Answer: f(x) = -0.016x² + 1.6x
Step-by-step explanation:
If the lenght of the road over the arch is 100m, we can consider a coordinate plane and say that the road starts at point (0,0) and finishes at (100,0). The vertice of the parabola is at point (50,40), because the maximum height is 40 and it is always in the middle point of the roots.
So, we have
(0,0) (50,40) (100,0)
A quadratic function is always on the form: f(x) = ax² + bx + c
0 = a0² + b0 + c
40 = a50² + b50 + c
0 = a100² + b100 + c
0 = a0² + b0 + c → c = 0 ∴
40 = a50² + b50
0 = a100² + b100
_________________________
2500a + 50b = 40 (*2)
10000a + 100b = 0
_________________________
5000a + 100b = 80
10000a + 100b = 0 (-)
__________________________
-5000a = 80
-a=80/5000
a=-0.016
∴
2500a + 50b = 40
2500.(-0.016) + 50b = 40
-40 + 50b = 40
50b = 80
b = 80/50
b = 1.6
This way f(x) = -0.016x² + 1.6x
3(2 + x)
3(2) + 3(x)
<span>With the distributive property, you can multiply numbers inside parenthesis by numbers outside a parenthesis.
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x(a + 1 + 4)
x(a) + x(1) + x(4)
ax + x + 4x
The number must be distributed across every term.
Answer: x = 20
Step-by-step explanation:
1) Move all terms to the left:
x-13-(x/2-3)=0
2) Get rid of parentheses
x-x/2+3-13=0
3) Multiply all the terms by the denominator
x*2-x+3*2-13*2=0
4) Add all the numbers together, and all the variables
-1x+x*2-20=0
5) Multiply elements
-1x+2x-20=0
6) Add all the numbers together, and all the variables
x-20=0
7) Move all terms containing x to the left, all other terms to the right
x=20
Hope This Helps (From My Notes)
Answer:
The histograms are missing, but ill try to answer it nonetheless.
Here we have that the standard deviation is bigger than the mean, this means that we will not see one of the ends (the smaller one) of our bell.
And we have a normal distribution, so we have a gaussian bell.
We will have that the peak of our bell is at the value x = 1.1
The histogram will start with a kinda high value at x = 0, it will get to the maximum at x = 1.1 and it will decrease as a normal bell, and knowing that the distance between the mean value and the point where the bell almost is almost zero, is equal to 3 standard deviations, we can expect to see this at x = 1.1 + 3*1.5 = 1.1 + 4.5 = 5.6
Answer:
Step-by-step explanation:
we are given equation as
Since, we have to solve for x
so, we will make all terms on left side
add both sides 16
Subtract both sides by x^2
now, we can factor it
now, we can solve for x
and we get