Answer:
20 inches
Step-by-step explanation:
Use the Pythagorean Theorem.
![a^2 + b^2 = c^2\\15^2 + b^2 = 25^2\\225 + b^2 = 625\\b^2 = 400\\b = \sqrt{400} \\b = 20](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%3D%20c%5E2%5C%5C15%5E2%20%2B%20b%5E2%20%3D%2025%5E2%5C%5C225%20%2B%20b%5E2%20%3D%20625%5C%5Cb%5E2%20%3D%20400%5C%5Cb%20%3D%20%5Csqrt%7B400%7D%20%5C%5Cb%20%3D%2020)
we know the diameter of it is 2, so its radius must be half that, and the central angle is 5π/3, so
![\textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=1\\ \theta =\frac{5\pi }{3} \end{cases}\implies s=(1)(\frac{5\pi }{3})\implies s\approx 5.24~meters](https://tex.z-dn.net/?f=%5Ctextit%7Barc%27s%20length%7D%5C%5C%5C%5C%20s%3Dr%5Ctheta%20~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20%5Ctheta%20%3D%5Cstackrel%7Bradians%7D%7Bangle%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D1%5C%5C%20%5Ctheta%20%3D%5Cfrac%7B5%5Cpi%20%7D%7B3%7D%20%5Cend%7Bcases%7D%5Cimplies%20s%3D%281%29%28%5Cfrac%7B5%5Cpi%20%7D%7B3%7D%29%5Cimplies%20s%5Capprox%205.24~meters)
Answer:
28 degrees
Step-by-step explanation:
Because a triangle equals 180, you can subtract 90 and 34 from triangle ABE to leave you with 56 degrees for angle B.
Since CBA is a straigth line with 180 degrees, you can subtract 56 to end up with 124 degrees for angle CBE.
Since line BD bisects angle EBC (splits in half), you can divide the 124 degrees into 62 degrees.
Now that we know angle CBE equals 62 degrees, we can add the 90 degrees and subtract them from the 180 degrees of the triangle.
62+90=152
180-152=28
<h3>
Answer: No, it is not a solution</h3>
Explanation:
Refer to the diagram below. The point (-4,3) marked in red is outside the blue shaded region. So it doesn't make both inequalities true, and therefore not considered a solution.
In contrast, a point like (-5,1) is a solution as it is in the shaded region.
Put another way, the set of all solution points must be below both the solid line and the dashed line. Points can be on the solid line, but must be adjacent to the blue shaded region. The fact (-4,3) is on the solid line doesn't count because its not below the dashed line.
M = (22 - 7)/(8 - 5) = 15/3 = 5
<span>using point (5, 7) </span>
<span>y - 7 = 5(x - 5) in point-slope form </span>
<span>y - 7 = 5x - 25 </span>
<span>y = 5x - 18 in slope-intercept form.</span>