Can you please solve this please and thank you.

Mathematics

1 answer:

ryzh [129]3 years ago

3 0

Step-by-step explanation:

No problem it's my pleasure

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Show that the points A(-1,2), B (5,2) and C (2,5) are the vertices of an isosceles triangle. Find the area of ∆ABC

EastWind [94]

Answer:

the area of ∆ABC = 9

Step-by-step explanation:

$CA=\sqrt{\left( -1-2\right)^{2} +\left( 2-5\right)^{2} } = \sqrt{18} =3\sqrt{2}$

$CB=\sqrt{\left( 5-2\right)^{2} +\left( 2-5\right)^{2} } = \sqrt{18} =3\sqrt{2}$

<em>Since</em> CA = CB <em>then</em> A(-1,2), B (5,2) and C (2,5) are the vertices of an isosceles triangle.

Area calculation:

Let The point H be the midpoint of side AB

$x_{H}=\frac{-1+5}{2} =2\\y_{H}=\frac{2+2}{2} =2$

Then

H(2 , 2)

therefore,

$CH=\sqrt{\left( 2-2{}\right)^{2} +\left( 2-5\right)^{2} } =3$

Finally,

$\text{the area of triangle ABC} =\frac{\text{CH} \times \text{AB} }{2} =\frac{3\times 6}{2} =9$

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2 years ago

Based on the quadratic formula, explain the solution to a quadratic equation if the value of bis smaller than the value of

lisabon 2012 [21]

Answer:

The discriminant is the part under the square root in the quadratic formula, b²-4ac. If it is more than 0, the equation has two real solutions. If it's less than 0, there are no solutions. If it's equal to 0, there is one solution.

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4 years ago

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An Olympic-sized swimming pool can hold approximately 6.60 x 105 gallons of water. Calculate the volume of the water in cubic me

shutvik [7]

The volume of the pool is 1.74*10^8 cubic meters

To solve this problem, we convert the volume of the water from gallons to m^3.

<h3 /><h3>Conversion of Unit</h3>

This is done to convert one unit of a substance to another unit of that particular substance. In this question, we are converting from gallon - meter cube

Data;