Answer:
The correct answer: a line
Answer:
The angle Rick must kick the ball to score is an angle between the lines BX and BZY which is less than or equal to 32°
Step-by-step explanation:
The given measures of the of the angle formed by the tangent to the given circle at X and the secant passing through the circle at Z and Y are;
![m\widehat{XZ} = 58^{\circ}](https://tex.z-dn.net/?f=m%5Cwidehat%7BXZ%7D%20%20%3D%2058%5E%7B%5Ccirc%7D)
![m\widehat{XY} = 122^{\circ}](https://tex.z-dn.net/?f=m%5Cwidehat%7BXY%7D%20%20%3D%20122%5E%7B%5Ccirc%7D)
The direction Rick must kick the ball to score is therefore, between the lines BX and BXY
The angle between the lines BX and BXY = ∠XBZ = ∠XBY
The goal is an angle between ![m\widehat{XY}](https://tex.z-dn.net/?f=m%5Cwidehat%7BXY%7D)
Let 'θ' represent the angle Rick must kick the ball to score
Therefore the angle Rick must kick the ball to score is an angle less than or equal to ∠XBZ = ∠XBY
By the Angle Outside the Circle Theorem, we have;
The angle formed outside the circle = (1/2) × The difference of the arcs intercepted by the tangent and the secant
![\therefore \angle XBZ = \dfrac{1}{2} \times \left (m\widehat{XY} -m\widehat{XZ} \right)](https://tex.z-dn.net/?f=%5Ctherefore%20%5Cangle%20XBZ%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Cleft%20%28m%5Cwidehat%7BXY%7D%20%20-m%5Cwidehat%7BXZ%7D%20%5Cright%29)
We get;
∠XBZ = (1/2) × (122° - 58°) = 32°
The angle Rick must kick the ball to score, θ = ∠XBZ ≤ 32°
Answer:
3x+4
Step-by-step explanation:
3 dollars per mile = 3x
plus 4 dollars for taxi ride.
Answer:
Step-by-step explanation:
Find the slope of the line
(x₁ , y₁) = (6 , 8) & (x₂ , y₂) = (0 , 5)
![Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{5-8}{0-6}\\\\=\frac{-3}{-6}\\\\=\frac{1}{2}](https://tex.z-dn.net/?f=Slope%20%3D%20%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B5-8%7D%7B0-6%7D%5C%5C%5C%5C%3D%5Cfrac%7B-3%7D%7B-6%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D)
m = 1/2 ;(x₁ , y₁) = (6 , 8)
y - y₁ = m(x - x₁)
![y - 8 = \frac{1}{2}(x - 6)\\\\y - 8 =\frac{1}{2}x -\frac{1}{2}*6\\\\y - 8 =\frac{1}{2}x- 3\\\\y = \frac{1}{2}x - 3 + 8\\\\y = \frac{1}{2}x + 5](https://tex.z-dn.net/?f=y%20-%208%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28x%20-%206%29%5C%5C%5C%5Cy%20-%208%20%3D%5Cfrac%7B1%7D%7B2%7Dx%20-%5Cfrac%7B1%7D%7B2%7D%2A6%5C%5C%5C%5Cy%20-%208%20%3D%5Cfrac%7B1%7D%7B2%7Dx-%203%5C%5C%5C%5Cy%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%20-%203%20%2B%208%5C%5C%5C%5Cy%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%20%2B%205)
Answer:
this is the chan of formula from 7=LW to
w =7/L
because we divided both sides by L.