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PtichkaEL [24]
3 years ago
11

Segments AB and CD intersect to form an angle of 88.5° as shown. What is the measure of <2

Mathematics
1 answer:
Darya [45]3 years ago
3 0

Answer:

91.8°

Step-by-step explanation:

180-88.2=91.8°

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XY is a diameter of a circle and Z is a point on the circle such that ZY=6. If the area of the triangle XYZ is 18 square root 3
nataly862011 [7]
<h2>Answer:</h2>

4π

<h2>Step-by-step explanation:</h2>

As shown in the diagram, triangle XYZ is a right triangle. Therefore, its area (A) is given by:

A = \frac{1}{2} x b x h      -------------(i)

Where;

A = 18\sqrt{3}

b = XZ = base of the triangle

h = YZ = height of the triangle = 6

<em>Substitute these values into equation(i) and solve as follows:</em>

18\sqrt{3} =  \frac{1}{2} x b x 6

18\sqrt{3} =  3b

<em>Divide through by 3</em>

6\sqrt{3} =  b

Therefore, b = XZ = 6\sqrt{3}

<em>Now, assume that the circle is centered at O;</em>

Triangle XOZ is isosceles, therefore the following are true;

(i) |OZ| = |OX|

(ii) XZO = ZXO = 30°

(iii) XOZ + XZO + ZXO = 180°   [sum of angles in a triangle]

=>  XOZ + 30° + 30° = 180°

=>  XOZ + 60° = 180°

=>  XOZ = 180° - 60°

=>  XOZ = 120°

Therefore we can calculate the radius |OZ| of the circle using sine rule as follows;

\frac{sin|XOZ|}{XZ} = \frac{sin|ZXO|}{OZ}

\frac{sin120}{6\sqrt{3} } = \frac{sin 30}{OZ}

\frac{\sqrt{3} /2}{6\sqrt{3} } = \frac{1/2}{|OZ|}

\frac{1}{12}  = \frac{1}{2|OZ|}

\frac{1}{6} = \frac{1}{|OZ|}

|OZ| = 6

The radius of the circle is therefore 6.

<em>Now, let's calculate the length of the arc XZ</em>

The length(L) of an arc is given by;

L = θ / 360 x 2 π r          ------------------(ii)

Where;

θ = angle subtended by the arc at the center.

r = radius of the circle.

In our case,

θ = ZOX = 120°

r = |OZ| = 6

Substitute these values into equation (ii) as follows;

L = 120/360 x 2π x 6

L = 4π

Therefore the length of the arc XZ is 4π

5 0
3 years ago
a table is 6 feet long and 3 feet wide. you extend the table by inserting two identical table/leaves. the longest side length of
Molodets [167]

Yep... so they says that the area of the extended leaf is 18+6x... You know that the area is length into breath... here the breath doesn't change.. so it'll be 3ft... can get the length by dividing area by 3... that is 6+2x... Now the new length wil be 2times that plus the previous 6ft length

6 0
3 years ago
The graph shows a proportional relationship.What is the unit rate? Enter your answer as an improper fraction in simplest form in
ruslelena [56]
That is the slope
rise/run
we see we have (2/5,1/2)
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((1/2)/(2/5)=(1/2)(2/5)=2/10=1/5

unit rate is y=(1/5)x
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3 years ago
The area of a rectangle is represented by the expression 6x³y5. Which of the following could be the
oee [108]

The length and width of the rectangle are: 2x^2y^2 , 3xy^3

<h3>What is the area of the rectangle?</h3>

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

The area of a rectangle is represented by the expression 6x^3y^5.

The area of the rectangle = 2x^2y^2 \times 3xy^3

                                          = 6x^3y^5

So, the length and width of the rectangle are: 2x^2y^2 , 3xy^3

Learn more about the area;

brainly.com/question/1658516

#SPJ1

7 0
2 years ago
The volume of a rectangular prism is 2,100 cm cubed , with length 25 cm and width 12 cm. What is the height, in cm?
BabaBlast [244]
This is easy the answer is 7
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3 years ago
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