x = 45°
Solution:
Given data:
Measure of larger arc = 152°
Measure of smaller arc = 62°
<em>If a tangent and a secant intersect at the exterior of a circle then the measure of angle formed is one-half the positive difference of the measures of the intercepted arcs.</em>
![$\Rightarrow x = \frac{1}{2}(\text{ larger arc }- \text{smaller arc} )](https://tex.z-dn.net/?f=%24%5CRightarrow%20%20x%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28%5Ctext%7B%20larger%20arc%20%7D-%20%5Ctext%7Bsmaller%20arc%7D%20%29)
![$\Rightarrow x = \frac{1}{2}(152^\circ-62^\circ)](https://tex.z-dn.net/?f=%24%5CRightarrow%20%20x%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28152%5E%5Ccirc-62%5E%5Ccirc%29)
![$\Rightarrow x = \frac{1}{2}(90^\circ)](https://tex.z-dn.net/?f=%24%5CRightarrow%20%20x%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2890%5E%5Ccirc%29)
⇒ x = 45°
The value of x is 45°.
Answer: The 20th term is 100
Step-by-step explanation: It adds by 6 each time
-14, -8, -2, 4, 10, 16, 22, 28, 34, 40, 46, 52, 58, 64, 70, 76, 82, 88, 94, 100
<h3>
The pattern is 0.01+</h3>
<u>So the next 4 digits are:</u>
<h3>
0.4243</h3><h3>
</h3>
0.34353637383940414243
Answer:
![\frac{y-2}{4}](https://tex.z-dn.net/?f=%5Cfrac%7By-2%7D%7B4%7D)
Step-by-step explanation:
Let's start by factoring everything:
![\dfrac{\frac{y^2+y}{y^2-2y}}{\frac{4y+4}{y^2-4y+4}}=](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac%7By%5E2%2By%7D%7By%5E2-2y%7D%7D%7B%5Cfrac%7B4y%2B4%7D%7By%5E2-4y%2B4%7D%7D%3D)
![\dfrac{\frac{y(y+1)}{y(y-2)}}{\frac{4(y+1)}{(y-2)^2}}=](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac%7By%28y%2B1%29%7D%7By%28y-2%29%7D%7D%7B%5Cfrac%7B4%28y%2B1%29%7D%7B%28y-2%29%5E2%7D%7D%3D)
Now, you can cancel out some terms:
![\dfrac{\frac{y+1}{y-2}}{\frac{4(y+1)}{(y-2)^2}}=](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac%7By%2B1%7D%7By-2%7D%7D%7B%5Cfrac%7B4%28y%2B1%29%7D%7B%28y-2%29%5E2%7D%7D%3D)
Now, when you divide a fraction by another fraction, that is the same as multiplying the first fraction by the reciprocal of the second one:
![\frac{y+1}{y-2}\cdot \frac{(y-2)^2)}{4(y+1)}=](https://tex.z-dn.net/?f=%5Cfrac%7By%2B1%7D%7By-2%7D%5Ccdot%20%5Cfrac%7B%28y-2%29%5E2%29%7D%7B4%28y%2B1%29%7D%3D)
![\frac{y-2}{4}](https://tex.z-dn.net/?f=%5Cfrac%7By-2%7D%7B4%7D)
Hope this helps!