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adelina 88 [10]
3 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]3 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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mat deposited $2,000.00 in the bank. if the rate of simple interest was 10%, what was the amount of money mat had in the bank af
Mekhanik [1.2K]
Principal amount of money deposited by Mat in the bank = $2000
Rate of simple interest given by the bank = 10%
Number of years for which the money is kept in the bank = 5 years
As no money was withdrawn from the account, so
Amount after 5 years = Principal [1 + (Rate * Time)]
                                  = 2000 [ 1 + (10/100) * 5]
                                  = 2000 [ 1 + (1/2)]
                                 = 2000 * (3/2)
                                 = 1000 * 3
                                 = 3000 dollars
So the amount of money made by Mat after 5 years will be $3000.00
8 0
3 years ago
Design a Roller Coaster Portfolio
scoray [572]

1) The domain is [0,300]. The range is [0,250]

2) The slope for the initial climb is 3.57. The equation of the line is y=3.57 x

3) The rate of change of the second hill is -1.4

4) The rate of change of the third hill is -2.1

5) The blue hill is steeper

6) It is not a function

Step-by-step explanation:

1)

The domain of a function is the set of values of x (the input) for which the function itself is defined.

Instead, the range of a function is the set of values of y (the output) that the function can take.

To find the domain, we have to look at the x-axis and see for which values of x the function is defined. By looking at the graph, we see that the function is defined between

x = 0 and x = 300

So, the domain is [0,300].

To find the range, we have to look at the y-axis and see for which values of y the function has an output. By looking at the graph, we see that the function has values of y between

y = 0 and x = 250

So, the range is [0,250].

2)

The slope of a function in a certain range is given by

m=\frac{\Delta y}{\Delta x}

where

\Delta y is the change in the y-coordinate

\Delta x is the change in the x-coordinate

For the initial climb (pink line), we have:

\Delta y = 250 - 0 = 250\\\Delta x = 70 - 0 = 70

Therefore, the slope in this part is

m=\frac{250}{70}=3.57

We can now write the equation of the line in the form

y = mx + b

where b is the y-intercept: since it is zero, the line has simply the form

y=mx \rightarrow y = 3.57 x

3)

Again, to calculate the slope of the hill, we use:

m=\frac{\Delta y}{\Delta x}

where

\Delta y is the change in the y-coordinate

\Delta x is the change in the x-coordinate

For the green hill, we have:

\Delta y = 60-200 = -140

\Delta x = 300-200 = 100

So the rate of change is

m=\frac{-140}{100}=-1.4

4)

As before, the rate of change of the hill is

m=\frac{\Delta y}{\Delta x}

For the blue hill, we have:

\Delta y = 30-230 = -300

\Delta x = 200-60 = 140

So the rate of change is

m=\frac{-300}{140}=-2.1

5)

To know which hill is steeper, we need to compare the magnitude of their rate of change.

In fact, both hills have rate of change negative - because we are going down along the slope. Therefore, we have to consider the magnitude of their slope.

For the green hill:

|m| = 1.4

For the blue hill:

|m|=2.1

We see that the blue hill has a greater slope (in magnitude): therefore, the blue hill is steeper.

6)

A function is defined as a mapping (operation between two sets of variables) in which to one value of x (the input) corresponds one and only one value of y (the output).

This means that a function cannot have multiple values of y for the same x (the input).

By looking at the graph, we see that this function does not respect this criterium: in fact, we see that certain values of x give multiple values of the output, y (for instance, at x=300 the function has two values). So, this is not a function.

Learn more about functions:

brainly.com/question/3511750

brainly.com/question/8243712

brainly.com/question/8307968

#LearnwithBrainly

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4 years ago
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Divide (15x^2+x-8)/(3x-1)
blondinia [14]
<span>Simplifying -15x2 + -2x + 8 = 0
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 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2
 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2
 Combine like terms: 0 + -2 = -2 -3x = -2
 Divide each side by '-3'. x = 0.6666666667
 Simplifying x = 0.6666666667
Subproblem 2
Set the factor '(4 + 5x)' equal to zero and attempt to solve:
 Simplifying 4 + 5x = 0
 Solving 4 + 5x = 0
 Move all terms containing x to the left, all other terms to the right.
 Add '-4' to each side of the equation. 4 + -4 + 5x = 0 + -4
 Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4
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Solutionx = {0.6666666667, -0.8}</span>
4 0
3 years ago
(30 points)
morpeh [17]
C) Basic unit of inheritance

Genes can be inherited by offspring from parent. They can determine a characteristic/trait, but usually many genes influence each. Genes can't be "measured" with a unit.
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3 years ago
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Mai is filling her fish tank. Water flows into the tank at a constant rate.
klasskru [66]

Answer:

Your answer is:

Time:     Water:

0.5          0.8

1               1.6

3              4.8

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Step-by-step explanation:

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3 years ago
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