The value would be more than c
Answer:
- <em><u>5.6875 in</u></em>
Explanation:
At the point of tangency, the <em>tangent </em>to a circle and the <em>radius</em> form a right triangle (the radius is perpendicular to the tangent).
Here you are given the length of the tangent (6in), and the distance from the bisected vertex to the circle (2.75 in)
I tried to upload the drawing but the tool is not allowing it now.
In the figure:
- The length of the tangent (6 in) is one leg of the triangle
- The distance from vertex and the circle (2.75in) along with the radius forms the hypotenuse of the right triangle: 2.75 + r.
- The other leg is the radius, r.
Then, you can use Pythagorean theorem:
Solve:
- r² + 36 = r² + 5.5r + 7.5625
The solution is in inches: r = 5.6875 inches ← answer
Mean: average of the numbers. Add them up, divide by how many numbers/entries there are.
-2 + -1 + 0 + 0 + 0 + 0 + 2 + 4 = 3
3 divided by 8 = 0.375
Your mean is 0.375
Median: write the data in numerical order, find the middle number.
-2, -1, 0, 0, 0, 0, 2, 4
In this data set, there are an even number of entries, so we average the middle two numbers. Thankfully, here, the middle two are the same, so your median is 0.
Mode: the number that appears the most often in the data set
Your mode is also 0, because there are more zeroes than any other number in the data set.
Range: the distance on a number line between the highest and lowest number.
The distance between -2 and 4 is 6.4 - (-2) = 6
Please LMK if you have questions
Answer:
b
Step-by-step explanation:
<h3>Answer: As a fraction, HC is 21/4 units long</h3><h3>In decimal form, HC is 5.25 units long.</h3>
==============================================
Work Shown:
Let x = HC and y = BH
AH = 12-x since AH = 12-HC and x = HC
---------------
See the attached drawing below. The altitude BH forms three similar triangles which makes the proportion below possible
HC/BH = BH/AH
x/y = y/(12-x) ... substitution
x(12-x) = y^2 ... cross multiply
y^2 = -x^2+12x
note how I isolated y^2 instead of y. We will use this equation later.
---------------
Focus on triangle AHB. Use the pythagorean theorem
(BH)^2 + (AH)^2 = (AB)^2
(y)^2 + (12-x)^2 = (9)^2
y^2 + 144-24x+x^2 = 81
-x^2+12x + 144-24x+x^2 = 81 ... replace y^2 with -x^2+12x
-x^2+12x + 144-24x+x^2-81 = 0
-12x + 63 = 0
-12x = -63
x = -63/(-12)
x = 5.25 <<-- answer in decimal form
x = 5 + 0.25
x = 5 + 1/4
x = 20/4 + 1/4
x = 21/4 <<-- answer as a fraction
