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2 years ago

Can somebody help me with that? Thank:)

Mathematics

1 answer:

Helga [31]2 years ago

3 0

The sum of the angles in a triangle is 180, so the equation will be :
2k+k+45= 180
add similar variables
3k+45=180
3k=135 (divide each side by 3)
k= 45
So 2k equals= 90
k=25
This is right angle triangle for your info!

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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

Substitute these values into equation(i) and solve as follows:

18 $\sqrt{3}$ = $\frac{1}{2}$ x b x 6

18 $\sqrt{3}$ = 3b

Divide through by 3

6 $\sqrt{3}$ = b

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

Now, assume that the circle is centered at O;

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.

Now, let's calculate the length of the arc XZ

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

2 years ago

Which equation and solution can be used to solve this problem?

maks197457 [2]

Answer:

Step-by-step explanation:

We need to convert these words into mathematical expressions:

- "Twenty-two less than a number"; "less than" indicates that we need to use subtraction, and since it's "twenty-two less than", we have: -22. Let's say the "number" is q. Then, we have -22 of q, which is q - 22.

- "is twenty-four"; "is" in math always means "equal", so we need an equal sign with 24 next to it: = 24

Put this altogether:

q - 22 = 24

The answer is thus D.

4 0

3 years ago

Read 2 more answers

Whats 4485 square feet of grass in 3/4 of an hour. How many square feet of grass can be fertilized per hour

alex41 [277]

4485 square feet of grass ... 3/4 of an hour
x square feet of grass = ? ... 1 hour

If you would like to know how many square feet of grass can be fertilized per hour, you can calculate this using the following steps:

4485 * 1 = 3/4 * x
4485 = 3/4 * x /*4/3
x = 4485 * 4 / 3
x = 5980 square feet

Result: 5980 square feet of grass can be fertilized in one hour.

7 0

3 years ago

A grocery store plans to use 75% of its area for food and beverages. If the grocery store has an area of 1,600 m², what is the a

zaharov [31]

Answer:

It's either 400 or 1,200.

Step-by-step explanation:

Other people are saying 400, I got 1,200 by multiplying 1,600 to 0.75 which gave me that answer. I do not know how other people got 400.

4 0

3 years ago

What is the interquartile range of the data set

Verizon [17]

There are many methods of doing this. This one finds the median; however, instead of halving, you can use quarters instead.

First order the data, ascendingly:

10, 17, 18, 18, 18, 20, 20, 25, 25, 30, 30

Find the median:

For an even number of values: The number of values / 2

For an odd number of values: The number of values + 1 / 2

11 is odd.

11 + 1 / 2

12 / 2 = 6

The median is at the 6th position.

10, 17, 18, 18, 18, 20, 20, 25, 25, 30, 30

The median is 20.

Other method:

You don't need this step.

Using the values lower than the median, exclusive, find the median of the lower values;

For an odd number of values: The number of values + 1 / 2

10, 17, 18, 18, 18

5 + 1 / 2 = 6 / 2 = 3

The median of the lower values is at position 3.

This is the lower quartile.

10, 17, 18, 18, 18

Other method:

For an odd number of values: The number of values + 1 / 4

11 + 1 / 4 = 12 / 4 = 3

10, 17, 18, 18, 18, 20, 20, 25, 25, 30, 30

Using the values greater than the median, exclusive, find the median:

For an odd number of values: The number of values + 1 / 2

20, 25, 25, 30, 30

5 + 1 / 2 = 6 / 2 = 3

The median of the upper values is at position 3.

20, 25, 25, 30, 30

This is 25.

This is the upper quartile.

Other method:

For an odd number of values: (The number of values + 1 / 4) * 3

(11 + 1 / 4) * 3 = (12 / 4) * 3 = 3 * 3 = 9

10, 17, 18, 18, 18, 20, 20, 25, 25, 30, 30

Your interquartile range is 3 - 25

25 - 3 = 21

8 0

3 years ago