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adelina 88 [10]
2 years ago
9

Given circle X with radius 10 units and chord AB with length 12 units, what is the length of segment CX, which bisects the chord

? A. 10 units B. 8 units C. 6 units D. 16 units

Mathematics
1 answer:
andrew-mc [135]2 years ago
7 0
Consider the circle with center X, as shown in the figure. 

Draw the diameter of the circle which is parallel to cherd AB, as shown in the figure.

Since the diameter and AB are parallel, then the line segment XC which bisects AB at C, will be perpendicular to AB.

SO triangle XCB is a right triangle. Thus the length of CX, by the Pythagorean theorem is  

\sqrt{ XB^{2}- CB^{2}} = \sqrt{ 10^{2}- CB^{6}}= \sqrt{100-36}= \sqrt{64}=8 units.


Answer: 8 units

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The length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58° to 3
viva [34]

Answer:

119.45 m

Step-by-step explanation:

Given:

When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.

To find:

Length of pole = ?

Solution:

Kindly refer to the attached image.

\triangle ABC represents the 1st angle of elevation of sun i.e.  58°

\triangle ABD represents the 2nd angle of elevation of sun i.e.  36°

Change in shadow is represented by CD = 90 m

Let height of pole, AB = h m

Let side BC = x m

Now, let us apply tangent rules in \triangle ABC, \triangle ABD one by one:

tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan58^\circ=\dfrac{AB}{BC}\\\Rightarrow tan58^\circ=\dfrac{h}{x}\\\Rightarrow x = 0.624h ..... (1)

tan36^\circ = \dfrac{h}{x+90}

Putting value of x using equation (1):

tan36^\circ = \dfrac{h}{0.624h+90}\\\Rightarrow 0.726\times 0.624h+0.726\times 90 = h\\\Rightarrow h-0.453h =65.34\\\Rightarrow \bold{h = 119.45\ m}

119.45 m is the height of pole.

7 0
2 years ago
If only two points are needed to determine a​ line, why are three ordered pair solutions or points found for a linear​ equation?
Alina [70]

To draw the graph of a linear equation , two points are more than enough to draw a line.

But sometimes we may commit a mistake and then if we draw the line, everything appears good. As two points shall always define a line irrespective of the points are correct or not.

So in order to make sure that the points we obtained are correct , we take a third point to ensure that the two points calculated earlier are correct and all points lie on the same line. If they don't we have committed some mistake.

Option A) is the right answer

7 0
2 years ago
How do you use a number line to solve 235+123
Novosadov [1.4K]
<span>Number line refers to a mathematical process of solving the equation with the use of lines.
=> 235 + 123
Starting from 0 you count 1 up to 235. Then starting from 235 you additionally count another 123.
Then from zero start counting the total number to the line you stopped when adding 123 to 235.

This simply equals to
=> 235 + 123
=> 358.
Pls. see attached image for illustration of number line.</span>Answer here

6 0
2 years ago
How is the graph of y = negative RootIndex 3 StartRoot x minus 4 EndRoot transformed to produce the graph of y = negative RootIn
SVEN [57.7K]

Answer:

Multiply by ∛2 and translate the graph to left by 4 units.

Step-by-step explanation:

The initial function given is:

y = -∛(x - 4)

The transformed function is:

y = -∛(2x - 4)

Consider the initial function.

y = -∛(x - 4)

(Represented by Black line in the graph)

Multiply the function by ∛2. The function becomes:

y = -∛(x - 4) × ∛2

y = -∛(2)(x-4)

y = -∛(2x-8)

(Represented by Red line in the graph represents this function)

Translate the graph 4 units to the left by adding 4 to the x component:

y = -∛(2x-8+4)

y= -∛(2x - 4)

(Represented by Blue line in the graph)

3 0
2 years ago
Read 2 more answers
Consider the equation StartFraction x over 5 EndFraction minus 2 = 11, where x represents the number of basketball players that
Free_Kalibri [48]

Answer:

just copy and paste below

Step-by-step explanation:

Step-by-step explanation:Sample Response: The equation could model a scenario determining the number of players on each team in a league of five teams, if 2 players have to be taken out of the possible players to be referees and to keep score. There will be 11 players on each team.

6 0
2 years ago
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