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DaniilM [7]
3 years ago
8

Solve the equation and enter the value of x below. x+ (9) = -15 X=

Mathematics
1 answer:
Wittaler [7]3 years ago
3 0

Answer:

x=-24 is the correct answer

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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 painting is purchased for $250. If the value of the painting doubles every 5 years, then
ch4aika [34]
After 5 years, value doubles.
Hence after 5 years, value is 250 x 2 = 500
After another 5 years, value doubles.
500 x 2 = 1000
Ans: $1000
7 0
2 years ago
a high school stage collapsed in Fullerton, California, when 250 students got on stage for the finale of a musical production. T
Lera25 [3.4K]

Answer:

91

Step-by-step explanation:

In this question, the important information we get from this is that the stage can support 12,750 students. We are asked, if the average weight of a student is 140 pounds, what is the maximum number of students that can be on the stage safely?

To solve, we simply divide 12,750 by 140.

x=\frac{12,750}{140}

x= 91.07

We get 91.07 as our answer. Since we are considering the maximum number of students, then we must round 91.07 to the nearest whole number which would be 91.

The maximum number of students who could safely be on the stage is 91.

6 0
3 years ago
Janet is 48 in tall and Lucy her younger sister is 32 in tall at 2:30 in the afternoon Lucy's Shadow extends 34 in how far does
Elis [28]
Janet is 50inches tall.
5 0
3 years ago
Given: AB with coordinates of AC-3, -1) and B(2, 1)
andrezito [222]

Answer:

up 2, right 3

Step-by-step explanation:

up 2, to the right 3.

8 0
3 years ago
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