parenthesis, 7, right parenthesis, equals, start color #ca337c, minus, 9, end color #ca337c.

The answer: AAA is mapped onto A'A

′

A, prime under a translation by \langle \tealD{3},\maroonD{-9} \rangle⟨3,−9⟩open angle, start color #01a995, 3, end color #01a995, comma, start color #ca337c, minus, 9, end color #ca337c, close angle.

Step-by-step explanation:

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