Answer:
![\boxed{ \bold{ \huge{ \boxed{ \sf{x = - 10}}}}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Cbold%7B%20%5Chuge%7B%20%5Cboxed%7B%20%5Csf%7Bx%20%3D%20%20-%2010%7D%7D%7D%7D%7D)
Step-by-step explanation:
![\sf{ \frac{5}{6} = \frac{x - 10}{3x + 6} }](https://tex.z-dn.net/?f=%20%5Csf%7B%20%5Cfrac%7B5%7D%7B6%7D%20%20%3D%20%20%5Cfrac%7Bx%20-%2010%7D%7B3x%20%2B%206%7D%20%7D)
Apply cross product property
⇒![\sf{5(3x + 6) = 6( x - 10)}](https://tex.z-dn.net/?f=%20%5Csf%7B5%283x%20%2B%206%29%20%3D%206%28%20x%20-%2010%29%7D)
Distribute 5 through the parentheses
⇒![\sf{15x + 30 = 6( x - 10)}](https://tex.z-dn.net/?f=%20%5Csf%7B15x%20%2B%2030%20%3D%206%28%20x%20-%2010%29%7D)
Distribute 6 through the parentheses
⇒![\sf{15x + 30 = 6x - 60}](https://tex.z-dn.net/?f=%20%5Csf%7B15x%20%2B%2030%20%3D%206x%20-%2060%7D)
Move 6x to left hand side and change it's sign
⇒![\sf{15x - 6x + 30 = - 60}](https://tex.z-dn.net/?f=%20%5Csf%7B15x%20-%206x%20%20%2B%2030%20%3D%20%20-%2060%7D)
Collect like terms
⇒![\sf{9x + 30 = - 60}](https://tex.z-dn.net/?f=%20%5Csf%7B9x%20%2B%2030%20%3D%20%20-%2060%7D)
Move 30 to right hand side and change it's sign
⇒![\sf{9x = - 60 - 30}](https://tex.z-dn.net/?f=%20%5Csf%7B9x%20%3D%20%20-%2060%20-%2030%7D)
Calculate
⇒![\sf{9x = - 90}](https://tex.z-dn.net/?f=%20%5Csf%7B9x%20%3D%20%20-%2090%7D)
Divide both sides of the equation by 9
⇒![\sf{ \frac{9x}{9} = \frac{ - 90}{9} }](https://tex.z-dn.net/?f=%20%5Csf%7B%20%5Cfrac%7B9x%7D%7B9%7D%20%20%3D%20%20%20%5Cfrac%7B%20-%2090%7D%7B9%7D%20%7D)
Calculate
⇒![\sf{x = - 10}](https://tex.z-dn.net/?f=%20%5Csf%7Bx%20%3D%20%20-%2010%7D)
Hope I helped!
Best regards!!
Answer:
20
Step-by-step explanation:
This sequence follows a pattern of doubling then subtracting by two. The last action was 12 to 10, which is subtracting by two, so the next must be multiplying by 2.
Answer:56%
Step-by-step explanation:
The correct value of the angle of rotation is 3π/5
Answer:
Distance travelled ≈ 22.6 ft
Step-by-step explanation:
We are given;
Radius;r = 12 ft
Angle of rotation; θ = 3π/5
The formula for calculating distance travelled is;
Distance travelled = rθ
So, plugging in the relevant values;
Distance travelled = 12 x 3π/5
Distance travelled ≈ 22.6 ft
(0, 5), (1, 1 ), ( - 1, 9 )
to test the points substitute the x-coordinate into the equation and if the value is equal to the y- coordinate then it is an ordered pair
(0, 5 ) → y = 0 + 5 = 5 ← ordered pair
(1, 1 ) → y = - 4 + 5 = 1 ← ordered pair
(- 1, 9 ) → y = 4 + 5 = 9 ← ordered pair
( - 1, - 1 ) → y = 4 + 5 = 9 ← not an ordered pair
( - 1, - 9 ) → y = 4 + 5 = 9 ← not an ordered pair
(1, - 1 ) → y = - 4 + 5 = 1 ← not an ordered pair
(- 1, 1 ) → y = 4 + 5 = 9 ← not an ordered pair