Answer:
c
Step-by-step explanation:
the function (x) = -3x+2 can be obtained by :
* stretching the function (x)=x in the y-axis by 3 units gives 3x
* then reflecting about x-axis gives -3x
* finally shifting it up by 2 units gives -3x+2
so the parent function is f(x) = x
The line that passes through (0 1) and (1 4) is a linear equation
The equation of the points is y = 3x + 1
<h3>How to determine the equation of the points?</h3>
The points are given as:
(x,y) = (0 1) and (1 4)
Start by calculating the slope (m)
m = (y₂ - y₁)/(x₂ - x₁)
So, we have:
m = (4 - 1)/(1 - 0)
Evaluate
m = 3
The equation is then calculated as:
y = m(x - x₁) + y₁
This gives
y = 3(x - 0) + 1
Evaluate the product
y = 3x + 1
Hence, the equation of the points is y = 3x + 1
Read more about linear equations at:
brainly.com/question/1884491
Answer:
B
Step-by-step explanation:
Answer:
7.5 ft³/min
Step-by-step explanation:
Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.
Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²
So, V = Ah = 2h = 2(10 - x)
The rate of change of volume is thus
dV/dt = d[2(10 - x)]/dt = -2dx/dt
Since dV/dt = 15 ft³/min,
dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min
Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt
= -dx/dt
= -(-7.5 ft³/min)
= 7.5 ft³/min
And the height at this point when x = 8 inches = 8 in × 1 ft/12 in = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft
I am pretty sure number 3 is the right answer