Mathematics, 23.11.2019 04:31 londonval

4. given abc with vertices at a(1,-4), b(-1,-2), and c(-2,-5), prove or disprove that abc is isosceles

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Answer from: cgkiepe5759

ABC is isosceles

Step-by-step explanation:

The coordinate of points given are:

A(1,-4)

B(-1, -2 )

C ( -2 , -5 )

For ABC to be isosceles , then AB must be equal to BC or AB = AC

The next thing to do is to find the value of AB , BC and AC using the formula for finding distance between two points which is given by:

D = $\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2}}$

Calculating AB first , we have

$\sqrt{(-1-1)^{2}+(-2+4)^{2} }$

= $\sqrt{4+4}$

= $\sqrt{8}$

Therefore:

AB = $\sqrt{8}$

Calculating BC , we have :

D = $\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2}}$

D = $\sqrt{(-2+1)^{2}+(-5+2)^{2} }$

D = $\sqrt{10}$

Therefore:

BC = $\sqrt{10}$

Calculating AC , we have :

D = $\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2}}$

D = $\sqrt{(-2-1)^{2}+(-5+4)^{2} }$

D = $\sqrt{10}$

Therefore:

AC = $\sqrt{10}$

Since AC = BC then triangle ABC is isosceles

Answer from: Quest

step-by-step explanation:

the 2000 florida legislature amended section 322.05, florida statutes, changing the requirements to obtain a class e license for a driver under the age of 18 holding a learner's license. the following requirements must be met in order to obtain a regular class e license if a learner's license is issued on or after october 1, 2000:

must hold a learner's license for at least 12 months or until the 18th birthday.

must have no convictions 12 months from the issue date of the learner's license.

may have one traffic conviction within 12 months from the issue date of the learner's license if adjudication is withheld.

a parent, legal guardian, or responsible adult over 21 years old must certify that the driver has 50 hours driving experience, including 10 hours of night time driving.

Answer from: Quest

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule