Answer:
x = 3.2
Step-by-step explanation:
4(x – 2) = 6(4 – x)
4x - 8 = 24 - 6x
10x - 8 = 24
10x = 32
x = 3.2
keeping in mind that standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
![\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-5})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{\cfrac{2}{3}}[x-\stackrel{x_1}{(-1)}]\implies y+5=\cfrac{2}{3}(x+1)](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B-1%7D~%2C~%5Cstackrel%7By_1%7D%7B-5%7D%29~%5Chspace%7B10em%7D%20%5Cstackrel%7Bslope%7D%7Bm%7D%5Cimplies%20%5Ccfrac%7B2%7D%7B3%7D%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20%5Ctextit%7Bpoint-slope%20form%7D%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%5Cimplies%20y-%5Cstackrel%7By_1%7D%7B%28-5%29%7D%3D%5Cstackrel%7Bm%7D%7B%5Ccfrac%7B2%7D%7B3%7D%7D%5Bx-%5Cstackrel%7Bx_1%7D%7B%28-1%29%7D%5D%5Cimplies%20y%2B5%3D%5Ccfrac%7B2%7D%7B3%7D%28x%2B1%29)
Answer:
33.33
Percentage Calculator: 120 is what percent of 360? = 33.33.
Answer:
192.5 ft²
Step-by-step explanation:
The large sector of the circle has a central angle measure of 360° -100° = 260°, so its area will be (260°/360°) of the circle, or ...
large sector area = (260/360)πr² = 13π/18·(8.35 ft)² ≈ 158.195 ft²
The area of the 100° triangle is ...
triangle area = (1/2)r²·sin(100°) = (1/2)(8.35 ft)²·sin(100°) ≈ 34.332 ft²
Then the shaded area is ...
shaded area = large sector area + triangle area
= 158.195 ft² +34.332 ft² ≈ 192.5 ft²
The shaded area is about 192.5 square feet.
Answer:
Step-by-step explanation:
The length of an arc with measure 
and radius 
is given by 
. From the figure, we know that the radius of arc ADC is 4, but we don't know the measure of the arc. Since there are 360 degrees in a circle, the measure of arc ADC is equal to the measure of the arc formed by 
subtracted from 360. The measure of the arc formed by consists of two congruent angles, 
and 
. To find them, we can use basic trigonometry for a right triangle, since by definition, tangents intersect a circle at a right angle.
In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse, or longest side, of the triangle.
We have:
Therefore, 
The measure of the central angle of 
must then be 
Thus, the length of is equal to:
(three significant figures as requested by question).
