By distributive property, 8 x (14 + 7) = (8 x 14) + (8 x 7)
Since the big triangle is an isosceles one, we conclude that the angles of the left triangle are: 32, 90 and 3x-10. Sinche the sum of this angles have to be 180° we have:
![(3x-10)+32+90=180](https://tex.z-dn.net/?f=%283x-10%29%2B32%2B90%3D180)
Solving for x, we have:
![\begin{gathered} (3x-10)+32+90=180 \\ 3x-10+32+90=180 \\ 3x=180+10-90-32 \\ 3x=68 \\ x=\frac{68}{3} \\ x=22.67 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%283x-10%29%2B32%2B90%3D180%20%5C%5C%203x-10%2B32%2B90%3D180%20%5C%5C%203x%3D180%2B10-90-32%20%5C%5C%203x%3D68%20%5C%5C%20x%3D%5Cfrac%7B68%7D%7B3%7D%20%5C%5C%20x%3D22.67%20%5Cend%7Bgathered%7D)
Therefore, x=22.67 and the answer is A.
Step 1.
Calculate measure of angle α:
![47^o-38^o=9^o](https://tex.z-dn.net/?f=47%5Eo-38%5Eo%3D9%5Eo)
Step 2.
Calculate what fraction of the angle 360° is the angle α:
![\dfrac{9^o}{360^o}=\dfrac{1}{40}](https://tex.z-dn.net/?f=%5Cdfrac%7B9%5Eo%7D%7B360%5Eo%7D%3D%5Cdfrac%7B1%7D%7B40%7D)
Step 3.
Calculate the circumference of the Earth (circle):
![C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi](https://tex.z-dn.net/?f=C%3D2%5Cpi%20r%5Cto%20C%3D2%5Cpi%5Ccdot4000%3D8000%5Cpi%5C%20mi)
Step 4.
The length of arc is equal 1/40 of the circumference:
![\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B40%7DC%3D%5Cdfrac%7B1%7D%7B40%7D%5Ccdot8000%5Cpi%3D200%5Cpi%5C%20mi)
![\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi](https://tex.z-dn.net/?f=%5Cpi%5Capprox3.14%5Cto%5Cdfrac%7B1%7D%7B40%7DC%5Capprox200%5Ccdot3.14%3D628%5C%20mi)
<h3>Answer: A) 628 miles</h3>
<h3>Original Equation:</h3>
![-\frac{1}{3}+2z=-\frac{5}{6}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B3%7D%2B2z%3D-%5Cfrac%7B5%7D%7B6%7D)
<h3>Steps:</h3>
<em>*To solve for a variable, isolate the desired variable onto one side.</em>
Firstly, we want to add 1/3 to each side however -5/6 and 1/3 do not share the same denominator, and we want them to have that and we can do that by finding the LCD, or lowest common denominator. To find the LCD, list the multiples of 6 and 3 and the lowest multiple that they share is their LCD. In this case, their LCD is 6. Multiply -1/3 by 2/2:
![-\frac{1}{3}\times \frac{2}{2}=-\frac{2}{6}\\\\-\frac{2}{6}+2z=-\frac{5}{6}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B3%7D%5Ctimes%20%5Cfrac%7B2%7D%7B2%7D%3D-%5Cfrac%7B2%7D%7B6%7D%5C%5C%5C%5C-%5Cfrac%7B2%7D%7B6%7D%2B2z%3D-%5Cfrac%7B5%7D%7B6%7D)
Now that we have common denominators, add both sides by 2/6:
![2z=-\frac{3}{6}\\\\2z=-\frac{1}{2}](https://tex.z-dn.net/?f=2z%3D-%5Cfrac%7B3%7D%7B6%7D%5C%5C%5C%5C2z%3D-%5Cfrac%7B1%7D%7B2%7D)
Next, you want to cancel out 2 to isolate z. Usually, one would divide both sides by 2, however remember that <u>dividing by a number is the same as multiplying by it's reciprocal.</u> To find a number's reciprocal, flip the numerator and denominator around. In this case, since 2 is a <em>whole number</em> this means that the denominator is 1. In this case: 2/1 would become 1/2. Multiply both sides by 1/2:
![\frac{1}{2}\times 2z= -\frac{1}{2}\times \frac{1}{2}\\\\z=-\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Ctimes%202z%3D%20-%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5Cz%3D-%5Cfrac%7B1%7D%7B4%7D)
<h3>Final Answer:</h3>
<u>Your final answer is z = -1/4.</u>
The answer is D. a1=2 an=an-1+3