Answer:
2 : 5
Step-by-step explanation:
Hey there!
Line passes through (4, -1) & is parallel to 2x -3y=9
Let's start off by identifying what our slope is. In the slope-intercept form y=mx+b, we know that "m" is our slope.
The given equation needs to be converted into slope-intercept form and we can do this by getting y onto its own side of the equal sign.
Start off by subtracting 2x from both sides.
-3y = -2x + 9
Then, divide both sides by -3.
y = (-2x + 9)/-3
Simplify.
y = 2/3x - 3
"M" is simply a place mat so if we look at our given line, the "m" value is 2/3. Therefore, our slope is 2/3.
We should also note that we're looking for a line that's parallel to the given one. This means that our new line has the same slope as our given line. Therefore, our new line has a slope of 2/3.
Now, we use point-slope form ( y-y₁=m(x-x₁) ) to complete our task of finding a line that passes through (4, -1). Our new slope is 2/3 & it passes through (4, -1).
y-y₁=m(x-x₁)
Let's start by plugging in 2/3 for m (our new slope), 4 for x1 and -1 for y1.
y - (-1) = 2/3(x - 4)
Simplify.
y + 1 = 2/3 + 8/3
Simplify by subtracting 1 from both sides.
y = 2/3x + 8/3 - 1
Simplify.
y = 2/3x + 5/3
~Hope I helped!~
45+10x the x stands for how many classes you take
Well if y represents the vertical distance of the ball then you want to solve the equation for when y is 0, since 0 would represent the ball being on the ground. So substitute 0 in for y and solve the equation.
0 = - 0.001x^2 + 0.3x
we have a common factor of x in both terms so we can take that out.
0 = x(-0.001x + 0.3)
Zero product property tells us that we can set both of those products equal to zero and solve
0 = x
0 = -0.001x + 0.3
our first answer is x = 0 is obvious bc thats when the ball starts before you hit it, means it traveled 0.
solving the second equation gives us x = 300
so the ball traveled 300 "yards" I suppose your problem starts, which is impossible, but no matter thats the answer :-)
Answer:
The distance the Bensons had traveled from their home 
hours after picking up their grand parents 292.5 miles
Step-by-step explanation:
The given equation for the distance the Benson family traveled from their home can be presented as follows;
d = 55·t + 100
Where;
d = The total distance that the Benson family has traveled from their home after traveling 100 miles to pick up their grandparents
t = The time duration the Benson family have been traveled from their grandparents home on the way to their vacation
To find how far from their home the Bensons will be after 3 1/2 hours of driving with their grand parents, we substitute t with 3 1/2 hours or 3.5 hours as follows;
d = 55·t + 100
When t = hours, we get;
Therefore, the distance the Bensons had traveled from their home hours after picking up their grand parents = 292.5 miles.
