Answer:
x ≈ 0.290640965127
Step-by-step explanation:
y subtracting the right side of the equation, we get a function that is zero at a real solution for x. The only x-intercept is at approximately 0.290640965127.
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The graph shows the x-intercept to be 0.2906. The value above was obtained by Newton's method iteration. The roots of this cubic will all be irrational.
The bisector of the angle at A (call it AQ) divides the segment BC into segments BQ:QC having the ratio AB:AC. Use this fact to find x.
.. 9:15 = (2x -1):3x
.. 15(2x -1) = 9*3x . . . . . the product of the means equals the product of extremes
.. 30x -15 = 27x
.. 3x = 15
.. x = 5
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According to the value of x, the bisector AQ divides the triangle into two isosceles triangles: ABQ, ACQ.
Answer:
Step-by-step explanation:
Lets use the compound interest formula provided to solve this:
<em>P = initial balance</em>
<em>r = interest rate (decimal)</em>
<em>n = number of times compounded annually</em>
<em>t = time</em>
First, change 6% into a decimal:
6% -> 
-> 0.06
Since the interest is compounded semi-annually, we will use 2 for n. Lets plug in the values now and your equation will be:
ANSWER
The length of the diagonal is 5 ft
EXPLANATION
The diagram of the rug with the diagonal is:
The diagonal and the sides form a right triangle, so we can use the Pythagorean theorem to find x, the length of the diagonal:
![\begin{gathered} x^2=3^2+4^2 \\ x=\sqrt[]{9+16} \\ x=\sqrt[]{25} \\ x=5 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5E2%3D3%5E2%2B4%5E2%20%5C%5C%20x%3D%5Csqrt%5B%5D%7B9%2B16%7D%20%5C%5C%20x%3D%5Csqrt%5B%5D%7B25%7D%20%5C%5C%20x%3D5%20%5Cend%7Bgathered%7D)
We know that the volume is: V = 1 gallon = 231 in³
Also : r = 3 in.
The volume of a cylinder: V = r² π h
231 = 3³ · 3.14 · h
231 = 9 · 3.14 · h
231 = 28.26 h
h = 231 : 28.26
h = 8.17 ≈ 8 in
Answer: C) 8 in.
