Answer:
10. y=2x+1 y = -1/2x +1
11. y=-1/3x +6 y = 3x -4
12. y=-5x-18 y=1/5x + 14/5
Step-by-step explanation:
To write the equation of a line we must have a slope and a point. To find the slope, we use the slope from the equations for parallel lines and modify it for perpendicular lines.
10. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form. The slope here is 2. The parallel slope is 2 and the perpendicular slope is the negative reciprocal or -1/2.
Parallel Perpendicular
(y-1)=2(x-0) (y-1)==-1/2(x-0)
y-1=2x y-1 = -1/2 x
y=2x+1 y = -1/2x +1
11. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form. The slope here is -1/3. The parallel slope is -1/3 and the perpendicular slope is the negative reciprocal or 3.
Parallel Perpendicular
(y-5)=-1/3(x-3) (y-5)=3(x-3)
y-5=-1/3x+1 y-5 = 3x - 9
y=-1/3x +6 y = 3x -4
12. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form. The slope here is -5. The parallel slope is -5 and the perpendicular slope is the negative reciprocal or 1/5.
Parallel Perpendicular
(y-2)=-5(x--4) (y-2)=1/5(x--4)
y-2=-5(x+4) y-2 = 1/5(x +4)
y-2=-5x -20 y-2 = 1/5x +4/5
y=-5x-18 y=1/5x + 14/5
Answer:
x=3
(Do not write a character less than what I have written; 3 is not the answer but x=3 is the answer.)
Step-by-step explanation:
Parabolas have a axis of symmetry; this is the line they are symmetrical about.
The line of symmetry will always go through the vertex.
Since your question says it is a function the line will be vertical and will be of the form x=a number.
The number is determine by the x-coordinate of the vertex.
I know the vertex of your problem is (3,-1) because it says that is the minimum point of the graph. The vertex of a parabola will always be it's maximum (this parabola is open down) or minimum (this parabola is open up).
So the axis of symmetry is just:
x=3.
You must actually write x=3.
3 is not the answer.
x=3 is the answer.
Little note down here:
(If it had said the parabola wasn't a function, the axis of symmetry would have been horizontal and therefore of the form y=a number where the number was the y-coordinate of the vertex.)
Solution: The speed of old freight train is 0.5 miles per minute and the speed of new dart express train is 1.5 miles per minute.
Explanation:
Let the speed of old freight train is x miles per minute and the speed of new dart express train is y miles per minute.
It is given that the speed of the dart express train is three times faster than the freight train. So, it can be written as,
....(1)
The trains are moving towards the opposite directions, therefore the distance between them is increased at the speed of 
miles per minute.
The distance between both train in 15 minutes is represented by 
.
According to the given information the distance between trains is 30 miles in 15 minutes.
Use equation (1) and put 
Put this value in equation (1), to find the value of y.
Therefore, the The speed of old freight train is 0.5 miles per minute and the speed of new dart express train is 1.5 miles per minute.
Answer:
160 miles away
Step-by-step explanation:
I am BIG brain
One-fourth of 12 bottles of water would equal 3 bottles of water
