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3 years ago

If AK= 14, EK=17, BK= 7 , What is the length of DK? 12.7 8.5 7.0 3.5

Mathematics

2 answers:

Elden [556K]3 years ago

8 0

To get the value of DK we use proportionality:
AK/EK=BK/KD
thus plugging the values we get:
14/17=7/KD
getting the reciprocal of getting both sides we have:

17/14=KD/7
thus
KD=17/14×7
KD=8.5
thus

Doss [256]3 years ago

7 0

Answer: the correct option is (B) 8.5.

Step-by-step explanation: Given that AK= 14, EK=17 and BK= 7 in the figure shown.

We are to find the length of DK.

From the figure, we note that

AD and BE are two chords of a circle intersecting at the point K.

We will be using the following theorem :

<u><em>Intersecting Chord Theorem :</em></u> When two chords intersect each other inside a circle, then the products of their segments are equal.

Applying the above theorem in the given circle, we get

$AK\times DK=BK\times EK\\\\\\\Rightarrow DK=\dfrac{BK\times EK}{AK}\\\\\\\Rightarrow DK=\dfrac{7\times 17}{14}\\\\\\\Rightarrow DK=\dfrac{17}{2}\\\\\Rightarrow DK=8.5.$

Thus, the length of DK is 8.5 units.

Option (B) is CORRECT.

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3 years ago

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2 years ago

The ratio of SAMs age to hank is 5 to 3. If the sum of their age is 24. How old is is hank?

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Lets consider SAM's age is 'x' and Hank's age is 'y'
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3 years ago

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Line A is parallel to line D.

Line A is perpendicular to line C.

Line C is perpendicular to line D.

=====================================================

Explanation:

Let's use the slope formula to calculate the slope of the line through (-1,-17) and (3,11)

$(x_1,y_1) = (-1,-17) \text{ and } (x_2,y_2) = (3,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - (-17)}{3 - (-1)}\\\\m = \frac{11 + 17}{3 + 1}\\\\m = \frac{28}{4}\\\\m = 7\\\\$

The slope of line A is 7

-------------

Now let's find the slope of line B.

$(x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (7,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 4}{7 - 0}\\\\m = -\frac{9}{7}\\\\$

-------------

Now onto line C.

$(x_1,y_1) = (7,1) \text{ and } (x_2,y_2) = (0,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 1}{0 - 7}\\\\m = \frac{1}{-7}\\\\m = -\frac{1}{7}\\\\$

-------------

Lastly we have line D.

$(x_1,y_1) = (-1,-6) \text{ and } (x_2,y_2) = (1,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - (-6)}{1 - (-1)}\\\\m = \frac{8 + 6}{1 + 1}\\\\m = \frac{14}{2}\\\\m = 7\\\\$

------------------------------

Here's a summary of the slopes we found

$\begin{array}{|c|c|} \cline{1-2}\text{Line} & \text{Slope}\\\cline{1-2}\text{A} & 7\\\cline{1-2}\text{B} & -9/7\\\cline{1-2}\text{C} & -1/7\\\cline{1-2}\text{D} & 7\\\cline{1-2}\end{array}$

Recall that parallel lines have equal slopes, but different y intercepts. This fact makes Line A parallel to line D.

Lines A and C are perpendicular to one another, because the slopes 7 and -1/7 multiply to -1. In other words, -1/7 is the negative reciprocal of 7, and vice versa. These two lines form a 90 degree angle.

Lines C and D are perpendicular for the same reasoning as the previous paragraph.

Line B unfortunately is neither parallel nor perpendicular to any of the other lines mentioned.

You can use a graphing tool like Desmos or GeoGebra to verify these answers.

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