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aliina [53]
3 years ago
15

ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually g

uess on my questions.

Mathematics
2 answers:
vredina [299]3 years ago
5 0

Answer:

Range : { -3,0,4,6}

Step-by-step explanation:

The range of the function is the output values

Range : { -3,0,4,6}

jok3333 [9.3K]3 years ago
3 0

Answer:

C. {-3, 0 ,4, 6}

Step-by-step explanation:

→The range is the total of y-intercepts/outputs. In this case, looking at the function, you can see that the y-intercepts/outputs are 0, -3, 4, and 6.

→The others numbers are the x-intercepts/inputs, which would be the domain of the function.

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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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