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2 years ago

Find the value of x.6 3 2 x

Mathematics

1 answer:

love history [14]2 years ago

3 0

Answer:

$x=4$

Step-by-step explanation:

To solve this problem, one must use the angle bisector theorem. This theorem provides a proportion between the sides formed by an angle bisector. One can apply this theorem here by forming the following proportion,

$\frac{BA}{BC}=\frac{AD}{DC}$

Substitute,

$\frac{x}{6}=\frac{2}{3}$

Cross products,

$3(x)=2(6)$

Simplify,

$3x=12$

Inverse operations,

$3x=12\\\\x = 4$

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Which number line shows the solution to 11x + 14 < –8?

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Answer:

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Step-by-step explanation:

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2 years ago

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Choose the option that best answers the question.The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle. If Angl

Sunny_sXe [5.5K]

Answer:

The correct option is 1.

Step-by-step explanation:

Given information: The coordinates of a right angled triangle ABC are A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6). Angle ABC = 90°.

It means AB and BC are legs of the right angled triangle ABC.

Side AB lies on the y-axis because the x-coordinate of both A and B is 0.

Two legs are perpendicular to each other. So, BC must be parallel to x-axis and the y-coordinate of both B and C is must be same.

$4a-5=2a+6$

$4a-2a=5+6$

$2a=11$

Divide both sides by 2.

$a=\frac{11}{2}$

The value of a is 2. So the coordinates of triangle ABC are

$B(0,4a-5)=B(0,4(\frac{11}{2})-5)\Rightarrow B(0,17)$

$C(2a+1,2a+6)=C(2(\frac{11}{2})+1,2(\frac{11}{2})+6)\Rightarrow C(12,17)$

The area of a triangle is

$Area=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

The area of triangle ABC is

$Area=\frac{1}{2}|0(17-17)+0(17-0)+12(0-17)|$

$Area=\frac{1}{2}|12(-17)|$

$Area=\frac{1}{2}|-204|$

$Area=\frac{1}{2}(204)$

$Area=102$

The area of triangle ABC is 102. Therefore the correct option is 1.

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3 years ago

4. The list below shows the number of songs that five students downloaded last week.

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Answer:

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Step-by-step explanation:

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2 years ago

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3 years ago

Find the value of x.6 3 2 x​

Find the value of x.6 3 2 x