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3 years ago

Simplify the expression 5x(-2x+4) - (-7)

Mathematics

1 answer:

Inessa [10]3 years ago

5 0

−10x2+20x+7

Step-by-step explanation:

Apply the distributive property.

5⋅−2x2+5x⋅4−(−7)

Multiply 44 by 55.

5⋅−2x2+20x−(−7)

Multiply 55 by −2-2.

−10x2+20x−(−7)

Multiply −1 by −7

−10x2+20x+7

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Vesna [10]

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:

A) Method 1

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. Upper triangle:

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

2. Lower triangle:

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

B) Method 2

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. Upper triangle:

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. Lower triangle:

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

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

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