Answer:
TS = 6.6 (nearest tenth)
Step-by-step explanation:
<u>Secant</u>: a straight line that intersects a circle at two points.
<u>Tangent</u>: a straight line that touches a circle at only one point.
<u>Theorem</u>
When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
Given:
- Tangent segment = QR
- Secant segment = TR
- External secant segment = SR
⇒ QR² = TR · SR
⇒ 19² = (TS + 16) · 16
⇒ 361 = (TS + 16) · 16
⇒ 22.5625 = TS + 16
⇒ TS = 22.5625 - 16
⇒ TS = 6.5625
⇒ TS = 6.6 (nearest tenth)
Answer:
60 + 2.5n ≥ 150
2.5n ≥ 90
n ≥ 36 She must clean 90 tables to earn at least $150.
Step-by-step explanation:
She earns $2.50 for each table she cleans so n represents the number of tables she cleans. You add that to $60. At least must mean that the inequality has to be equal to or bigger than 60 + 2.5n.
Now we just have to solve, which I do for you above in the 'Answer' section.
I hope this helps you!! ^-^
Answer:
C. (y + 3)²/64 - (x + 1)²/36 = 1
Step-by-step explanation:
This is a hyperbola with a vertically tranversed axis, so the general equation for it is:
![\frac{(y-k)^{2} }{a^{2}}-\frac{(x-h)^{2} }{b^{2}}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28y-k%29%5E%7B2%7D%20%7D%7Ba%5E%7B2%7D%7D-%5Cfrac%7B%28x-h%29%5E%7B2%7D%20%7D%7Bb%5E%7B2%7D%7D%3D1)
where h and k are the coordinate for the center (h, k)
we're given center is (−1, −3), so
h = -1
k = -3
![\frac{(y-(-3))^{2} }{a^{2}}-\frac{(x-(-1))^{2} }{b^{2}}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28y-%28-3%29%29%5E%7B2%7D%20%7D%7Ba%5E%7B2%7D%7D-%5Cfrac%7B%28x-%28-1%29%29%5E%7B2%7D%20%7D%7Bb%5E%7B2%7D%7D%3D1)
![\frac{(y+3)^{2} }{a^{2}}-\frac{(x+1)^{2} }{b^{2}}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28y%2B3%29%5E%7B2%7D%20%7D%7Ba%5E%7B2%7D%7D-%5Cfrac%7B%28x%2B1%29%5E%7B2%7D%20%7D%7Bb%5E%7B2%7D%7D%3D1)
The information about "<em>One focus of a hyperbola is located at (−1, 7). One vertex of the hyperbola is located at (−1, 5)</em>" are irrelevant because the a and b values are the same for all the answers. So we literally only needed the center of the hyperbola to find our answer.
The only answer with (y+3) and (x+1) is C.
You are looking for the shaded region that would be contained in both of the inequalities.
You have:
![x+y \leq 80](https://tex.z-dn.net/?f=x%2By%20%5Cleq%2080)
![5x+10y\ \textgreater \ 500](https://tex.z-dn.net/?f=%205x%2B10y%5C%20%5Ctextgreater%20%5C%20500)
If you graph an shade the correct half-plane for those equations, you will see there is a triangular region on the left side of the first quadrant.