-2x + 5 = -1
subtract 5 from both sides: -2x = -6
divide each side by -2: x = 3
plug in 3: 5(3)
multiply: 15
the value of 5x is 15.
Answer:
t is approximately 10.41 seconds
Step-by-step explanation:
s = 16t^2
1734 = 16t^2
divide by 16
1734/16 = 16t^2/16
1734/16 = t^2
take the square root of each side
sqrt(1734/16) = sqrt(t^2)
we only take the positive square root because time must be positive
sqrt(1734/16) = t
t is approximately 10.41 seconds
Answer:
y = x + 7
Step-by-step explanation:
The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept.
Looking at the graph, we can see that the line intersects the y-axis at y = 7. So 7 would be our y-intercept.
To find the slope, we would divide the rise of the line by the run. Or m = rise/run. From looking at the graph, we can see that for every 1 unit the line moves in the x-direction, the line moves in the y-direction by 1 unit. Therefore, the rise would be 1 and the run would be 1. 1/1 = 1 so the slope of the line would be 1.
Plugging in 7 for b and 1 for m into the equation for the slope-intercept form, we get:
y = x + 7
So that would be the equation for the line in slope-intercept form.
I hope you find my answer and explanation to be helpful. Happy studying.
Answer:
Change in area=24
-48
Step-by-step explanation:
Let s will be the side of square and r will be the radius of circle.
Then two given conditions are
1)dr/dt=2 m/s
2)ds/dt=1 m/s
Area enclosed=(Area of square)-(Area of circle)
Area of square=
Area of circle=
Area enclosed=
dA/dt=2
r(dr/dt)-2s(ds/dt)
At s=24,and r=6
dA/dt=2(
)(6)(2)-2(24)(1)
Change in area=24
-48
We use P = i•e^rt for exponential population growth, where P = end population, i = initial population, r = rate, and t = time
P = 2•i = 2•15 = 30, so 30 = 15 [e^(r•1)],
or 30/15 = 2 = e^(r)
ln 2 = ln (e^r)
.693 = r•(ln e), ln e = 1, so r = .693
Now that we have our doubling rate of .693, we can use that r and our t as the 12th hour is t=11, because there are 11 more hours at the end of that first hour
So our initial population is again 15, and P = i•e^rt
P = 15•e^(.693×11) = 15•e^(7.624)
P = 15•2046.94 = 30,704