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ruslelena [56]
3 years ago
10

Miguel and Maria are washing the windows in their home. Together, they can complete the task in 1 hours. If Maria can wash windo

ws twice as fast as Miguel, how many minutes would it take her to wash them by herself? In your answer, include the equation you used to solve the problem.
Mathematics
2 answers:
Talja [164]3 years ago
6 0

Let's correct what the person above said. 1 and a half hour = 90 minutes.

x: amount of time Miguel uses to complete the task.

y: amount of time Maria uses to complete the task.

We write the system of equations:

x + y = 90

y = (1/2) x

Solving the system we have:

x = 60 minutes

y = 30 minutes

(Verify:)

30 + 60 = 90

90 = 90 (correct)

Answer:

it take her to wash them by herself about:

y = 30 minutes

Orlov [11]3 years ago
5 0
For this case, the first thing we must do is define variables.
 x: amount of time Miguel uses to complete the task.
 y: amount of time Maria uses to complete the task.
 We write the system of equations:
 x + y = 60
 y = (1/2) x
 Solving the system we have:
 x = 40 minutes
 y = 20 minutes
 Answer:
 
it take her to wash them by herself about:
 
y = 20 minutes
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A = lw + 0.5bh
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2 years ago
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Answer:

Find below the calculations of the two areas, each with two methods. The results are:

  • Upper triangle:

                     Area=5000\sqrt{3}units^2

  • Lower triangle:

                     Area=14,530m^2

Explanation:

<u>A) Method 1</u>

When you are not given the height, but you are given two sides and the included angle between the two sides, you can use this formula:

           Area=side_1\times side_2\times sin(\alpha)

Where, \alpha is the measure of the included angle.

1. <u>Upper triangle:</u>

          side_1=200units\\ \\ side_2=100units\\ \\ \alpha =60\º\\ \\ Area=200units\times 100units\times sin(60\º)/2\\ \\ Area=5000\sqrt{3}units^2

2. <u>Lower triangle:</u>

         side_1=231m\\ \\ side_2=150m\\ \\ \alpha =123\º\\ \\ Area=231m\times 150m\times sin(123\º)/2\\ \\ Area=14,529.96m^2\approx14,530m^2

<u></u>

<u>B) Method 2</u>

You can find the height of the triangle using trigonometric properties, and then use the very well known formula:

            Area=(1/2)\times base\times height

Use it for both triangles.

3. <u>Upper triangle:</u>

The trigonometric ratio that you can use is:

                    sine(\alpha)=opposite\text{ }leg/hypotenuse

Notice the height is the opposite leg to the angle of 60º, and the side that measures 100 units is the hypotenuse of that right triangle. Then:

         sin(60\º)=height/100units\\ \\ height=sin(60\º)\times100units\\ \\ height=50\sqrt{3}units

Area=(1/2)\times base\times height=(1/2)\times 200units\times 50\sqrt{3}units=5,000\sqrt{3}units^2

3. <u>Lower triangle:</u>

<u />

         sin(180\º-123\º)=height/231m\\ \\ height=sin(57\º)\times 231m\\ \\ height=193.7329m^2<u />

<u />

<u />Area=(1/2)\times base\times height=(1/2)\times 150m\times 193.7329m^2\\\\  Area=14,529.96m^2\approx 14,530m^2<u />

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3<br> y=-=X+2<br> 4.<br> What is the slope
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Check the picture below.

we could also look at it from the inscribed angle theorem, bearing in mind that the intercepted arc is 180°.

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The sum of the first and third consecutive add integers is 131 less than 3 times the second integer.Find the 3 integers.Pls writ
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3 consecutive odd integers....x, x + 2, and x + 4

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x + 2 = 129 + 2 = 131
x + 4 = 129 + 4 = 133

so ur 3 odd numbers are : 129,131, and 133 <==
6 0
2 years ago
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